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BROWSE VOLUME

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BROWSE EARLY VOLUMES

October 2009

Volume 21, Issue 10,  Articles (10xxxx)

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Cover image from Denis Martinand, Eric Serre, and Richard M. Lueptow, Phys. Fluids 21, 104102 (2009).

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LETTERS

A simple wall-layer model for large eddy simulation with immersed boundary method

F. Roman, V. Armenio, and J. Fröhlich

Phys. Fluids 21, 101701 (2009) (4 pages)

Online Publication Date: 7 October 2009

Full Text: PDF (174 kB)

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A wall-layer model is proposed for large eddy simulation of high Reynolds number turbulent flows in conjunction with immersed boundaries. The model is based on two main steps: the reconstruction of the velocity field at the first grid point off the immersed body and the modelization of the actual wall shear stress at the immersed boundary through imposition of a Reynolds averaged Navier–Stokes-like eddy viscosity obtained by means of analytical considerations. The model is tested in a turbulent plane channel flow with walls reproduced by immersed boundaries considering both Cartesian and curvilinear grids. Even with coarse and distorted grids the proposed methodology is able to reproduce accurately both first- and second-order turbulent statistics.
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47.27.nb, 47.27.nd, 47.60.Dx, 47.10.ad, 47.27.Jv, 47.27.ep

Tube geometry can force switchlike transitions in the behavior of propagating bubbles

A. de Lózar, A. Heap, F. Box, A. L. Hazel, and A. Juel

Phys. Fluids 21, 101702 (2009) (4 pages)

Online Publication Date: 9 October 2009

Full Text: PDF (306 kB)

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Microscale process engineering requires precise control of bubbles and droplets. We investigate geometry-induced control and find that a centered constriction in the cross section of rectangular tubes can lead to new families of steadily propagating bubbles, which localize in the least-constricted regions of the cross section. Tuning the constriction geometry can cause a switchlike transition from centered to localized bubbles at a critical value of the flow rate: a mechanism for flow-rate-driven bubble control. The accompanying large change in bubble volume could be significant for liquid recovery applications.
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47.85.Np, 47.27.nf, 47.55.D-, 47.60.Dx, 47.61.-k

Exact and asymptotic conditions on traveling wave solutions of the Navier–Stokes equations

Y. Charles Li and Divakar Viswanath

Phys. Fluids 21, 101703 (2009) (4 pages)

Online Publication Date: 12 October 2009

Full Text: PDF (133 kB)

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We derive necessary conditions that traveling wave and other solutions of the Navier–Stokes equations must satisfy in the pipe, Couette, and channel flow geometries. Some conditions are exact and must hold for any traveling wave solution or periodic solution irrespective of the Reynolds number (Re). Other conditions are asymptotic in the limit Re-->[infinity]. For the pipe flow geometry, we give computations up to Re=100 000 showing the connection of our asymptotic conditions to critical layers that accompany vortex structures at high Re.
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47.10.ad, 47.60.Dx, 47.15.Rq, 47.27.nf, 47.27.nd, 47.32.cb
FREE

Response modes of a flexible filament in the wake of a cylinder in a flowing soap film

Lai-Bing Jia and Xie-Zhen Yin

Phys. Fluids 21, 101704 (2009) (4 pages)

Online Publication Date: 29 October 2009

Full Text: PDF (247 kB)

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Flow induced vibrations are observed in many engineering applications. A flexible body located in the wake of an obstacle is usually forced to vibrate by the periodic vortices shedding from the obstacle. Here we focus on the response of the flexible body in the wake. Soap film tunnels are used to provide two-dimensional flow. Cylinders and flexible filaments are employed as obstacles and flexible bodies, respectively. The filaments exhibit lock-in behavior to the wake. Three response modes are found by changing the distance between the filaments and cylinders. The observations are illuminated in terms of waving plate theory.
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47.32.-y, 47.15.gm
FREE

Chaos in a cylinder wake due to forcing at the Strouhal frequency

Paris G. Perdikaris, Lambros Kaiktsis, and George S. Triantafyllou

Phys. Fluids 21, 101705 (2009) (3 pages)

Online Publication Date: 29 October 2009

Full Text: PDF (339 kB)

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In this letter we show that a cylinder oscillating harmonically in line with an incoming flow at a frequency equal to the natural frequency of vortex shedding induces for certain amplitudes of oscillation a chaotic state in the flow, characterized by an aperiodic lift force. The result is obtained through numerical simulation of the Navier–Stokes equations for two-dimensional flow. The chaos is attributed to the competition between two modes: the natural mode of the wake and the mode forced by the moving cylinder, which have entirely different spatial structures.
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47.52.+j, 47.27.wb, 47.32.-y, 47.10.ad, 47.11.-j
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ARTICLES

Biofluid Mechanics

On intra- and intersubject variabilities of airflow in the human lungs

Jiwoong Choi, Merryn H. Tawhai, Eric A. Hoffman, and Ching-Long Lin

Phys. Fluids 21, 101901 (2009) (17 pages)

Online Publication Date: 13 October 2009

Full Text: PDF (2454 kB)

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The effects of intra- and intersubject variabilities in airway geometry on airflow in the human lungs are investigated by large eddy simulation. The airway models of two human subjects consisting of extra- and intrathoracic airways are reconstructed from CT images. For intrasubject study, airflows at two inspiratory flow rates are simulated on the airway geometries of the same subject with four different levels of truncation. These airway models are the original complete geometry and three geometries obtained by truncating the original one at the subglottis, the supraglottis, and the laryngopharynx, respectively. A comparison of the airflows in the complete geometry model shows that the characteristics of the turbulent laryngeal jet in the trachea are similar regardless of Reynolds number in terms of mean velocities, turbulence statistics, coherent structures, and pressure distribution. The truncated airway models, however, do not produce the similar flow structures observed in the complete geometry. An improved inlet boundary condition is then proposed for the airway model truncated at the laryngopharynx to improve the accuracy of solution. The new boundary condition significantly improves the mean flow. The spectral analysis shows that turbulent characteristics are captured downstream away from the glottis. For intersubject study, although the overall flow characteristics are similar, two morphological factors are found to significantly affect the flows between subjects. These are the constriction ratio of the glottis with respect to the trachea and the curvature and shape of the airways.
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87.19.Wx, 47.63.Ec

Micro- and Nanofluid Mechanics

Entrainment of a film on a surface from the meniscus of a liquid wedge during coating

S. N. Reznik, W. Salalha, Y. Sorek, D. Avramov, and E. Zussman

Phys. Fluids 21, 102001 (2009) (14 pages)

Online Publication Date: 1 October 2009

Full Text: PDF (451 kB)

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The shape evolution of an entrained film from the meniscus of a liquid wedge is studied, both experimentally and theoretically. The liquid wedge is formed by a droplet of liquid injected between a substrate and a tilted plate. When the substrate moves relative to the tilted plate with a constant velocity, a film of a constant slope is entrained on it, while another film remains on the tilted plate. The numerical and analytical investigation of the process provides the dependence of the length and slope of the entrained film after the end of drawing process, as well as the maximum thickness of the film on the tilted plate, on the capillary number. The length of the entrained film was found to be minimal for infinitely large capillary numbers when the surface tension effects are negligibly small. Experimental data confirm the predicted characteristic geometry of the film for capillary numbers up to 0.75.
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47.55.Hd, 68.08.Bc, 68.03.Cd, 47.55.dr, 47.55.nb, 68.15.+e

