Volume 20, Issue 8, August 2008

Intense vortices in the wake of a circular cylinder are investigated in a rotating parabolic (polar) plane fluid. This system has a background potential vorticity (PV) field that supports Rossby waves and causes vortices to migrate and radiate. A method for imagingrotating flows, which we call “altimetric imaging velocimetry” is employed. Optical color coding of slopes of the freesurface elevation field yields the pressure, geostrophic and gradient wind velocity, and potential vorticity fields with very high spatial resolution, limited largely by the pixel resolution of the available imaging sensors. Cylinder wakes on the polar plane exhibit strikingly different regimes as it is translated azimuthally, eastward or westward. Selfarrangement of vortices after the cylinder was stopped drives an intense eastward jet formed by the rows of anticyclones and cyclones on its flanks. In agreement with the idea of a PV staircase, this jet has a strong PV gradient at its center, while PV is homogenized by the vortices on either side. A slowly translating cylinder generates Rossby waves with phase propagation locked to the cylinder, and intermediate cases show a widespread vortex/wave interaction.
 LETTERS


Instability of a fluid inside a precessing cylinder
View Description Hide DescriptionIn this letter, we report experimental results on the stability of a fluid inside a precessing and resonant cylinder. Above a critical Reynolds number, the Kelvin mode forced by precession triggers an instability which saturates at intermediate Re and which leads to a turbulent flow at high Reynolds numbers. Particle imagevelocimetrymeasurements in two different sections of the cylinder have revealed the threedimensional structure of this instability. It is composed of two free Kelvin modes whose wavenumbers and frequencies respect the conditions for a triadic resonance with the forced Kelvin mode, as is obtained for the elliptical instability. Moreover, an experimental diagram of stability has been established by varying both the precessing angle and the Reynolds number. It shows a good agreement with a scaling analysis based on a triadic resonance mechanism.

Anomalous bubble propagation in elastic tubes
View Description Hide DescriptionAirway reopening is an important physiological event, as exemplified by the first breath of an infant that inflates highly collapsed airways by driving a finger of air through its fluidfilled lungs. Whereas fundamental models of airway reopening predict the steady propagation of only one type of bubble with a characteristic rounded tip, our experiments reveal a surprising selection of novel bubbles with counterintuitive shapes that reopen strongly collapsed, liquidfilledelastic tubes. Our multiple bubbles are associated with a discontinuous relationship between bubble pressure and speed that sets exciting challenges for modelers.

Aerodynamic drag reduction by heat addition into the shock layer for a large angle blunt cone in hypersonic flow
View Description Hide DescriptionReduction in aerodynamic drag for a large angle blunt cone flying at hypersonic Mach number by heat addition into the shock layer is demonstrated in HST2 hypersonic shock tunnel. The heat addition is achieved by the exothermic reaction of chromium atoms ablated from the stagnation region of the chromiumcoated blunt cone with the atomic oxygen behind the shock wave. The measurements show about 47% reduction in the drag coefficient for a 60° apex angle blunt cone in a Mach 8 flow of specific enthalpy. The reduction in drag is measured using the accelerometer based force balance system and the heat addition into the shock layer is identified by the surface mounted thin film heat flux gauges and the corresponding movement of the shock wave is visualized by schlieren pictures.
 Top

 ARTICLES

 Interfacial Flows

Thermocapillary migration of nondeformable drops
View Description Hide DescriptionIn this paper, we present a numerical study on the thermocapillary migration of drops. The Navier–Stokes equations coupled with the energy conservation equation are solved by the finitedifference fronttracking scheme. The axisymmetric model is adopted in our simulations, and the drops are assumed to be perfectly spherical and nondeformable. The benchmark simulation starts from the classical initial condition with a uniform temperature gradient. The detailed discussions and physical explanations of migration phenomena are presented for the different values of (1) the Marangoni numbers and Reynolds numbers of continuous phases and drops and (2) the ratios of drop densities and specific heats to those of continuous phases. It is found that fairly large Marangoni numbers may lead to fluctuations in drop velocities at the beginning part of simulations. Finally, we also discuss the influence of initial conditions on the thermocapillary migrations.

