Volume 15, Issue 6, June 2003
 LETTERS


Spectra of the very large anisotropic scales in turbulent channels
View Description Hide DescriptionThe spectra of numerically simulated channels at and in very large boxes are described and analyzed. They support a model in which the structures can be decomposed in two components. The first one is formed by structures of size which span most of the channel height, and penetrate into the buffer layer. The second one has maximum intensity in the nearwall region, where it is highly anisotropic and scales in inner units. It widens, lengthens, and becomes more isotropic in the outer layer, where it scales with The cospectrum exhibits an analogous quasiisotropic range, whose width grows linearly with wall distance. At the present Reynolds numbers, nothing can be said about a possible streamwise similarity, due to limited scale separation. An extensive set of statistics from the simulations is downloadable from ftp://torroja.dmt.upm.es/channels.

Flow induced patterning at the air–water interface
View Description Hide DescriptionPatterns on the air–water interface of a swirling cylinder flow are produced via hydrodynamic symmetrybreaking instability of the bulk flow. The patterns are rotating waves breaking the axisymmetry of the system and are longitudinal at the free surface (i.e., not surface deforming). Qualitative observations and quantitative measurements of velocity and vorticity are provided. Threedimensional Navier–Stokes computations identify the symmetrybreaking mode responsible for the waves. These waves are then used to patternLangmuir monolayers at concentrations sufficiently below saturation.
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 ARTICLES


A molecular dynamics study of drop spreading on a solid surface
View Description Hide DescriptionIn this paper, the effects of size of the chains composed of the drop and initial velocity of the drop on the drop terraced spreading are studied. The chain size effects on the base radius of drop are studied at zero initial velocity. A logarithm dependence of the drop base radius on the time is found for 2atom to 16atom flexible chain systems with large lattice dimension of solid and a power law for small lattice dimension of solid. The longer the chain, the slower is the spreading. With a nonzero initial velocity, the drop base radius increases with increasing initial velocity before the drop splits into smaller separated drops. As the initial velocity increases, the transition from a logarithm to a power law relation for the time dependence of the drop base radius is first noted here.

Contact line instability and pattern selection in thermally driven liquid films
View Description Hide DescriptionLiquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability of the flow can be altered, or patterns selected, using feedback control. We show that thermal perturbations of certain spatial structure imposed behind the contact line and proportional to the deviation of the contact line from its mean position can completely suppress the instability. Due to the presence of mean flow and a spatially nonuniform nature of spreading liquid films the dynamics of disturbances is governed by a nonnormal evolution operator, opening up a possibility of transient amplification and nonlinear instabilities. We show that in the case of thermal driving the nonnormality can be significant, especially for small wavenumber disturbances, and trace the origin of transient amplification to a close alignment of a large group of eigenfunctions of the evolution operator. However, for values of noise likely to occur in experiments we find that the transient amplification is not sufficiently strong to either change the predictions of the linear stability analysis or invalidate the proposed control approach.

A model for the mixing time scale of a turbulent reacting scalar
View Description Hide DescriptionCurrent micromixingmodels in transported PDF (probability density functionequation)modeling of initially nonpremixed, turbulent reacting flows ignore the direct influence of chemistry on the dissipation rate of reacting scalar fluctuations. Following mapping closure, a model for the time scale of reactive scalar mixing in the flamelet regime is developed and comparisons made with direct numerical simulations of a turbulent reacting jet. The modeling results show a significant improvement over the generally used estimate of substituting the time scale of the reacting scalar by that of a conserved scalar in traditional transported PDF approaches. The model can readily be applied to many existing mixing submodels used in transported PDF modeling when the time scales of the reacting scalars appear explicitly in the formulation. The submodels allow the transported PDF approach to now encompass the fast as well as slow chemistry regimes.

Shapepreserving solutions for quantum vortex motion under localized induction approximation
View Description Hide DescriptionThe motion of a quantum vortex in superfluidhelium is considered in the localized induction approximation. In this approximation the instantaneous velocity of quantum vortex is proportional to the local curvature and is parallel to the vector, which is a linear combination of the local binormal and the principal normal to the vortex line. The motion in the direction of the principal normal is specific for a quantum vortex and implies that the vortex shrinks, in contrast to the classical vortex in an ideal fluid. In the present work we deal with two fourparameter classes of shapepreserving solutions (one with increasing and one with decreasing spatial scale) resulting from equations governing the curvature and the torsion. The solutions describe vortex lines whose motion is equivalent to a transformation being a superposition of a homothety and a rotation. In a particular case when the transformation is a pure homothety, we find analytic solutions for the curvature and the torsion. In the general case, when the transformation is a superposition of a nontrivial rotation and a homothety, the asymptotics of the solutions of the first class are given explicitly and are related to the parameters characterizing the transformation. It is found that the solutions of the second class (with decreasing scale) either have asymptotes or are periodic (when the transformation is a pure homothety) or else exhibit chaotic behavior.