Transport properties of Brownian particles confined to a narrow channel by a periodic potential

Xinli Wang and German Drazer

Phys. Fluids 21, 102002 (2009) (7 pages)

Online Publication Date: 2 October 2009

Full Text: PDF (162 kB)

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We investigate the transport of Brownian particles in a two-dimensional potential moving under the action of an external force or convected by a flow field. The potential is periodic in one direction and confines the particles to a narrow channel of varying cross section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick–Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of a parabolic potential in the cross section. We obtain excellent agreement for the marginal probability distribution, the average velocity of the Brownian particles, and the asymptotic dispersion coefficient over a wide range of Péclet numbers.
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05.40.Jc, 47.60.Dx
FREE

Nucleation threshold and deactivation mechanisms of nanoscopic cavitation nuclei

Bram M. Borkent, Stephan Gekle, Andrea Prosperetti, and Detlef Lohse

Phys. Fluids 21, 102003 (2009) (9 pages)

Online Publication Date: 19 October 2009

Full Text: PDF (424 kB)

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The acoustic nucleation threshold for bubbles trapped in cavities has theoretically been predicted within the crevice theory by Atchley and Prosperetti [“The crevice model of bubble nucleation,” J. Acoust. Soc. Am. 86, 1065 (1989)]. Here, we determine this threshold experimentally, by applying a single pressure pulse to bubbles trapped in cylindrical nanoscopic pits (“artificial crevices”) with radii down to 50 nm. By decreasing the minimum pressure stepwise, we observe the threshold for which the bubbles start to nucleate. The experimental results are quantitatively in good agreement with the theoretical predictions of Atchley and Prosperetti. In addition, we provide the mechanism which explains the deactivation of cavitation nuclei: gas diffusion together with an aspherical bubble collapse. Finally, we present superhydrophobic nuclei which cannot be deactivated, unless with a high-speed liquid jet directed into the pit.
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47.55.dp, 68.08.Bc, 47.55.D-

Measurements of tangential momentum accommodation coefficient for various gases in plane microchannel

I. A. Graur, P. Perrier, W. Ghozlani, and J. G. Méolans

Phys. Fluids 21, 102004 (2009) (9 pages)

Online Publication Date: 30 October 2009

Full Text: PDF (205 kB)

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Mass flow rate measurements in a single silicon microchannel were carried out for various gases in isothermal steady flows. The results obtained from hydrodynamic to near free molecular regime by using a powerful experimental platform allowed us to deduce interesting information, notably about the reflection/accommodation process at the wall. In the 0–0.3 Knudsen range, a continuum analytic approach was derived from the NS equations, associated with first or second order slip boundary conditions. Identifying the experimental mass flow rate curves to the theoretical ones the tangential momentum accommodation coefficient (TMAC) of various gases was extracted. Over the full Knudsen range [0–30] the experimental results were compared with theoretical values calculated from the kinetic approaches: using variable accommodation coefficient values as fitting parameter, the theoretical curves were fitted to the experimental ones. Whatever the Knudsen range and whatever the theoretical approach, the TMAC values are found decreasing when the molecular weights of the gas increase (as long as the different gases are compared using the same approach). Moreover, the values of the various accommodation coefficients are rather close to one another but sufficiently smaller than unity indicating that the full accommodation modeling is not satisfactory to describe the gas/wall interaction.
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47.60.Dx, 47.61.-k, 47.45.Gx, 47.10.ad

Interfacial Flows

Nonmodal and nonlinear dynamics of a volatile liquid film flowing over a locally heated surface

Naveen Tiwari and Jeffrey M. Davis

Phys. Fluids 21, 102101 (2009) (14 pages)

Online Publication Date: 1 October 2009

Full Text: PDF (1135 kB)

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The stability of a thin, volatile liquid film falling under the influence of gravity over a locally heated, vertical plate is analyzed in the noninertial regime using a model based on long-wave theory. The model is formulated to account for evaporation that is either governed by thermodynamic considerations at the interface in the one-sided limit or limited by the rate of mass transfer of the vapor from the interface. The temperature gradient near the upstream edge of the heater induces a gradient in surface tension that opposes the gravity-driven flow, and a pronounced thermocapillary ridge develops in the streamwise direction. Recent theoretical analyses predict that the ridge becomes unstable above a critical value of the Marangoni parameter, leading to the experimentally observed rivulet structure that is periodic in the direction transverse to the bulk flow. An oscillatory, thermocapillary instability in the streamwise direction above the heater is also predicted for films with sufficiently large heat loss at the free surface due to either evaporation or strong convection in the adjoining gas. This present work extends the recent linear stability analysis of such flows by Tiwari and Davis [Phys. Fluids 21, 022105 (2009)] to a nonmodal analysis of the governing non-self-adjoint operator and computations of the nonlinear dynamics. The nonmodal analysis identifies the most destabilizing perturbations to the film and their maximum amplification. Computations of the nonlinear dynamics reveal that small perturbations can be sufficient to destabilize a linearly stable film for a narrow band of wave numbers predicted by the nonmodal, linearized analysis. This destabilization is linked to the presence of stable, discrete modes that appear as the Marangoni parameter approaches the critical value at which the film becomes linearly unstable. Furthermore, the thermocapillary instability leads to a new, time-periodic base state. This transition corresponds to a Hopf bifurcation with increasing Marangoni parameter. A linear stability analysis of this time-periodic state reveals further instability to transverse perturbations, with the wave number of the most unstable mode about 50% smaller than for the rivulet instability of the steady base state and exponential growth rate about three times larger. The resulting film behavior is reminiscent of inertial waves on locally heated films, although the wave amplitude is larger in the present case near the heater and decays downstream where the Marangoni stress vanishes. The film's heat transfer coefficient is found to increase significantly upon the transition to the time-periodic flow.
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47.20.Ky, 47.27.te, 47.55.nb, 47.52.+j

Enhanced slip on a patterned substrate due to depinning of contact line

Peng Gao and James J. Feng

Phys. Fluids 21, 102102 (2009) (10 pages)

Online Publication Date: 26 October 2009

Full Text: PDF (477 kB)

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We perform numerical simulations of a shear flow over a periodically patterned substrate with entrapped gas bubbles. A diffuse-interface model is employed to handle the liquid-gas interface deformation and the three-phase contact line. Depending on the shear rate and the pattern geometry, four flow regimes are observed. The contact lines can be pinned, depinned, or eliminated depending on the competition between the shear force and the surface tension. The effective slip length is found to be dependent on the morphology of the menisci and hence on the shear rate. In particular, the bubbles are transformed into a continuous gas film when the shear rate is larger than a critical value, resulting in a significantly enhanced slip length proportional to the liquid-gas viscosity ratio. The present results have interesting implications for effective slip on superhydrophobic surfaces.
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47.45.Gx, 02.60.-x, 68.03.Cd, 47.55.D-, 66.20.-d, 83.50.-v

Electrowetting with contact line pinning: Computational modeling and comparisons with experiments

Shawn W. Walker, Benjamin Shapiro, and Ricardo H. Nochetto

Phys. Fluids 21, 102103 (2009) (16 pages) Multimedia

Online Publication Date: 30 October 2009

Full Text: PDF (1194 kB)