Weightedresidual integral boundarylayer model for the nonlinear dynamics of thin liquid films falling on an undulating vertical wall
View Description Hide DescriptionA set of firstorder weightedresidual integral boundarylayer equations describing the nonlinear dynamics of a thin liquid film falling on a corrugated periodic vertical wall is derived. The spatiotemporal dynamics of the films is analyzed analytically and numerically in the framework of this set. A steadystate flow is found in the case of an asymptotically small wall corrugation and its stability is investigated. It is found that steady flow regimes arise in the case of a relatively small wall wavelength for the Reynolds number below its critical value corresponding to the flatwall flow and for larger amplitudes of the wall corrugation when the Reynolds number exceeds its critical value. In the case of a larger wall wavelength, the emerging flows are either genuinely nonstationary or time periodic. The temporal period of the timeperiodic flows increases with the amplitude of the wall corrugation and decreases with the Reynolds number. A possibility of the emergence of reverse flows is also discussed.

Splashing on elastic membranes: The importance of earlytime dynamics
View Description Hide DescriptionWe study systematically the effect of substrate compliance on the threshold for splashing of a liquid drop using an elastic membrane under variable tension. We find that the splashing behavior is strongly affected by the tension in the membrane and splashing can be suppressed by reducing this tension. The deflection of the membrane upon dropletimpact is measured using a laser sheet, and the results allow us to estimate the energy absorbed by the film upon dropimpact.Measurements of the velocity and acceleration of the spreading drop after impact indicate that the splashing behavior is set at very early times after, or possibly just before, impact, far before the actual splash occurs. We also provide a model for the tension dependence of the splashing threshold based on the pressure in the drop upon impact that takes into account the interplay between membrane tension and drop parameters.

Hydrodynamic loads during early stage of flat plate impact onto water surface
View Description Hide DescriptionThe hydrodynamic loads during the water entry of a flat plate are investigated. Initially the water is at rest and the plate is floating on the water surface. Then the plate starts suddenly its vertical motion. The analysis is focused on the early stage during which the highest hydrodynamic loads are generated. The liquid is assumed ideal and incompressible; gravity and surface tension effects are not taken into account. The flow generated by the impact is two dimensional and potential. The penetration depth is either a given function of time or calculated by using the equation of the body motion. A theoretical estimate of the loads during the early stage of the water impact is derived with the help of the method of matched asymptotic expansions. The ratio of the plate displacement to the plate halfwidth plays the role of a small parameter. The secondorder uniformly valid solution of the problem is derived. In order to evaluate the hydrodynamic loads, the secondorder pressure distribution is asymptotically integrated along the plate. It is shown that the initial asymptotics of the loads involve a logarithmic term and a negative noninteger power of the nondimensional plate displacement, the latter contribution is related to the inner solution. In addition to the theoretical estimate, a numerical model of the unsteady freesurface flow generated by plate impact is developed. The hydrodynamic loads are numerically evaluated and compared to their asymptotic estimates. A fairly good agreement between the theoretical and numerical predictions of the hydrodynamic loads just after the impact has been found. In the case of constant velocity of the body, it is shown that the relative difference between the theoretical and numerical predictions of the hydrodynamic force is less than 5% when the nondimensional plate displacement is onefifth and rises to 20% when the nondimensional plate displacement is equal to unity. Similar results are found in the free fall case when the comparison is established in terms of hydrodynamic loads. The theoretical and numerical predictions are remarkably close to each other, even for moderate displacements of the plate, if the comparison is established in terms of the entry velocity.

Flowinduced melting of condensed domains within a dispersed Langmuir film
View Description Hide DescriptionDuring phase transition from the liquidexpanded to the liquidcondensed state, a dispersed Langmuir film of pentadecanoic acid is submitted to an annular shear flow of moderate Reynolds number. The mesoscopic morphology of this twophase Langmuir film is investigated based on area fraction distribution of the condensed phase after a permanent regime is established. The distribution demonstrates radially inwards packing along the liquid surface induced by centripetal flow originating from centrifugation of the subphase along the rotating floor. For a growing level of centrifugation, a circular Reynolds ridge arises along the liquid surface. The Langmuir film experiences a strong morphological transition driven by a balance between surface shear and reduced line tension. As a result, a shearinduced melting of the condensed domains generates a new patterning which can be described as a regular and monodispersed matrix of tiny condensed droplets.

