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Aug 2008

Volume 20, Issue 8, Articles (08xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 20, 086604 (2008); http://dx.doi.org/10.1063/1.2968451 (9 pages)

Y. D. Afanasyev, P. B. Rhines, and E. G. Lindahl
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Instability of a fluid inside a precessing cylinder

Romain Lagrange, Christophe Eloy, François Nadal, and Patrice Meunier

Phys. Fluids 20, 081701 (2008); http://dx.doi.org/10.1063/1.2963969 (4 pages) | Cited 9 times

Online Publication Date: 12 August 2008

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In 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 image velocimetry measurements in two different sections of the cylinder have revealed the three-dimensional 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.
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47.20.Hw Morphological instability; phase changes
47.27.Cn Transition to turbulence
47.15.Fe Stability of laminar flows
47.80.Cb Velocity measurements
47.32.Ef Rotating and swirling flows

Anomalous bubble propagation in elastic tubes

Alexandra Heap and Anne Juel

Phys. Fluids 20, 081702 (2008); http://dx.doi.org/10.1063/1.2963495 (4 pages) | Cited 4 times

Online Publication Date: 13 August 2008

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Airway 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 fluid-filled 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, liquid-filled elastic tubes. Our multiple bubbles are associated with a discontinuous relationship between bubble pressure and speed that sets exciting challenges for modelers.
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87.19.Wx Pneumodyamics, respiration
47.63.Ec Pulmonary fluid mechanics

Aerodynamic drag reduction by heat addition into the shock layer for a large angle blunt cone in hypersonic flow

Vinayak Kulkarni, G. M. Hegde, G. Jagadeesh, E. Arunan, and K. P. J. Reddy

Phys. Fluids 20, 081703 (2008); http://dx.doi.org/10.1063/1.2944982 (4 pages) | Cited 4 times

Online Publication Date: 27 August 2008

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Reduction 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 chromium coated 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 3.4 MJ/kg 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.
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47.40.Ki Supersonic and hypersonic flows
47.40.Nm Shock wave interactions and shock effects
47.70.Fw Chemically reactive flows
82.60.Cx Enthalpies of combustion, reaction, and formation
47.80.Jk Flow visualization and imaging
47.27.te Turbulent convective heat transfer
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back to top Interfacial Flows

Thermocapillary migration of nondeformable drops

Z. Yin, P. Gao, W. Hu, and L. Chang

Phys. Fluids 20, 082101 (2008); http://dx.doi.org/10.1063/1.2965549 (20 pages) | Cited 10 times

Online Publication Date: 7 August 2008

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In 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 finite-difference front-tracking 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.
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47.55.dm Thermocapillary effects
47.10.ad Navier-Stokes equations
47.11.Bc Finite difference methods
47.55.pf Marangoni convection
68.03.Cd Surface tension and related phenomena
65.20.-w Thermal properties of liquids

Weighted-residual integral boundary-layer model for the nonlinear dynamics of thin liquid films falling on an undulating vertical wall

Alexander Oron and Christian Heining

Phys. Fluids 20, 082102 (2008); http://dx.doi.org/10.1063/1.2969410 (16 pages) | Cited 14 times

Online Publication Date: 12 August 2008

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A set of first-order weighted-residual integral boundary-layer 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 steady-state 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 flat-wall 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 time-periodic 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.
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47.20.-k Flow instabilities
68.15.+e Liquid thin films

Splashing on elastic membranes: The importance of early-time dynamics

Rachel E. Pepper, Laurent Courbin, and Howard A. Stone

Phys. Fluids 20, 082103 (2008); http://dx.doi.org/10.1063/1.2969755 (8 pages) | Cited 17 times

Online Publication Date: 18 August 2008

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We 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 droplet impact is measured using a laser sheet, and the results allow us to estimate the energy absorbed by the film upon drop impact. 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.
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47.55.D- Drops and bubbles

Hydrodynamic loads during early stage of flat plate impact onto water surface

Alessandro Iafrati and Alexander A. Korobkin

Phys. Fluids 20, 082104 (2008); http://dx.doi.org/10.1063/1.2970776 (13 pages) | Cited 8 times

Online Publication Date: 20 August 2008

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The 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 half-width plays the role of a small parameter. The second-order uniformly valid solution of the problem is derived. In order to evaluate the hydrodynamic loads, the second-order 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 free-surface 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 one-fifth 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.
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47.55.N- Interfacial flows
47.55.db Drop and bubble formation
47.20.-k Flow instabilities
47.11.Hj Boundary element methods