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This work describes the modeling and simulation of planar electrowetting on dielectric devices that move fluid droplets by modulating surface tension effects. The fluid dynamics are modeled by Hele-Shaw type equations with a focus on including the relevant boundary phenomena. Specifically, we include contact angle saturation and a contact line force threshold model that can account for hysteresis and pinning effects. These extra boundary effects are needed to make reasonable predictions of the correct shape and time scale of liquid motion. Without them the simulations can predict droplet motion that is much faster than in experiments (up to 10–20 times faster). We present a variational method for our model, and a corresponding finite element discretization, which is able to handle surface tension, conservation of mass, and the nonlinear contact line pinning in a straightforward and numerically robust way. In particular, the contact line pinning is captured by a variational inequality. We note that all the parameters in our model are derived from first principles or from independent experiments except one (the parameter Dvisc that accounts for the extra resistive effect of contact angle hysteresis and is difficult to measure directly). We quantitatively compare our simulation to available experimental data for four different cases of droplet motion that include splitting and joining of droplets and find good agreement with experiments.
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85.50.-n, 68.08.Bc, 68.03.Cd, 47.11.Fg, 47.55.D-, 47.65.-d

Viscous and Non-Newtonian Flows

Axisymmetric instabilities in electrospinning of highly conducting, viscoelastic polymer solutions

Colman P. Carroll and Yong Lak Joo

Phys. Fluids 21, 103101 (2009) (10 pages)

Online Publication Date: 12 October 2009

Full Text: PDF (693 kB)

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In this paper the axisymmetric instabilities observed during the electrospinning of highly electrically conducting, viscoelastic poly(ethylene oxide) (PEO)/water solutions are investigated. In our theoretical study, a linear stability analysis is coupled with a model for the stable electrospun jet. The combined model is used to calculate the expected bead growth rate and wave number for given electrospinning conditions. In the experimental section of the study, PEO/water solutions are electrospun and the formation of axisymmetric beads is captured using high-speed photography. Experimental values for the bead growth rate and wave number are extracted and compared with the model predictions. An energy analysis is then carried out on the stability results to investigate the mechanism of instability via the coupling between base flow and perturbation. The analysis reveals that the unstable axisymmetric mode for electrically driven, highly conducting jets is not a capillary mode, but is mainly driven by electrical forces due to the interaction of charges on the jet. We note that this axisymmetric, conducting mode often exhibits a growth rate too small to be observed during electrospinning. However, both our experiments and stability analysis demonstrate that the axisymmetric instability with a high growth rate can be seen in practice when the electrical force is effectively coupled with viscoelastic forces.
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47.57.Ng, 47.55.nb, 81.20.-n, 47.60.Kz

Coating flow of viscous Newtonian liquids on a rotating vertical disk

Nilesh H. Parmar, Mahesh S. Tirumkudulu, and E. J. Hinch

Phys. Fluids 21, 103102 (2009) (8 pages)

Online Publication Date: 22 October 2009

Full Text: PDF (251 kB)

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We study a Newtonian viscous liquid coating a vertical rotating disk in the creeping flow regime. Experiments were performed at varying disk rotation speeds and liquid volumes, and the thickness profile at steady state was measured. While the maximum liquid supported by the rotating disk varied with rotation rate and liquid viscosity, the numerical value of a dimensionless number signifying the ratio of gravity to viscous forces was the same in all the cases, gamma=0.30. A lubrication analysis for the time evolution of the film thickness that accounted for gravity, surface tension, and viscous forces was solved numerically to steady state. The predicted thickness profiles are in quantitative agreement with those obtained experimentally. The lubrication equation at steady state was solved analytically in the absence of surface tension to obtain constant height contours that were circular and symmetric about the horizontal axis. However to obtain a complete solution, knowledge of the height variation across the contours is required, and this is controlled by the surface tension. On including this effect, we derived an asymptotic solution to predict thickness profiles that agree well with measurements for large values of viscosity or rotation rates.
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47.15.gm, 47.85.mf, 47.32.Ef, 68.03.Cd, 68.15.+e

Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers

A. Vikhansky

Phys. Fluids 21, 103103 (2009) (7 pages)

Online Publication Date: 28 October 2009

Full Text: PDF (855 kB)

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We consider the effect of yield stress on the Rayleigh–Bénard convection of a viscoplastic material. First we consider the model problem of convection in a differentially heated loop, which is described by the (modified) Lorenz equations. The presence of the yield stress significantly alters the dynamics of the system. In particular, the chaotic motion can stop suddenly (sometimes, after a period of chaotic oscillations). Guided by the model equations we performed direct numerical simulations of convection of the Bingham liquid in a square cavity heated from bellow. Our interest has been concentrated on the situation when both buoyancy and plastic forces are large. The obtained results are in a reasonable agreement with the predictions by the Lorenz equations.
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47.50.-d, 47.52.+j, 47.55.pb

Particulate, Multiphase, and Granular Flows

Lattice Boltzmann simulation of the rise and dissolution of two-dimensional immiscible droplets

Cheng Chen and Dongxiao Zhang

Phys. Fluids 21, 103301 (2009) (11 pages)

Online Publication Date: 22 October 2009

Full Text: PDF (1037 kB)

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We used a coupled multiphase lattice Boltzmann (LB) model to simulate the dissolution of immiscible liquid droplets in another liquid during the rising process resulting from buoyancy. It was found that there existed a terminal rise velocity for each droplet, and there was a power law relationship between the Eötvös (Eo) number and the terminal Reynolds (Re) number. Our simulation results were in agreement with the empirical correlation derived for predicting bubble rise. When more than two identical droplets rose simultaneously in a close proximity, the average terminal rise velocity was lower than that of a single droplet with the same size because of the mutual resistant interactions. The droplet trajectories at the noncentral positions were not straight because of the nonzero net horizontal forces acting on the droplets. The Damkohler (Da) and Peclet (Pe) numbers were varied to investigate the coupling between droplet size, flow field, dissolution at the interface, and solute transport. For a given Pe, increasing Da led to a higher dissolution rate. For a given Da, increasing Pe led to a higher dissolution rate. For a large Da and a small Pe, the process near the interface was diffusion limited, and the advective flow relative to the droplet resulting from droplet rise was unable to move the accumulated solute away from the interface quickly. In this case, it was favorable to split the single droplet into as many small ones as possible in order to increase the interface area per unit mass and consequently enhance the whole dissolution process. For a small Da and a large Pe, the process was dissolution limited near the interface. The mass of accumulated solute near the interface was little, so the advective flow at the top side of the droplet was able to clean the solute quickly. In this case it was favorable to keep the droplet as a single one in order to obtain a high rise velocity and consequently enhance the whole dissolution process. By studying the coupling between Da and Pe, we qualitatively proposed to construct a Da-Pe phase plane and found the interface dividing the plane into regions 1 and 2. Region 1 was the collection of points where it was favorable to break down the droplet into as many small ones as possible in order to accelerate dissolution, while region 2 was the collection of points where it was favorable to keep the droplet in a single one for the same purpose. Based on our LB simulations, we found that the interface was an increasing function of Pe. Region 1 was the portion above the interface, while region 2 was the portion below it. In real applications, if both Pe and Da are obtained, it will be easy to judge whether it is favorable to break down the droplet or not in order to accelerate dissolution by checking whether (Pe, Da) falls in region 1 or 2.
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47.11.Qr, 47.55.D-, 64.70.fh, 64.75.Bc