Crawling beneath the free surface: Water snail locomotion
View Description Hide DescriptionLand snails move via adhesivelocomotion. Through muscular contraction and expansion of their foot, they transmit waves of shear stress through a thin layer of mucus onto a solid substrate. Since a free surface cannot support shear stress, adhesivelocomotion is not a viable propulsion mechanism for water snails that travel inverted beneath the free surface. Nevertheless, the motion of the freshwater snail, Sorbeoconcha physidae, is reminiscent of that of its terrestrial counterparts, being generated by the undulation of the snail foot that is separated from the free surface by a thin layer of mucus. Here, a lubrication model is used to describe the mucus flow in the limit of smallamplitude interfacial deformations. By assuming the shape of the snail foot to be a traveling sine wave and the mucus to be Newtonian, an evolution equation for the interface shape is obtained and the resulting propulsive force on the snail is calculated. This propulsive force is found to be nonzero for moderate values of the capillary number but vanishes in the limits of high and low capillary number. Physically, this force arises because the snail’s foot deforms the free surface, thereby generating curvature pressures and lubrication flows inside the mucus layer that couple to the topography of the foot.

Asymptotic solution of thermocapillary convection in a thin annular pool of silicon melt
View Description Hide DescriptionThe free surface of the silicon melt in a thin annular pool is subjected to a radial temperature gradient. Since the surface tension depends on the temperature, it will create a thermocapillary force on the free surface and, in turn, yield to thermocapillary convection in the bulk of the liquid by the viscous traction. This paper presents an investigation on the steady twodimensional thermocapillary convection in a differentially heated annular pool of the silicon melt using the asymptotical way. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the pool height to the gap width, goes to zero. The numerical experiments are also carried out to compare to the asymptotic solution of the steady twodimensional thermocapillary convection. The results indicate that the expressions of velocity and temperature fields in the core region from the asymptotic solution are found to be valid in the limit of small aspect ratio.
 Viscous and NonNewtonian Flows

A model of transluminal flow of an antiHIV microbicide vehicle: Combined elastic squeezing and gravitational sliding
View Description Hide DescriptionElastohydrodynamic lubrication over soft substrates is of importance in a number of biomedical problems: From lubrication of the eye surface by the tear film, to lubrication of joints by synovial fluid, to lubrication between the pleural surfaces that protect the lungs and other organs. Such flows are also important for the drug delivery functions of vehicles for antiHIV topical microbicides. These are intended to inhibit transmission into vulnerable mucosa, e.g., in the vagina. First generation prototype microbicides have gel vehicles, which spread after insertion and coat luminal surfaces. Effectiveness derives from potency of the active ingredients and completeness and durability of coating. Delivery vehicle rheology, luminal biomechanicalproperties, and the force due to gravity influence the coating mechanics. We develop a framework for understanding the relative importance of boundary squeezing and body forces on the extent and speed of the coating that results. A single dimensionless number, independent of viscosity, characterizes the relative influences of squeezing and gravitational acceleration on the shape of spreading in the Newtonian case. A second scale, involving viscosity, determines the spreading rate. In the case of a shearthinning fluid, the Carreau number also plays a role. Numerical solutions were developed for a range of the dimensionless parameter and compared well with asymptotic theory in the limited case where such results can be obtained. Results were interpreted with respect to tradeoffs between wall elasticity, longitudinal forces, bolus viscosity, and bolus volume. These provide initial insights of practical value for formulators of gel delivery vehicles for antiHIV microbicidal formulations.
 Particulate, Multiphase, and Granular Flows

Pattern formation in a rotating suspension of nonBrownian buoyant particles
View Description Hide DescriptionThis study examines the concentration and velocitypatterns observed in a horizontal rotating cylinder completely filled with a monodisperse suspension of nonBrownian buoyant particles. The unique patterns or phases are mapped by varying both the rotation rate and the solventviscosity. Individual phases are identified using both frontal ( plane) and axial ( plane) views. Phase boundaries are compared to those obtained recently for suspensions of nonbuoyant particles. Expressing the boundaries in terms of dimensionless parameters unifies the data for several samples at low rotation rates. When centrifugal force dominates, the behavior becomes quite different from previous studies.
 Laminar Flows