Power laws for rough wall turbulent boundary layers
View Description Hide DescriptionAn assessment of the ability of power laws to describe the mean velocity profile in the overlap region of a zero pressure gradient turbulent boundary layer is reported. The experiments were performed in a wind tunnel on smooth and four different types of rough surfaces at moderate Reynolds numbers. A novel modification to the power law velocity profile is proposed to account for the effect of surface roughness in the overlap region. This modification is analogous to the use of a roughness function to produce a downward shift in the logarithmic velocity profile. The roughness parameters in the proposed equation more accurately follow the effect of roughness on skin friction than does the roughness shift The present study shows that power laws can be used to effectively describe the mean velocity profile over a wider range than a log law for both smooth and rough surfaces.

Bifurcation of and ghost effect on the temperature field in the Bénard problem of a gas in the continuum limit
View Description Hide DescriptionA gas in a timeindependent state under a uniform weak gravity in a general domain is considered. The asymptotic behavior of the gas in the limit that the Knudsen number of the system tends to zero (or in the continuum limit) is investigated on the basis of the Boltzmann system for the case where the flow velocity vanishes in this limit, and the fluiddynamictype equations and their associated boundary conditions describing the behavior of the gas in the continuum limit are derived. The equations, different from the Navier–Stokes ones, contain thermal stress and infinitesimal velocity amplified by the inverse of the Knudsen number. The system is applied to analysis of the behavior of a gas between two parallel plane walls heated from below (Bénard problem), and a bifurcated strongly distorted temperature field is found in infinitesimal velocity and gravity. This is an example showing that the Navier–Stokes system fails to describe the correct behavior of a gas in the continuum limit.

Control of aeolian tones radiated from a circular cylinder in a uniform flow
View Description Hide DescriptionEffects of artificial forcing on the generation and propagation mechanisms of the sound generated by a circular cylinder in a uniform flow are investigated by direct solution of the twodimensional, unsteady, compressible Navier–Stokes equations. Two types of forcing are considered: rotation of the cylinder at a constant angular velocity and periodic blowing/suction from the (nonrotating) cylinder surface. For the case of a rotating cylinder, results show that the sound generation can be controlled by controlling the periodic shedding of (Kármán) vortices from the cylinder surface into its wake. On the other hand, results for the case of periodic blowing/suction show that the generation and propagation of the sound can be effectively controlled without drastic changes of the vortex shedding. It is found in this case that the interactions among the lift dipole (which is generated by the vortex shedding), the drag dipole and the monopole (both of which are generated by the periodic blowing/suction) play a principal role in the control process of the generation and propagation of the sound.

Stochastic simulations of buoyancyreversal experiments
View Description Hide DescriptionBuoyancy reversal occurs when the mixing of two fluids, initially stably stratified, produces a mixture which is more dense than either pure fluid. The resulting instability generates turbulent mixing, and may play an important role in geophysical and astrophysical flows. In this work, a stochastic onedimensional model is used to simulate these systems. Model validation is accomplished using experimental comparisons. Scalings inferred from the model simulations are used to suggest extrapolations from experimental results to natural systems.

Cavitation luminescence in a water hammer: Upscaling sonoluminescence
View Description Hide DescriptionOscillatory acceleration and deceleration of a column of water leads to a pipe hammer as well as cavitation. With a small amount of xenon gas dissolved in the water, we can detect a stream of predominantly ultraviolet subnanosecond flashes of light which are attributed to collapsing bubbles. The observed emission can exceed for a single collapse and has a peak power over 0.4 W.

Direct numerical simulation of stagnation region flow and heat transfer with freestream turbulence
View Description Hide DescriptionA direct numerical simulation is performed for stagnationregion flow with freestream turbulence. A fully implicit secondorder timeadvancement scheme with fourthorder finite differences and an optimized scheme are employed. The optimized scheme is developed to save computational cost. The freestream turbulence is a precomputed field of isotropic turbulence. The present DNS results in the “damping” and “attached amplifying” regimes are found to be similar to those of the organized inflow disturbances. Emphasis is placed on the flow and temperature fields in the “detached amplifying” regime. The contours of instantaneous flow field illustrate that streamwise vortices are stretched in the streamwise direction by mean strain rate. The temperature field is also stretched in the streamwise direction near the wall. The surface contours reveal that the temperature field is influenced significantly by streamwise vorticity. Due to the dominance of the mean strain, the loglaw region is not observed for and the inner scaling fails, but the outer scaling works. The singlepoint turbulence statistics and the turbulent statistics budgets are obtained. The flow statistics reflect the typical characteristics of stagnationregion flow which are generically different from those of other canonical shear flows. One of the typical features of the budgets is that the velocity pressure correlation and the turbulenttransport play significant roles in the stagnationregion flow. Finally, the present simulation data are compared with experimental results. It is found that the effect of largescale eddies on the enhancement of wall heat transfer is substantial in the turbulent stagnationregion heat transfer.