Effects of geometric shape on the hydrodynamics of a self-propelled flapping foil

Xing Zhang, Saizhen Ni, Shizhao Wang, and Guowei He

Phys. Fluids 21, 103302 (2009) (7 pages) Multimedia

Online Publication Date: 22 October 2009

Full Text: PDF (2186 kB)

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The hydrodynamics of a free flapping foil is studied numerically. The foil undergoes a forced vertical oscillation and is free to move horizontally. The effect of chord-thickness ratio is investigated by varying this parameter while fixing other ones such as the Reynolds number, the density ratio, and the flapping amplitude. Three different flow regimes have been identified when we increase the chord-thickness ratio, i.e., left-right symmetry, back-and-forth chaotic motion, and unidirectional motion with staggered vortex street. It is observed that the chord-thickness ratio can affect the symmetry-breaking bifurcation, the arrangement of vortices in the wake, and the terminal velocity of the foil. The similarity in the symmetry-breaking bifurcation of the present problem to that of a flapping body under constraint is discussed. A comparison between the dynamic behaviors of an elliptic foil and a rectangular foil at various chord-thickness ratios is also presented.
Show PACS
47.20.Ky, 47.32.-y, 47.15.Tr, 47.40.-x, 89.20.Kk, 47.52.+j

Effects of viscosity ratio and three dimensional positioning on hydrodynamic interactions between two viscous drops in a shear flow at finite inertia

Rajesh Kumar Singh and Kausik Sarkar

Phys. Fluids 21, 103303 (2009) (9 pages)

Online Publication Date: 26 October 2009

Full Text: PDF (3036 kB)

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Drops driven toward each other by shear at finite inertia follow two distinct types of trajectories. Type I trajectory is similar to the one in Stokes flow where drops slide past each other. However, at finite inertia, drops display a new type II trajectory, where they reverse their paths. Increasing viscosity ratio results in a transition from type II to type I trajectory. The transition is caused by decreased drop deformation and increased alignment with the flow at higher drop viscosity; both decrease the zone of reversed streamlines that accompanies a drop at finite inertia. The transition is delineated in a phase diagram of Reynolds number and viscosity ratio for different capillary numbers. The critical viscosity ratio, where a type II transitions into type I, increases with Reynolds number except at higher capillary numbers, where the critical viscosity ratio shows a slight nonmonotonic variation with Reynolds number. Also, it is nonmonotonic with capillary numbers in that for a fixed Reynolds number, the critical viscosity ratio first increases with increasing capillary number and then decreases. Similar to the Stokes regime, increased viscosity ratio leads to a decreased postcollision cross-stream separation effectively decreasing the shear induced diffusion. Higher viscosity ratio results in an increased separation between drops during encounter, which results in a smaller interaction time. With drops placed initially at different shear planes, drops come under the influence of the reversed flow zone around a single drop that broadens off the central shear plane. Consequently, the trajectory changes from type I to type II as the offset in the vorticity direction increases. The change depends on the initial offset in the shear direction as well. The final displacement in the shear direction varies linearly with the initial offset. The net relative displacement in the shear direction shows a gradual decrease with increasing offset. The net relative displacement in the vorticity direction with increasing offset first increases from a zero value when drops are placed at the same shear plane to a maximum and then decreases. For certain cases, it reaches a negative value.
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47.55.D-, 47.55.nb, 47.32.-y, 66.20.-d, 66.10.C-

Sedimentation of a sphere in a fluid channel

Olivier Pitois, Christelle Fritz, Laurentiu Pasol, and Michèle Vignes-Adler

Phys. Fluids 21, 103304 (2009) (5 pages)

Online Publication Date: 26 October 2009

Full Text: PDF (526 kB)

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We studied both experimentally and numerically the sedimentation velocity of small solid particles through liquid channels merging at the intersection of three soap films. The wall mobility induces a nontrivial behavior for the particle drag coefficient, providing particular transport properties that are not observed for channels with rigid walls. It is shown that for sufficiently small particles, slow and fast motions are observed for the particle along the channel, depending on the particle position within the channel cross section and the sphere/channel size ratio. The velocity corresponding to fast motions can be as high as twice the Stokes velocity in an unbounded fluid. Moreover, the fast motions are not observed anymore when the size ratio exceeds a critical value, which has been found to be approximately equal to 0.5. As another major difference with the solid wall channel, the sphere velocity does not vanish when the size ratio reaches unity. Instead, the smallest value is found to be (1/4) of the Stokes velocity.
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47.55.-t, 47.15.Rq, 47.60.Dx, 47.50.-d

Laminar Flows

Sound propagation through a rarefied gas confined between source and receptor at arbitrary Knudsen number and sound frequency

Denize Kalempa and Felix Sharipov

Phys. Fluids 21, 103601 (2009) (14 pages)

Online Publication Date: 13 October 2009

Full Text: PDF (367 kB)

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A sound propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation taking into account the influence of receptor. A plate oscillating in the normal direction to its own plane is considered as a sound source, while a stationary parallel plate is considered as being the receptor of sound. The main parameters determining the solution of the problem are the oscillation speed parameter, which is defined as the ratio of intermolecular collision frequency to the sound frequency, and the rarefaction parameter defined as the ratio of the distance between source and receptor to the molecular mean free path. The kinetic equation is solved via a discrete velocity method with a numerical error of 0.1%. The numerical calculations are carried out for wide ranges of the oscillation and rarefaction parameters. The concept of integral phase parameter is introduced to obtain the sound speed correctly in all regimes of the gas rarefaction and sound frequency. Analytical solutions are obtained in the limits of small and large parameters of frequency and rarefaction.
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47.45.-n

Influence of inlet radius on Stokes flow in a circular tube via the Hamiltonian systematic method

G. P. Wang, X. S. Xu, and Y. X. Zhang

Phys. Fluids 21, 103602 (2009) (9 pages)

Online Publication Date: 23 October 2009

Full Text: PDF (846 kB)

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This paper presents a new semianalytical method, Hamiltonian systematic method, for solving axisymmetric problems of Stokes flow. In the system, nonzero-eigenvalue solutions can describe local effect near the boundary and therefore the influence of inlet radius on the flow can be investigated. A rule of minimal entrance length is discussed on the basis of the criteria which are defined by axial flow deviating from the full developed (Hagen–Poseuille) flow. Numerical results show that the entrance length is related to the inlet radius, and there is one minimal point on the relationship curve, namely, there is one minimal entrance length. Besides, pressures have the characteristic too and the minimal point is same. The method can also be generalized to other fields.
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47.60.Dx

On steady rotational cyclonic flows: The viscous bidirectional vortex

Joseph Majdalani and Martin J. Chiaverini

Phys. Fluids 21, 103603 (2009) (15 pages)

Online Publication Date: 28 October 2009

Full Text: PDF (600 kB)