Interaction of a skewed Rankine vortex pair
View Description Hide DescriptionAn analytical investigation is carried out to study the kinematics of a fluid particle in an interacting field of a skewed pair of fixed Rankine vortices. A general formulation governing the kinematics of a fluid particle has been presented based on the superposition of the velocity field due to each vortex in the pair. The kinematics of a Lagrangian fluid particle is found to be governed by a nonlinear dynamical system. The fixed or stationary points of the dynamical system have been identified analytically and their existence is confirmed by the nature of particle paths in the neighborhood of fixed points. The nature of the particle path and velocity signal is reported for general as well as special configurations of the vortex pair in the presence and absence of an external uniform flow. As a specific application of the proposed problem, superimposition of the translational velocity on a semiinfinite field of longitudinal vortices generated by vortex generators mounted on fin plates of heat exchangers has also been studied.

Mass flowrate control through time periodic electroosmotic flows in circular microchannels
View Description Hide DescriptionThe present study is directed towards devising a scientific strategy for obtaining controlled timeperiodic mass flowrate characteristics through the employment of pulsating electric fields in circular microchannels by exploiting certain intrinsic characteristics of periodic electroosmosis phenomenon. Within the assumption of thin electrical double layers, the governing equations for potential distribution and fluid flow are derived, corresponding to a steady base state and a timevarying perturbed state, by assuming periodic forms of the imposed electrical fields and the resultant velocity fields. For sinusoidal pulsations of the electric field superimposed over its mean, a signature map depicting the amplitudes of the mass flow rate and the electrical field as well as their phase differences is obtained from the theoretical analysis as a function of a nondimensional frequency parameter for different ratios of the characteristic electric double layer thickness relative to the microchannel radius. Distinctive characteristics in the signature profiles are obtained for lower and higher frequencies, primarily attributed to the finite time scale for momentum propagation away from the walls. The signature characteristics, obtained from the solution of the prescribed sinusoidal electric field, are subsequently used to solve the “inverse” problem, where the mass flow rate is prescribed in the form of sinusoidal pulsations and the desired electric fields that would produce the required mass flowrate variations are obtained. The analysis is subsequently extended for controlled triangular and trapezoidal pulsations in the mass flow rate and the required electric fields are successfully obtained. It is observed that the higher the double layer thickness is in comparison to the channel radius, the more prominent is the deviation of the shape of the required electric field pulsation from the desired transience in the mass flowrate characteristics. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.
 Instability and Transition

Thermomagnetic convection in a vertical layer of ferromagnetic fluid
View Description Hide DescriptionLinear stability of convectionflow of ferromagneticfluid between two vertical differentially heated plates placed in a uniform external magnetic field perpendicular to the plates is studied. Complete stability diagrams for two and threedimensional disturbances are presented. It is shown that two distinct mechanisms, thermogravitational and magnetic, are responsible for the appearance of three instability modes. The physical nature of all three modes is investigated in detail and the most prominent features are identified to provide guidance for future experimental investigation. Depending on the governing parameters, the instability patterns are shown to consist of vertical stationary magnetoconvection rolls and/or vertically or obliquely counterpropagating thermogravitational or thermomagnetic waves.

Energyenstrophy stability of plane Kolmogorov flow with drag
View Description Hide DescriptionWe develop a nonlinear stability method, the energyenstrophy method, that is specialized to twodimensional hydrodynamics and basic state flows consisting of a single Helmholtz eigenmode. The method is applied to a plane flow driven by a sinusoidal body force and retarded by drag with damping time scale . The standard energy method [H. Fukuta and Y. Murakami, J. Phys. Soc. Jpn.64, 3725 (1995)] shows that the laminar solution is monotonically and globally stable in a certain portion of the parameter space. The method proves nonlinear stability in a larger portion of the parameter space than does the energy method. Moreover, by penalizing high wavenumbers, the method identifies a most strongly amplifying disturbance that is more physically realistic than that delivered by the energy method. Linear instability calculations are used to determine the region of the parameter space where the flow is unstable to infinitesimal perturbations. There is only a small gap between the linearly unstable region and the nonlinearly stable region, and full numerical solutions show only small transient amplification in that gap.