Exact selfsimilarity solution of the Navier–Stokes equations for a porous channel with orthogonally moving walls
View Description Hide DescriptionThis article describes a selfsimilarity solution of the Navier–Stokes equations for a laminar, incompressible, and timedependent flow that develops within a channel possessing permeable, moving walls. The case considered here pertains to a channel that exhibits either injection or suction across two opposing porous walls while undergoing uniform expansion or contraction. Instances of direct application include the modeling of pulsating diaphragms, sweat cooling or heating, isotope separation, filtration, paper manufacturing,irrigation, and the grain regression during solid propellant combustion. To start, the stream function and the vorticityequation are used in concert to yield a partial differential equation that lends itself to a similarity transformation. Following this similarity transformation, the original problem is reduced to solving a fourthorder differential equation in one similarity variable η that combines both space and time dimensions. Since two of the four auxiliary conditions are of the boundary value type, a numerical solution becomes dependent upon two initial guesses. In order to achieve convergence, the governing equation is first transformed into a function of three variables: The two guesses and η. At the outset, a suitable numerical algorithm is applied by solving the resulting set of twelve firstorder ordinary differential equations with two unspecified startup conditions. In seeking the two unknown initial guesses, the rapidly converging inverse Jacobian method is applied in an iterative fashion. Numerical results are later used to ascertain a deeper understanding of the flow character. The numerical scheme enables us to extend the solution range to physical settings not considered in previous studies. Moreover, the numerical approach broadens the scope to cover both suction and injection cases occurring with simultaneous wall motion.

A subgridscale mixing model for largeeddy simulations of turbulent reacting flows using the filtered density function
View Description Hide DescriptionThe filtered density function approach [Colucci et al., Phys. Fluids 10, 499 (1999); Jaberi et al., J. Fluid Mech. 401, 85 (1999)] for largeeddy simulations of initially nonpremixed turbulent reacting flows is extended to encompass the flamelet regime. This is done by developing a model which describes the effect of realistic, Arrhenius chemical kinetics on the subgrid mixing time scale for reactive scalars. The model is based on mapping closure and flamelet modeling and can readily be applied to many existing micromixing models where the time scales of the reacting scalars appear explicitly in the formulation. Testing of the model using spatially filtered direct numerical simulation data of a turbulent reacting jet [Boersma, Center for Turbulence Research Annual Research Briefs (Stanford University/NASA Ames, 1999), pp. 59–72] show a significant improvement over the generally used estimate of substituting the time scale of the reacting scalars by that of a conserved scalar. The impact of internal intermittency on the performance of the new model is discussed.

On the optimization of mixing protocol in a certain class of threedimensional Stokes flows
View Description Hide DescriptionMixing in a special class of threedimensional, noninertial periodic flows is studied numerically. In the type of flow considered here, the crosssectional velocity components are independent of the axial flow and the axial flow is independent of the axial coordinate. Using the eccentric helical annular mixer as a prototype, we consider the counterrotating case with steady rotation of the outer cylinder and sinusoidal modulation of the inner one. Apart from the mixer geometry, the behavior of the system is governed by two dimensionless parameters obtained by scaling the crosssectional stirring protocol with respect to the characteristic residence time of the fluid in the mixer. The first parameter is related to the average number of turns of the outer cylinder and the second one is related to the average number of modulation periods of the inner cylinder. The convectiondiffusion equation is solved numerically, with temperature as a passive scalar, at high Péclet number. For a given threedimensional mixer geometry and axial flow rate we show that there is an optimum modulation frequency for which the exit standard deviation of the temperature field is a minimum. Lagrangian simulations at infinite Péclet number and the use of other tools to study mixing, such as stretching calculations and tracer tracking methods, confirm that the optimized protocol does result in very effective mixing.