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This study is focused on the tangential boundary layers of a bidirectional vortex, specifically those forming at the core and the sidewall of a swirl-driven cyclonic chamber. Our analysis is based on the regularized, tangential momentum equation which is rescaled in a manner to capture the forced vortex near the chamber axis and the no slip requirement at the sidewall. After identifying the coordinate transformations needed to resolve the rapid changes in the regions of nonuniformity, two inner expansions are constructed. These expansions are then matched with the outer, free vortex solution that is sandwiched between the core and the hard wall. By combining inner and outer expansions, uniformly valid approximations are subsequently obtained for the swirl velocity, vorticity, and pressure. These are shown to be strongly influenced by a dimensionless grouping that we refer to as the vortex Reynolds number, V. This keystone parameter appears as a ratio of the mean flow Reynolds number and the product of the swirl number and the chamber aspect ratio. Based on V, several fundamental features of the bidirectional vortex are quantified. Among them are the thicknesses of the viscous core and sidewall boundary layers; these decrease with V1/2 and V, respectively. The converse may be said of the peak velocity which increases with V1/2. In the same vein, the angular speed of the rigid-body rotation of the forced vortex is found to be linearly proportional to V. Our laminar swirl velocity is reminiscent of Sullivan's two-cell vortex except for its additional dependence on the aspect ratio of the chamber. For the purpose of verification, theoretical predictions are compared to particle image velocimetry measurements and Navier–Stokes simulations at high vortex Reynolds numbers. By properly accounting for the turbulent eddy viscosity in the analytical model, local agreement is obtained with both laboratory measurements and computer simulations.
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47.10.ad, 47.15.ki, 47.32.-y

Influence of flow confinement on the drag force on a static cylinder

B. Semin, J. P. Hulin, and H. Auradou

Phys. Fluids 21, 103604 (2009) (9 pages)

Online Publication Date: 30 October 2009

Full Text: PDF (237 kB)

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The influence of confinement on the drag force F on a static cylinder in a viscous flow inside a rectangular slit of aperture h0 has been investigated from experimental measurements and numerical simulations. At low enough Reynolds numbers, F varies linearly with the mean velocity and the viscosity, allowing for the precise determination of drag coefficients lambda|| and lambda[perpendicular] corresponding, respectively, to a mean flow parallel and perpendicular to the cylinder length L. In the parallel configuration, the variation in lambda|| with the normalized diameter beta=d/h0 of the cylinder is close to that for a two-dimensional (2D) flow invariant in the direction of the cylinder axis and does not diverge when beta=1. The variation in lambda|| with the distance from the midplane of the model reflects the parabolic Poiseuille profile between the plates for beta<<1 while it remains almost constant for beta~1. In the perpendicular configuration, the value of lambda[perpendicular] is close to that corresponding to a 2D system only if beta<<1 and/or if the clearance between the ends of the cylinder and the side walls is very small: in that latter case, lambda[perpendicular] diverges as beta-->1 due to the blockage of the flow. In other cases, the side flow between the ends of the cylinder and the side walls plays an important part to reduce lambda[perpendicular]: a full three-dimensional description of the flow is needed to account for these effects.
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47.60.Dx, 47.50.-d, 47.27.nf, 47.50.Cd, 47.27.E-, 89.20.Kk

Instability and Transition

Absolute and convective instabilities of an inviscid compressible mixing layer: Theory and applications

P. Caillol

Phys. Fluids 21, 104101 (2009) (17 pages)

Online Publication Date: 7 October 2009

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This study aims to examine the effect of compressibility on unbounded and parallel shear flow linear instabilities. This analysis is of interest for industrial, geophysical, and astrophysical flows. We focus on the stability of a wavepacket as opposed to previous single-mode stability studies. We consider the notions of absolute and convective instabilities first used to describe plasma instabilities. The compressible-flow modal theory predicts instability whatever the Mach number. Spatial and temporal growth rates and Reynolds stresses nevertheless become strongly reduced at high Mach numbers. The evolution of disturbances is driven by Kelvin–Helmholtz instability that weakens in supersonic flows. We wish to examine the occurrence of absolute instability, necessary for the appearance of turbulent motions in an inviscid and compressible two-dimensional mixing layer at an arbitrary Mach number subject to a three-dimensional disturbance. The mixing layer is defined by a parametric family of mean-velocity and temperature profiles. The eigenvalue problem is solved with the help of a spectral method. We ascertain the effects of the distribution of temperature and velocity in the mixing layer on the transition between convective and absolute instabilities. It appears that, in most cases, absolute instability is always possible at high Mach numbers provided that the ratio of slow-stream temperature over fast-stream temperature may be less than a critical maximal value but the temporal growth rate present in the absolutely unstable zone remains small and tends to zero at high Mach numbers. The transition toward a supersonic turbulent regime is therefore unlikely to be possible in the linear theory. Absolute instability can be also present among low-Mach-number coflowing mixing layers provided that this same temperature ratio may be small, but nevertheless, higher than a critical minimal value. Temperature distribution within the mixing layer also has an effect on the growth rate, this diminishes when the slow stream is heated. These results are applied to the dynamics of mixing layers in the interstellar medium and to the dynamics of the heliopause, frontier between the interstellar medium, and the solar wind.
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47.20.Ft, 47.27.W-, 47.40.Ki, 47.51.+a, 95.30.Lz, 96.50.Ek

Absolute and convective instability of cylindrical Couette flow with axial and radial flows

Denis Martinand, Eric Serre, and Richard M. Lueptow

Phys. Fluids 21, 104102 (2009) (13 pages)

Online Publication Date: 7 October 2009

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Imposing axial flow in the annulus and/or radial flow through the cylindrical walls in a Taylor–Couette system alters the stability of the flow. Theoretical methods and numerical simulations were used to determine the impact of imposed axial and radial flows, homogeneous in the axial direction, on the first transition of Taylor–Couette flow in the framework of convective and absolute instabilities. At low axial Reynolds numbers the convective instability is axisymmetric, but convective helical modes with an increasing number of helices having a helicity opposite that of the base flow dominate as the axial flow increases. The number of helices and the critical Taylor number are affected only slightly by the radial flow. The flow becomes absolutely unstable at higher Taylor numbers. Absolutely unstable axisymmetric modes occur for inward radial flows, while helical absolute instability modes having a helicity identical to that of the base flow occur at high enough axial Reynolds numbers for outward radial flow.
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47.11.-j, 47.20.-k, 47.20.Qr, 47.27.te, 47.55.P-

Centrifugal instabilities in curved compressible wakes

Li Lin and Sharon O. Stephen

Phys. Fluids 21, 104103 (2009) (13 pages)

Online Publication Date: 16 October 2009

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This investigation is concerned with the linear development of Görtler vortices in the high-Reynolds-number laminar compressible wake behind a flat plate which is aligned with the centerline of a curved mixing-layer system. The Görtler modes were previously found to exist within curved compressible mixing layers by Owen et al. [Phys. Fluids 8, 2506 (1997)]. This study extends that investigation and demonstrates the effect a wake has on the growth rate and location of such modes. The investigations were made by examining the growth rate and the location of the Görtler modes in the limit of large Görtler number and high wave number within the wake-dominated curved compressible mixing-layer systems based on three wake flow models. An analytic Gaussian wake profile is first used to model the behavior of the basic flow within the mixing layer at the trailing edge of the splitter plate. It is found that the wake has an amplification effect on the growth of the Görtler instability within the concavely curved or “unstably” curved compressible mixing layers. It is also found that within the convexly curved or “stably” curved compressible mixing layers wake modes can occur that behave differently to the “thermal modes,” which were previously found within the plain curved compressible system by Owen et al. Another analytic composite model which has some practical applications is then used to predict the behavior of the modes within the systems. Solutions from a numerical wake flow model have been compared with the predictions based on the analytic wake flow models.
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47.15.Tr, 47.15.ki, 47.20.-k, 47.32.-y, 47.40.-x