Flow-induced melting of condensed domains within a dispersed Langmuir film

Laurent Davoust, Yu-Lin Huang, and Shuo-Hung Chang

Phys. Fluids 20, 082105 (2008); http://dx.doi.org/10.1063/1.2974831 (8 pages) | Cited 1 time

Online Publication Date: 25 August 2008

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During phase transition from the liquid-expanded to the liquid-condensed state, a dispersed Langmuir film of pentadecanoic acid is submitted to an annular shear flow of moderate Reynolds number (Re = 10–100). The mesoscopic morphology of this two-phase 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 shear-induced melting of the condensed domains generates a new patterning which can be described as a regular and monodispersed matrix of tiny condensed droplets.
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47.15.K- Inviscid laminar flows
47.15.St Free shear layers
47.57.eb Diffusion and aggregation
47.32.Ef Rotating and swirling flows
64.70.K- Solid-solid transitions

Crawling beneath the free surface: Water snail locomotion

Sungyon Lee, John W. M. Bush, A. E. Hosoi, and Eric Lauga

Phys. Fluids 20, 082106 (2008); http://dx.doi.org/10.1063/1.2960720 (10 pages) | Cited 6 times

Online Publication Date: 26 August 2008

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Land snails move via adhesive locomotion. 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, adhesive locomotion 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 small-amplitude 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.
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47.63.M- Biopropulsion in water and air
47.55.nb Capillary and thermocapillary flows
46.55.+d Tribology and mechanical contacts
68.08.-p Liquid-solid interfaces
68.15.+e Liquid thin films

Asymptotic solution of thermocapillary convection in a thin annular pool of silicon melt

You-Rong Li, Xin-Xing Zhao, Shuang-Ying Wu, and Lan Peng

Phys. Fluids 20, 082107 (2008); http://dx.doi.org/10.1063/1.2975172 (9 pages) | Cited 4 times

Online Publication Date: 27 August 2008

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The 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 two-dimensional 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 two-dimensional 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.
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47.55.P- Buoyancy-driven flows; convection
68.03.Cd Surface tension and related phenomena
66.20.Ej Studies of viscosity and rheological properties of specific liquids
back to top Viscous and Non-Newtonian Flows

A model of transluminal flow of an anti-HIV microbicide vehicle: Combined elastic squeezing and gravitational sliding

Andrew J. Szeri, Su Chan Park, Stéphane Verguet, Aaron Weiss, and David F. Katz

Phys. Fluids 20, 083101 (2008); http://dx.doi.org/10.1063/1.2973188 (10 pages) | Cited 10 times

Online Publication Date: 21 August 2008

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Elastohydrodynamic 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 anti-HIV 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 biomechanical properties, 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 shear-thinning 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 trade-offs between wall elasticity, longitudinal forces, bolus viscosity, and bolus volume. These provide initial insights of practical value for formulators of gel delivery vehicles for anti-HIV microbicidal formulations.
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83.80.Kn Physical gels and microgels
68.08.Bc Wetting
47.57.Qk Rheological aspects
87.85.gf Fluid mechanics and rheology
87.85.J- Biomaterials
back to top Particulate, Multiphase, and Granular Flows

Pattern formation in a rotating suspension of non-Brownian buoyant particles

Makrand G. Kalyankar, W. R. Matson, Penger Tong, and Bruce J. Ackerson

Phys. Fluids 20, 083301 (2008); http://dx.doi.org/10.1063/1.2970156 (10 pages)

Online Publication Date: 19 August 2008

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This study examines the concentration and velocity patterns observed in a horizontal rotating cylinder completely filled with a monodisperse suspension of non-Brownian buoyant particles. The unique patterns or phases are mapped by varying both the rotation rate and the solvent viscosity. Individual phases are identified using both frontal (θ-z plane) and axial (r-θ 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.
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47.57.E- Suspensions
47.32.Ef Rotating and swirling flows
back to top Laminar Flows

Interaction of a skewed Rankine vortex pair

S. Jayavel, Pratish P. Patil, and Shaligram Tiwari

Phys. Fluids 20, 083601 (2008); http://dx.doi.org/10.1063/1.2969115 (9 pages)

Online Publication Date: 13 August 2008

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An 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 semi-infinite field of longitudinal vortices generated by vortex generators mounted on fin plates of heat exchangers has also been studied.
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47.32.-y Vortex dynamics; rotating fluids
05.45.-a Nonlinear dynamics and chaos