Linear and nonlinear stability analyses of thermal convection for OldroydB fluids in porous media heated from below
View Description Hide DescriptionBased on a modified Darcy–Brinkman–Oldroyd model, linear and nonlinear thermal stability analyses of a horizontal layer of an OldroydB fluid in a porous medium heated from below were performed. By using the linear stability theory, the critical Rayleigh number, wave number, and frequency for stationary and oscillatory convections were determined. The effects of the viscoelastic parameters and the porous parameter on the critical Rayleigh number for oscillatory convection were analyzed. Based on the results of the linear stability analysis, a nonlinear stability analysis was also conducted. It is shown that the onset of stationary convection has the form of a supercritical and stable bifurcation independent of the viscoelastic parameters. However, the onset of oscillatory convection has the forms of supercritical or subcritical bifurcations. The nature of the oscillatory mode depends strongly on the viscoelastic parameters. The variation of the Nusselt number with respect to the Rayleigh number is derived for stationary and oscillatory convection modes. Although the critical Rayleigh number for stationary convection is independent of the viscoelastic parameters, the Nusselt number depends on the viscoelastic parameters of the fluids, which is different from that for the modified Darcy–Oldroyd model.

Spatial linear stability of a hypersonic shear layer with nonequilibrium thermochemistry
View Description Hide DescriptionWe examine the spatial linear stability of a shear layer in a hypervelocity flow where high temperature effects such as chemical dissociation and vibrational excitation are present. A shock triple point is used to generate a free shear layer in a model problem which also occurs in several aerodynamic applications such as shockboundary layer interaction. Calculations were performed using a stateresolved, threedimensional forced harmonic oscillator thermochemicalmodel. An extension of an existing molecularmolecular energy transfer rate model to higher collisional energies is presented and verified. Nonequilibrium model results are compared with calculations assuming equilibrium and frozen flows over a range of (frozen) convective Mach numbers from 0.341 to 1.707. A substantial difference in two and threedimensional perturbation growth rates is observed among the three models.Thermochemical nonequilibrium has a destabilizing effect on shearlayer perturbations for all convective Mach numbers considered. The analysis considers the evolution of the molecular vibrational quantum distribution during the instability growth by examining the perturbation eigenfunctions. Oxygen and nitrogen preserve a Boltzmann distribution of vibrational energy, while nitric oxide shows a significant deviation from equilibrium. The difference between translational and vibrational temperature eigenfunctions increases with the convective Mach number.Dissociation and vibration transfer effects on the perturbation evolution remain closely correlated at all convective Mach numbers.

Modal versus energy stability analysis of kinematic dynamos in cylindrical configurations
View Description Hide DescriptionThe kinematic dynamo problem is solved in a cylindrical geometry using Galerkin expansions of the magnetic field components. The difference with the modal Galerkin analysis [L. Marié et al., Phys. Fluids18, 017102 (2006)] concerns the weighting functions which here belong to the same set as the trial functions. The new procedure allows to determine the magnetic Reynolds number for energy growth. Lower bounds on the value of are derived for magnetic modes of azimuthal wavenumber . Using a variational principle, more accurate values of are obtained in the case of helical flows. It is found that the threshold value for the axisymmetric magnetic mode is slightly higher than its value for the antisymmetric mode . Although excluded by Cowling’s theorem the mode exhibits transient energy growth and could play a role in the nonlinear equilibration of cylindrical dynamos.
 Turbulent Flows

Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900
View Description Hide DescriptionThis work contributes to the study of flow over a circular cylinder at Reynolds number. Although this classical flow is widely documented in the literature, especially for this precise Reynolds number that leads to a subcritical flow regime, there is no consensus about the turbulence statistics immediately just behind the obstacle. Here, the flow is investigated both numerically with large eddy simulation and experimentally with hotwire anemometry and particle image velocimetry. The numerical simulation is performed using highorder schemes and a specific immersed boundary method. The present study focuses on turbulence statistics and power spectra in the near wake up to ten diameters. Statistical estimation is shown to need large integration times increasing the computational cost and leading to an uncertainty of about 10% for most flow characteristics considered in this study. The present numerical and experimental results are found to be in good agreement with previous large eddy simulation data. Contrary to this, the present results show differences compared to the experimental data found in the literature, the differences being larger than the estimated uncertainty range. Therefore, previous numericalexperimental controversy for this flow seems to be reduced with the data presented in this article.