Turbulent Flows

A unified probability density function formulation to model turbulence modification in two-phase flow

Gaurav Anand and Patrick Jenny

Phys. Fluids 21, 105101 (2009) (17 pages)

Online Publication Date: 7 October 2009

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In the present study, a unified probability density function formulation for capturing the phenomena of turbulence modification of the continuous phase due to the dispersed phase turbulence is presented. A stochastic model based on dispersed phase turbulence length scale has been proposed for the purpose. The model has been validated with experimental data [Poelma et al., “Particle fluid interactions in grid-generated turbulence,” J. Fluid Mech. 589, 315 (2007)] on the decay of turbulence of the flow seeded with ceramic particles in a vertical recirculating water channel. The obtained simulation results are in good agreement with the experimental data. Numerical experiments have been performed to investigate the influence of gravity on the decay of the continuous phase Reynolds stresses. For comparison, the influence of dispersed phase turbulence on the continuous phase turbulence without taking gravity into consideration has also been studied.
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47.27.nd, 47.27.eb, 47.55.-t, 02.50.Fz, 47.60.Dx, 02.60.-x

A multiscale subgrid model for both free vortex flows and wall-bounded flows

L. Bricteux, M. Duponcheel, and G. Winckelmans

Phys. Fluids 21, 105102 (2009) (12 pages)

Online Publication Date: 15 October 2009

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A new subgrid-scale (SGS) model which has an adequate behavior in both vortical flows and wall-bounded flows is proposed. In wall-bounded flows with “wall-resolved” large eddy simulation (LES), the theory predicts that the SGS dissipation should vanish as y+3 near the wall. In free vortex flows, one needs to have models which do not dissipate energy in the strongly vortical and essentially laminar part of the flow, e.g., in the vortex core regions. The wall adapting local eddy (WALE) viscosity model of Nicoud and Ducros [Flow, Turbul. Combust. 62, 183 (1999)] has the correct near-wall behavior. It is, however, demonstrated here that it produces values of effective eddy viscosity which are too high in vortical flows: this constitutes a major drawback for LES of vortex flows. On the other hand, the regularized variational multiscale models are suitable to simulate vortical flows as demonstrated by Cocle et al. [Complex Effects in LES (Springer, New York, 2007), p. 56], but they do not have a correct behavior in wall-bounded flows as shown by Jeanmart and Winckelmans [Phys. Fluids 19, 055110 (2007)]. The model presented here aims at combining the strengths of the two models: it is a multiscale model, thus acting on the high pass filtered LES field, and for which the SGS viscosity is evaluated using the WALE model, itself also computed using the high pass filtered field. Hence, this model is only active when there is locally a significant high wavenumber content in the flow and it has a natural near-wall damping behavior. The ability of this model to simulate vortex and wall-bounded flows is demonstrated on three test cases. The first case is the turbulent channel flow at Retau=395 and Retau=590. The second test concerns a counter-rotating four-vortex system at ReGamma=20 000. The third case concerns a two-vortex system in ground effect at ReGamma=20 000. It is shown that the model allows to perform successfully the LES of these flows with the proper dissipative behavior in both the near-wall and the vortical regions.
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47.32.Ef, 47.27.nd, 47.60.Dx, 47.27.ep

Fluid-acoustic interactions in self-sustained oscillations in turbulent cavity flows. I. Fluid-dynamic oscillations

Hiroshi Yokoyama and Chisachi Kato

Phys. Fluids 21, 105103 (2009) (13 pages)

Online Publication Date: 23 October 2009

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The fluid-acoustic interactions in a flow over a two-dimensional rectangular cavity are investigated by directly solving the compressible Navier–Stokes equations. The upstream boundary layer is turbulent. The depth-to-length ratio of the cavity is 0.5. Phase-averaged flow fields reveal the mechanism for the acoustic radiation. Large-scale vortices form in the shear layer that separates from the upstream edge of the cavity. When a large-scale vortex collides with the downstream wall, the low-pressure fluid in the vortex spreads along the downstream wall. As a result, a local downward velocity is induced by the local pressure gradient, causing the upstream fluid to expand. Finally, an expansion wave propagates to the outside of the cavity. The large-scale vortices originate from the convective disturbances that develop in the shear layer. The disturbances grow due to the Kelvin–Helmholtz instability, similar to the growth of those in a laminar cavity flow. To clarify the mechanism for the generation of the initial convective disturbances, computations for backward-facing step flows with an artificial acoustic source are also performed. As the artificial acoustic waves become more intense, the initial convective disturbances in the shear layer become more intense while the spatial growth rate of these disturbances does not change. This means that the initial convective disturbances in the shear layer are induced by the acoustic waves.
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47.27.nb, 47.55.P-, 47.32.cb, 47.20.Ib, 47.27.E-, 89.20.Kk

Theoretically based optimal large-eddy simulation

Robert D. Moser, Nicholas P. Malaya, Henry Chang, Paulo S. Zandonade, Prakash Vedula, Amitabh Bhattacharya, and Andreas Haselbacher

Phys. Fluids 21, 105104 (2009) (19 pages)

Online Publication Date: 23 October 2009

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Large eddy simulation (LES), in which the large scales of turbulence are simulated while the effects of the small scales are modeled, is an attractive approach for predicting the behavior of turbulent flows. However, there are a number of modeling and formulation challenges that need to be addressed for LES to become a robust and reliable engineering analysis tool. Optimal LES is a LES modeling approach developed to address these challenges. It requires multipoint correlation data as input to the modeling, and to date these data have been obtained from direct numerical simulations (DNSs). If optimal LES is to be generally useful, this need for DNS statistical data must be overcome. In this paper, it is shown that the Kolmogorov inertial range theory, along with an assumption of small-scale isotropy, the application of the quasinormal approximation and a mild modeling assumption regarding the three-point third-order correlation are sufficient to determine all the correlation data required for optimal LES modeling. The models resulting from these theoretically determined correlations are found to perform well in isotropic turbulence, with better high-wavenumber behavior than the dynamic Smagorinsky model. It is expected that these theory-based optimal models will be applicable to a wide range of turbulent flows, in which the small scales can be modeled as isotropic and inertial. The optimal models developed here are expressed as generalized quadratic and linear finite-volume operators. There are significant quantitative differences between these optimal LES operators and standard finite-volume operators, and these differences can be interpreted as the model of the subgrid effects. As with most other LES models, these theory-based optimal models are expected to break down near walls and other strong inhomogeneities.
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47.27.ep, 02.70.-c, 47.11.Df

Theoretical prediction of turbulent skin friction on geometrically complex surfaces

Yulia Peet and Pierre Sagaut

Phys. Fluids 21, 105105 (2009) (19 pages)