Mass flow-rate control through time periodic electro-osmotic flows in circular microchannels

Suman Chakraborty and Subhashis Ray

Phys. Fluids 20, 083602 (2008); http://dx.doi.org/10.1063/1.2949306 (11 pages) | Cited 8 times

Online Publication Date: 14 August 2008

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The present study is directed towards devising a scientific strategy for obtaining controlled time-periodic mass flow-rate characteristics through the employment of pulsating electric fields in circular microchannels by exploiting certain intrinsic characteristics of periodic electro-osmosis 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 time-varying 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 flow-rate 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 flow-rate characteristics. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.
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47.85.L- Flow control
47.60.Dx Flows in ducts and channels
back to top Instability and Transition

Thermomagnetic convection in a vertical layer of ferromagnetic fluid

Sergey A. Suslov

Phys. Fluids 20, 084101 (2008); http://dx.doi.org/10.1063/1.2952596 (18 pages) | Cited 1 time

Online Publication Date: 5 August 2008

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Linear stability of convection flow of ferromagnetic fluid 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 three-dimensional 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.
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47.65.Cb Magnetic fluids and ferrofluids
47.55.pb Thermal convection
44.25.+f Natural convection
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)

Energy-enstrophy stability of β-plane Kolmogorov flow with drag

Yue-Kin Tsang and William R. Young

Phys. Fluids 20, 084102 (2008); http://dx.doi.org/10.1063/1.2958321 (10 pages) | Cited 3 times

Online Publication Date: 11 August 2008

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We develop a nonlinear stability method, the energy-enstrophy (EZ) method, that is specialized to two-dimensional hydrodynamics and basic state flows consisting of a single Helmholtz eigenmode. The method is applied to a β-plane flow driven by a sinusoidal body force and retarded by drag with damping time scale μ−1. 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 (μ,β)-parameter space. The EZ method proves nonlinear stability in a larger portion of the (μ,β)-parameter space than does the energy method. Moreover, by penalizing high wavenumbers, the EZ 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 (μ,β)-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.
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47.15.Fe Stability of laminar flows
47.20.-k Flow instabilities

Linear and nonlinear stability analyses of thermal convection for Oldroyd-B fluids in porous media heated from below

Zhiyong Zhang, Ceji Fu, and Wenchang Tan

Phys. Fluids 20, 084103 (2008); http://dx.doi.org/10.1063/1.2972154 (12 pages) | Cited 9 times

Online Publication Date: 20 August 2008

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Based on a modified Darcy–Brinkman–Oldroyd model, linear and nonlinear thermal stability analyses of a horizontal layer of an Oldroyd-B 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.
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47.55.P- Buoyancy-driven flows; convection
47.56.+r Flows through porous media
47.50.-d Non-Newtonian fluid flows
47.20.-k Flow instabilities

Spatial linear stability of a hypersonic shear layer with nonequilibrium thermochemistry

L. Massa and J. M. Austin

Phys. Fluids 20, 084104 (2008); http://dx.doi.org/10.1063/1.2972937 (19 pages) | Cited 4 times

Online Publication Date: 22 August 2008

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We 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 shock-boundary layer interaction. Calculations were performed using a state-resolved, three-dimensional forced harmonic oscillator thermochemical model. An extension of an existing molecular-molecular 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 three-dimensional perturbation growth rates is observed among the three models. Thermochemical nonequilibrium has a destabilizing effect on shear-layer 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.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.40.Ki Supersonic and hypersonic flows
47.40.Nm Shock wave interactions and shock effects
47.70.Fw Chemically reactive flows
47.55.pb Thermal convection
82.40.Fp Shock wave initiated reactions, high-pressure chemistry

Modal versus energy stability analysis of kinematic dynamos in cylindrical configurations

C. Normand

Phys. Fluids 20, 084105 (2008); http://dx.doi.org/10.1063/1.2972889 (11 pages) | Cited 1 time

Online Publication Date: 25 August 2008

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The 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. Fluids 18, 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 RmE for energy growth. Lower bounds on the value of RmE are derived for magnetic modes of azimuthal wavenumber m. Using a variational principle, more accurate values of RmE are obtained in the case of helical flows. It is found that the threshold value for the axisymmetric magnetic mode m = 0 is slightly higher than its value for the antisymmetric mode m = 1. Although excluded by Cowling’s theorem the mode m = 0 exhibits transient energy growth and could play a role in the nonlinear equilibration of cylindrical dynamos.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.20.-k Flow instabilities
47.11.Fg Finite element methods
02.30.Xx Calculus of variations
back to top Turbulent Flows

Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900

Philippe Parnaudeau, Johan Carlier, Dominique Heitz, and Eric Lamballais

Phys. Fluids 20, 085101 (2008); http://dx.doi.org/10.1063/1.2957018 (14 pages) | Cited 20 times

Online Publication Date: 1 August 2008

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This work contributes to the study of flow over a circular cylinder at Reynolds number Re = 3900. 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 hot-wire anemometry and particle image velocimetry. The numerical simulation is performed using high-order 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 numerical-experimental controversy for this flow seems to be reduced with the data presented in this article.
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47.27.Cn Transition to turbulence
47.27.ep Large-eddy simulations
47.80.Cb Velocity measurements
47.80.Jk Flow visualization and imaging

The vortex merger rate in freely decaying, two-dimensional turbulence

J. H. LaCasce

Phys. Fluids 20, 085102 (2008); http://dx.doi.org/10.1063/1.2957020 (14 pages)

Online Publication Date: 8 August 2008

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New numerical simulations of decaying two-dimensional turbulence are examined, with a focus on the statistics of the coherent vortices. The number of vortices decays as a power law, as in previous studies, but the rate varies between experiments. While the rate is not significantly affected by changes in the initial conditions, it does depend on the choice of small scale dissipation. In contrast, the vortex dispersion rate is approximately the same in all the experiments. Assuming energy conservation, the decay rate can be determined from the dispersion rate. The prediction agrees well with the rate observed in the least dissipative experiments. In the more dissipative experiments, the decay rate is greater because the dissipation increases lateral extent of the vortices and hence their collision cross section. In such cases, the density decay rate can be predicted from a scaling relation involving the collision time, given the observed growth rate of the mean vortex area.
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47.32.cd Vortex stability and breakdown
47.32.C- Vortex dynamics
47.27.E- Turbulence simulation and modeling
47.11.-j Computational methods in fluid dynamics

Near-dissipation range in nonlocal turbulence

A. Bershadskii

Phys. Fluids 20, 085103 (2008); http://dx.doi.org/10.1063/1.2969473 (8 pages) | Cited 1 time

Online Publication Date: 12 August 2008

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Viscous perturbations to scaling are studied in the near-dissipation range of isotropic turbulence. A quantitative relationship between effective strain of the nonlocal interactions and viscosity has been found. It is shown that nonlocal interactions determine the energy spectrum in isotropic turbulence at small Reynolds numbers. It is also shown that for moderate Reynolds numbers the bottleneck effect is determined by the same nonlocal interactions. The role of the large- and small-scale covariances at the nonlocal interactions and in energy balance has been investigated. A possible hydrodynamic mechanism of the nonlocal solution instability at large scales has been briefly discussed. Analogous approach has also been developed for passive scalar and for the energy dissipation rate spectrum. All results are supported by a comparison with the data of the laboratory experiments and numerical simulations.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.20.Gv Viscous and viscoelastic instabilities
47.11.Kb Spectral methods
02.60.Cb Numerical simulation; solution of equations

On the formation of cyclones and anticyclones in a rotating fluid

Binod Sreenivasan and P. A. Davidson

Phys. Fluids 20, 085104 (2008); http://dx.doi.org/10.1063/1.2966400 (11 pages) | Cited 6 times

Online Publication Date: 15 August 2008

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It is commonly observed that the columnar vortices that dominate the large scales in homogeneous, rapidly rotating turbulence are predominantly cyclonic. This has prompted us to ask how this asymmetry arises. To provide a partial answer to this we look at the process of columnar vortex formation in a rotating fluid and, in particular, we examine how a localized region of swirl (an eddy) can convert itself into a columnar structure by inertial wave propagation. We show that, when the Rossby number (Ro) is small, the vortices evolve into columnar eddies through the radiation of linear inertial waves. When the Rossby number is large, on the other hand, no such column is formed. Rather, the eddy bursts radially outward under the action of the centrifugal force. There is no asymmetry between cyclonic and anticyclonic eddies for these two regimes. However, cyclones and anticyclones behave differently in the intermediate regime of Ro ∼ 1. Here we find that the transition from columnar vortex formation to radial bursting occurs at lower values of Ro for anticyclones, with the transition for anticyclones occurring at Ro ∼ 0.5, and that for cyclones at Ro ∼ 2. Thus, in a homogeneous turbulence experiment conducted at, say, Ro = 1, we would expect to see more cyclones than anticyclones. The reason for this asymmetry at Ro ∼ 1 is explained.
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47.32.Ef Rotating and swirling flows