Homotopy of exact coherent structures in plane shear flows
View Description Hide DescriptionThreedimensional steady states and traveling wave solutions of the Navier–Stokes equations are computed in plane Couette and Poiseuille flows with both freeslip and noslip boundary conditions. They are calculated using Newton’s method by continuation of solutions that bifurcate from a twodimensional streaky flow then by smooth transformation (homotopy) from Couette to Poiseuille flow and from freeslip to noslip boundary conditions. The structural and statistical connections between these solutions and turbulent flows are illustrated. Parametric studies are performed and the parameters leading to the lowest onset Reynolds numbers are determined. In all cases, the lowest onset Reynolds number corresponds to spanwise periods of about 100 wall units. In particular, the rigidfree plane Poiseuille flow traveling wave arises at for and in excellent agreement with observations of the streak spacing. A simple onedimensional map is proposed to illustrate the possible nature of the “hard” transition to shear turbulence and connections with the unstable exact coherent structures.

Twoway coupling simulations of instabilities in a plane bubble plume
View Description Hide DescriptionIn the present study we aim at investigating the instabilities in a plane bubble plume by means of twoway coupling simulations. The continuous phase motion is obtained by direct numerical solution of the Navier–Stokes equations forced by the presence of the bubbles. The collective effects induced by the presence of the bubbles are modeled by a spatiotemporal distribution of momentum. Time evolution of the dispersed phase is solved by Lagrangian tracking of all the bubbles. In the present study, the motion of the carrying fluid is initiated and driven by the induced buoyancy of bubbles released from a source located in an initially quiescent fluid layer. A quantitative analysis of the flowtransition is thus investigated for several plume widths and for various fluid viscosities over a range of Grashof numbers based on the injection conditions. An analogy is drawn with buoyant singlephase flows for the steady laminar region. Following the similarity formulation of Fujii [Int. J. Heat Mass Transfer6, 597 (1963)] under boundary layer approximations for free thermal plumes, the velocity profiles can be collapsed to a single selfsimilar plot. Nevertheless, this analogy with singlephase flow shows some discrepancies in the description of the transition. Numerical data emphasize that the key parameter controlling the height of transition is the Grashof number, which is based on injection conditions of the dispersed phase. Our results concur with the recent experiments of Alam and Arakeri [J. Fluid Mech. 254, 363 (1993)]. Although the Grashof number also determines the transition in thermal plumes [Wakitani and Yosinobu, Fluid Dyn. Res. 2, 363 (1988)], the twophase configuration is more unstable. These new results underline the important role played by the slip velocity of the bubbles in plume stability. Indeed, it tends to delay the plume transition when the slip velocity increases and approaches the buoyancyinduced velocity. This feature should also be related to the lack of diffusion by the bubble cloud in the Lagrangian transport of the density gradient.

Capillary rise in nesting cylinders
View Description Hide DescriptionWe investigate computationally recent results concerning the question of whether liquid necessarily rises higher in a capillary tube of smaller section, when tubes are placed vertically in an infinite reservoir. The numerical results corroborate for a particular example a striking discontinuous behavior that was predicted mathematically.

An extension of generalized Taylor dispersion in unbounded homogeneous shear flows to runandtumble chemotactic bacteria
View Description Hide DescriptionIn the absence of flow, the biased random walk of bacteria such as Escherichia coli is modeled by straight runs punctuated by random changes in direction, tumbles. We modelchemotaxis by allowing the tumble rate of a run to depend on the component of swimming velocity in the direction of the chemoattractant gradient. In the wellstudied situation of weak bias in tumble rate, bacteria disperse over a diffusive time scale, and the evolution of density satisfies the classic Keller–Segel advectiondiffusion equation. In this paper, we model swimming bacteria being advected and rotated by an unbounded homogeneous shear flow. The flow field alters the trajectories of individuals and thus affects the macroscopic dispersion of a population. We adapt the formal framework of generalized Taylor dispersion theory to make it applicable for runandtumble bacteria with an arbitrary bias in tumble rate. This enables us to obtain a macroscopic description of the dispersion of bacteria. For the particular case of simple shear flow, we calculate explicitly the effect of flow on the diffusiontensor and mean swimming velocity.

Laminar flamelet decomposition for conditional sourceterm estimation
View Description Hide DescriptionA new decomposition approach to conditional sourceterm estimation (CSE) is proposed and discussed. The new approach is tested in the a priori sense using direct numerical simulations (DNS). It is found that—where CSE had previously been found to provide closure for chemical sourceterms with arbitrary chemistry in the large eddy simulation paradigm—it can provide this closure in the Reynolds averaged Navier–Stokes paradigm as well. Using the proposed decomposition improves the predictions of CSE considerably. Only the assumptions that gradients in conditional averages are small and that the probability density function of mixture fraction can be adequately approximated using a presumed functional form are needed. The computational cost of the new laminar flamelet decomposition approach to CSE is also substantially lower than that of the original approach.