Online Publication Date: 28 October 2009

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This article can be considered as an extension of the paper of Fukagata et al. [Phys. Fluids 14, L73 (2002)] which derived an analytical expression for the constituent contributions to skin friction in a turbulent channel, pipe, and plane boundary layer flows. In this paper, we extend the theoretical analysis of Fukagata et al. (formerly limited to canonical cases with two-dimensional mean flow) to a fully three-dimensional situation allowing complex wall shapes. We start our analysis by considering arbitrarily shaped surfaces and then formulate a restriction on a surface shape for which the current analysis is valid. A theoretical formula for skin friction coefficient is thus given for streamwise and spanwise homogeneous surfaces of any shape, as well as some more complex configurations, including spanwise-periodic wavy patterns. The theoretical analysis is validated using the results of large eddy simulations of a turbulent flow over straight and wavy riblets with triangular and knife-blade cross-sections. Decomposition of skin friction into different constituent contributions allows us to analyze the influence of different dynamical effects on a skin friction modification by riblet-covered surfaces.
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47.60.Dx, 47.27.-i, 47.27.E-

Compressible Flows

Numerical study of boundary layer separation control using magnetogasdynamic plasma actuators

Chiranjeev S. Kalra, Mikhail N. Shneider, and Richard B. Miles

Phys. Fluids 21, 106101 (2009) (9 pages)

Online Publication Date: 2 October 2009

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In this study, an efficient, time dependent, two-dimensional Navier–Stokes numerical code for shockwave boundary layer interaction in air is developed. Nonthermal surface plasma actuation is evaluated for effective shockwave induced boundary layer separation control within supersonic inlets. Specifically, high speed magnetogasdynamic plasma actuators are of interest. In these, localized ionization is produced close to the wall surface and then the flow is accelerated using strong magnetic fields. To replicate the experiments done at large boundary layer thickness, the code is divided into time independent and time dependent regimes to significantly reduce computation time. Computational results are in good agreement with experiments in terms of the flow structure as shown by Schlieren imaging, acetone planar laser scattering, and the static pressure profile on the test section wall.
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52.30.Cv, 52.35.Tc, 52.40.Hf, 52.50.Lp, 52.65.Kj

Discrete self-similarity in ultrarelativistic type-II strong explosions

Yonatan Oren and Re'em Sari

Phys. Fluids 21, 106102 (2009) (7 pages)

Online Publication Date: 12 October 2009

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A solution to the ultrarelativistic strong explosion problem with a nonpower law density gradient is delineated. We consider a blast wave expanding into a density profile falling off as a steep radial power law with small, spherically symmetric, and log-periodic density perturbations. We find discretely self-similar solutions to the perturbation equations and compare them to numerical simulations. These results are then generalized to encompass small spherically symmetric perturbations with arbitrary profiles.
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47.40.Rs, 47.10.A-, 47.75.+f, 47.53.+n

Comparison between Mach 2 rarefied airflow modification by an electrical discharge and numerical simulation of airflow modification by surface heating

J. D. Parisse, L. Léger, E. Depussay, V. Lago, and Y. Burtschell

Phys. Fluids 21, 106103 (2009) (9 pages)

Online Publication Date: 16 October 2009

Full Text: PDF (557 kB)

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This study is devoted to numerical and experimental investigations about the influence of an electrical discharge over a flat plate immersed in a rarefied Mach 2 airflow. Regarding the experimental work, a negative dc discharge is created by applying a potential difference gap between two spanwise aluminum electrodes flush mounted on the plate. The electrode placed close to the leading edge is connected to the negative dc voltage, the second one is grounded. The influence due to the presence of the electric discharge is investigated with a glass Pitot tube by measuring the pressure proles above the flat plate. These experimental results are compared to the numerical work, where the effect of a surface temperature increase is simulated. Different effects can be attributed to the electrical discharge: the ionization of the gas above the plate with the creation of charged species, the acceleration of the positive charged species, the heat of the gas volume above the flat plate, and the heating of the surface of the flat plate. The Pitot probe measurements have shown a thickening of the boundary layer and the increasing of the angle of the shock wave, and the simulation of the surface temperature increase shows the same effect. These arguments let to think that the heating effect due to the temperature increase in the flat plate is the major one among the other effects mentioned above.
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47.45.-n, 47.40.Nm, 47.11.-j, 47.15.Cb

Purely analytic solutions of the compressible boundary layer flow due to a porous rotating disk with heat transfer

M. Turkyilmazoglu

Phys. Fluids 21, 106104 (2009) (12 pages)

Online Publication Date: 21 October 2009

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The motivation of the present study is to obtain exact analytical solution of the steady laminar flow of a compressible viscous fluid over a rotating disk subjected to a uniformly applied suction or blowing. Classical Von Karman problem of a rotating disk is extended to account for the compressibility effects with insulated and isothermal wall conditions. Using Von Karman similarity transformation the compressible nonlinear equations of motion are reduced to a boundary value problem whose solution was first obtained by Ackroyd [J. A. D. Ackroyd, “On the steady flow produced by a rotating disc with either surface suction of injection,” J. Eng. Phys. 12, 207 (1978)] for the velocity field in terms of a series of exponentially decaying functions. This kind of an approach, however, besides being incapable of resolving the velocity field for higher values of injection (see the conclusion of Ackroyd) is also shown not to be suitable for the temperature distribution of the compressible flow, necessitating the use of a Chebyshev collocation technique in such circumstances. A universally valid analytical technique based on the homotopy analysis method is next applied to obtain solutions corresponding to both velocity and temperature fields. This method yields explicit analytic solutions converging uniformly to the exact solution having the form of exponentially decaying functions for the full range of parameters considered. The effects of suction and blowing together with compressibility on the physically relevant and significant parameters are rigorously explored from the exact formulas extracted.
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47.40.-x, 02.30.-f, 47.10.A-, 47.32.Ef, 47.56.+r, 47.15.Cb

Numerical study of self-induced transonic flow oscillations behind a sudden duct enlargement

Thomas Emmert, Philippe Lafon, and Christophe Bailly

Phys. Fluids 21, 106105 (2009) (15 pages)

Online Publication Date: 28 October 2009

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A sonic flow in a plane duct passing an abrupt increase in cross section is studied using compressible large-eddy simulations. Different flow patterns are likely to appear in this configuration according to the ratio between the downstream ambient pressure and the upstream reservoir pressure. For low pressure ratios, the flow is entirely supersonic in the channel and a steady symmetrical shock pattern is observed. For higher pressure ratios, the flow can be attached to one side of the channel with a jet-like shock cell structure, or can be characterized by strong oscillations of a single normal shock located near the sudden expansion, known as base-pressure oscillations in literature. A hysteresis phenomenon is found experimentally and the state reached by the transonic flow depends on the path followed by the pressure ratio. Moreover, a coupling of these base-pressure oscillations with the quarter-wavelength resonance of the duct can occur. All these regimes are numerically investigated and the results are favorably compared to available experimental data. A case of frequency locking of this self-excited mechanism is also reproduced, in agreement with a modeling of the resonator. The governing equations are solved using high-order central finite differences combined with an overset grid approach. The large-eddy simulations are based on a relaxation filtering and a nonlinear shock-capturing scheme is also implemented for shock waves.
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47.11.Bc, 47.40.Hg, 47.40.Ki, 47.40.Nm, 47.60.Dx

Geophysical Flows

Nonlinear development of inertial instability in a barotropic shear

Riwal Plougonven and Vladimir Zeitlin

Phys. Fluids 21, 106601 (2009) (15 pages)