Numerical assessment of local forcing on the heat transfer in a turbulent channel flow

Guillermo Araya, Stefano Leonardi, and Luciano Castillo

Phys. Fluids 20, 085105 (2008); http://dx.doi.org/10.1063/1.2963140 (22 pages) | Cited 2 times

Online Publication Date: 18 August 2008

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The influence of local forcing on an incompressible turbulent channel flow is numerically investigated. The extensive information provided by the direct numerical simulations enables us to have a better understanding of the physical mechanism responsible for local heat transfer enhancement. Time-periodic blowing/suction is applied by means of thin spanwise slots located at the lower and upper walls. The molecular Prandtl number is 0.71 and the Reynolds number based on the wall friction velocity and the channel half-height, Reτ, is 394 for the unforced case. The normal perturbing velocity is varied sinusoidally in time at several perturbing frequencies between 0.16<math<1.6 or 0.011<f+<0.11 and at a fixed amplitude of Ao = 0.2. A phase-averaging procedure is employed to discriminate between the coherent and incoherent fluctuating components. It is shown that coherent thermal fluctuations reach peak values near the forcing slot, then sharply decay and almost disappear in a short distance downstream. The incoherent thermal fluctuations also show peak values next the source; however, they decay downstream to resemble the incoherent fluctuations of the unperturbed channel. It was concluded that the forcing frequency of math = 0.64 or f+ = 0.044 produced the largest local increase in the skin friction in the region 0.1<x/Lx<0.3 (where Lx is the channel length), followed by the highest augmentation of the Stanton number. It is found that augmentation of the wall shear stress fluctuations is the major cause of skin friction, wall heat flux, and Stanton number enhancement downstream from the local forcing source. On the other hand, local maxima of Reynolds shear stresses, wall-normal turbulent heat fluxes, and the incoherent component of streamwise vorticity fluctuations exhibited analogous behavior along the streamwise direction.
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47.27.te Turbulent convective heat transfer
47.27.nd Channel flow
47.27.nb Boundary layer turbulence
47.27.ek Direct numerical simulations
47.32.Ef Rotating and swirling flows

Modeling of compressible magnetohydrodynamic turbulence in electrically and heat conducting fluid using large eddy simulation

A. A. Chernyshov, K. V. Karelsky, and A. S. Petrosyan

Phys. Fluids 20, 085106 (2008); http://dx.doi.org/10.1063/1.2969472 (13 pages) | Cited 7 times

Online Publication Date: 19 August 2008

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Many electrically and heat conducting fluid flows cannot be described within the framework of incompressible medium or by compressible magnetohydrodynamic equations on the assumption of polytropic (or adiabatic) process. Therefore, we consider a heat conducting compressible fluid with the use of an energy equation. Application of large eddy simulation approach to heat conducting compressible magnetohydrodynamics is considered. The system of the filtered magnetohydrodynamic equations with the total energy equation using the mass-weighted filtering procedure has been obtained. It is shown that novel subgrid-scale terms arise in the Favre-filtered equations due to the presence of a magnetic field in the total energy equation. Parametrizations of these extra terms are developed. In order to derive these subgrid-scale terms, we use an approach based on generalized central moments. Computations at various Mach numbers are made for decaying compressible magnetohydrodynamic turbulence. The obtained numerical large eddy simulation results are analyzed on the basis of comparison with results of numerical experiments performed by direct numerical simulation. Validity of large eddy simulation method is thus demonstrated. It is shown that consideration of the subgrid-scale terms in the total energy equation scarcely affects the kinetic and the magnetic energy for low and even high Mach number, while for the temperature the presence of subgrid-scale models in the energy equation is an important condition for improvement in calculation accuracy of thermodynamic quantities. The technique with the mass-weighted filtering and with the use of various types of subgrid-scale models provides good calculation accuracy for different problems for compressible fluid in the absence of discontinuities, associated with the appearance of shocks, in other words, when the value of the Mach number is low or moderate (that is, the flow is subsonic). For supersonic magnetohydrodynamic flows, it is necessary to use special numerical methods.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.27.ep Large-eddy simulations
47.40.Nm Shock wave interactions and shock effects
47.40.Dc General subsonic flows
47.40.Ki Supersonic and hypersonic flows
02.60.Cb Numerical simulation; solution of equations
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