Online Publication Date: 9 October 2009

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Inertial instability is investigated numerically in a two-dimensional setting in order to understand its nonlinear stage and saturation. To focus on fundamental mechanisms, a simple barotropic shear U(y)=tanh y on the f-plane is considered. The linear stability problem is first solved analytically, and the analytical solutions are used to benchmark numerical simulations. A simple scenario of the nonlinear development of the most unstable mode was recurrently observed in the case of substantial diffusivity: while reaching finite amplitude the unstable mode spreads laterally, distorting the initially vertical instability zone. This process produces strong vertical gradients which are subsequently annihilated by diffusion, making the flow barotropic again but with the shear spread over a wider region. In the course of such evolution, unexpectedly, strong negative absolute vorticity anomalies are produced. In weakly diffusive simulations, the horizontal spreading of the unstable motions and the enhancement of the anticyclonic vorticity extremum persist, but small-scale motions/instabilities render the flow considerably more complex. It is known that the barotropic component of the final state can be predicted from the conservation of momentum. Our simulations confirm the relevance of this simple prediction in the cases investigated regardless of resolution and diffusion. The baroclinic component of the final state is also analyzed and three types of structures are identified: persistent stationary stratification layers, subinertial waves trapped in the anticyclonic shear, and freely propagating inertia-gravity waves. The subinertial waves and the stratification staircase have clear signatures and can therefore help to identify the regions that have undergone inertial instability.
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52.35.Qz, 52.35.We, 52.65.-y

Waves on a columnar vortex in a strongly stratified fluid

Paul Billant and Stéphane Le Dizès

Phys. Fluids 21, 106602 (2009) (9 pages)

Online Publication Date: 12 October 2009

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This paper investigates the discrete bounded waves sustained by a vertical columnar Rankine vortex in a strongly stratified fluid. We show that these waves are very different from their well-known counterpart in homogeneous fluid (Kelvin vortex waves); they exist only for nonzero azimuthal wavenumber m, their frequency lies in the interval [0,mOmega] (Omega is the angular velocity in the vortex core) and they are unstable because of an outward radiation from the vortex. The instability mechanism is explained in terms of an over-reflection phenomenon by means of a Wentzel–Kramers–Brillouin–Jeffreys analysis for large axial wavenumber.
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47.55.Hd, 47.32.-y, 47.35.-i, 47.20.-k

A Lagrangian approach to droplet condensation in atmospheric clouds

Ryan S. R. Sidin, Rutger H. A. IJzermans, and Michael W. Reeks

Phys. Fluids 21, 106603 (2009) (16 pages)

Online Publication Date: 23 October 2009

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The condensation of microdroplets in model systems, reminiscent of atmospheric clouds, is investigated numerically and analytically. Droplets have been followed through a synthetic turbulent flow field composed of 200 random Fourier modes, with wave numbers ranging from the integral scales [[script O](102  m)] to the Kolmogorov scales [[script O](10−3  m)]. As the influence of all turbulence scales is investigated, direct numerical simulation is not practicable, making kinematic simulation the only viable alternative. Two fully Lagrangian droplet growth models are proposed: a one-way coupled model in which only adiabatic cooling of a rising air parcel is considered, and a two-way coupled model which also accounts for the effects of local vapor depletion and latent heat release. The simulations with the simplified model show that the droplet size distribution becomes broader in the course of time and resembles a Gaussian distribution. This result is supported by a theoretical analysis which relates the droplet surface-area distribution to the dispersion of droplets in the turbulent flow. Although the droplet growth is stabilized by vapor depletion and latent heat release in the two-way coupled model, the calculated droplet size distributions are still very broad. The present results may provide an explanation for the rapid growth of droplets in the coalescence stage of rain formation, as broad size distributions are likely to lead to enhanced collision rates between droplets.
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47.55.df, 64.70.fm, 92.60.Jq, 92.60.hk, 47.27.tb, 47.11.-j

On fully nonlinear, vertically trapped wave packets in a stratified fluid on the f-plane

M. Stastna, F. J. Poulin, K. L. Rowe, and C. Subich

Phys. Fluids 21, 106604 (2009) (13 pages)

Online Publication Date: 29 October 2009

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The ubiquity of solitary and solitarylike internal waves in the coastal ocean has been recognized for some time. Recent theoretical studies of a strongly nonlinear, weakly nonhydrostatic set of layer-averaged model equations have predicted that rotation, for example, on the f-plane, can lead to the decay and subsequent reemergence of internal solitary waves. We reconsider this problem using high resolution numerical simulations of the rotating stratified Euler equations. We find that in certain cases the initial disturbances indeed fission into nonlinear wave packets, with the constituent waves making up the wave packet being, in themselves, nonlinear. However, for typical coastal ocean parameters this only occurs at rotation rates higher than those on Earth on the time scales we are able to simulate. We confirm, using the Dubreil–Jacotin–Long equation, that the vertical structure of the wave-induced currents is well predicted by the fully nonlinear theory of nonrotating internal solitary waves and that weakly nonlinear Korteweg–de Vries equation-based theory fails to describe this structure accurately. Subsequently, we consider flat-crested solitary waves that allow us to fix the wave amplitude while varying the horizontal wavelength. We find that as the waves' horizontal extent nears the baroclinic Rossby radius more energy is deposited into the wave tail. However, no wave overtaking is observed, and an explanation for this fact is proposed. Finally, we discuss the effects of the horizontal component of the rotation vector and derive an exact equation for rotation modified waves near the equator. This equation demonstrates that in this situation, rotation modifies the structure of the fully nonlinear waves but does not lead to solitary wave decay.
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92.10.Hm, 47.32.Ef, 47.35.Fg, 47.55.Hd

Others

Spectral and particle dispersion properties of steady two-dimensional multiscale flows

M. Priego and J. C. Vassilicos

Phys. Fluids 21, 107101 (2009) (12 pages)

Online Publication Date: 6 October 2009

Full Text: PDF (1175 kB)

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The spectral and particle dispersion characteristics of steady multiscale laminar thin-layer flows are investigated through numerical simulations of a two-dimensional layer-averaged model. The model assumes a semiparabolic velocity profile and is solved using a semi-Lagrangian spline method. The main features of the flows are turbulentlike and consistent with previous experimental studies. The Eulerian wavenumber spectra and the Lagrangian frequency spectra oscillate around power laws that reflect the self-similarity of the forcing. In the weak forcing regime, the exponents of these power laws can be related to the multiscale geometry and the intensity scaling of the forcing. The Lagrangian spectra also show low-frequency plateaus, which arise from the slow motions far away from the applied forces. The absolute dispersion of tracer particles in these steady planar flows presents a ballistic stage followed by a diffusive regime, which results from the decorrelated motions of particles lying on streamlines of different periods. Relative dispersion shows an additional intermediate stage consisting of several separation bursts, which originate from the intense strain regions imposed by the different forcing scales. While these bursts can cause locally superquadratic mean square separation, the trapping by steady recirculation regions rules out an intermediate relative dispersion power law regardless of the number of scales in the flow.
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47.11.-j, 47.15.-x, 47.27.E-, 47.27.-i
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ERRATA

FREE

Retraction: “Direct numerical simulation of the Ekman layer: A step in Reynolds number, and cautious support for a log law with a shifted origin” [Phys. Fluids 20, 101507 (2008)]

Philippe R. Spalart, Gary N. Coleman, and Roderick Johnstone

Phys. Fluids 21, 109901 (2009) (3 pages)

Online Publication Date: 28 October 2009

Full Text: PDF (87 kB)

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 Abstract Unavailable
Show PACS
99.10.Ln, 47.27.nb, 47.27.E-

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