Phys. Fluids (1994-Present) - Physics of Fluids

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T. P. Schulze

Phys. Fluids 11, 3573 (1999); http://dx.doi.org/10.1063/1.870223 (4 pages) | Cited 5 times

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When a fluid system is subject to time-periodic forcing, it is well known that it may exhibit both harmonic and subharmonic instabilities, the classic example being Faraday oscillations. When the forcing is confined to a periodic shearing motion, however, it has been observed that the subharmonic response is absent. The underlying mathematical feature that unifies these systems is a conjugate-translation symmetry [A. C. Or, J. Fluid Mech. 335, 213 (1997)]. We show that any subharmonic solutions of periodically driven systems with conjugate-translation symmetry must have Floquet multipliers with multiplicity greater than one. The effect of this constraint is that subharmonic solutions are very difficult to locate within the system’s parameter space and, more importantly, that phase locking cannot occur for such systems. © 1999 American Institute of Physics.

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47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.35.-i	Hydrodynamic waves

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Computational and experimental analysis of dynamics of drop formation

Edward D. Wilkes, Scott D. Phillips, and Osman A. Basaran

Phys. Fluids 11, 3577 (1999); http://dx.doi.org/10.1063/1.870224 (22 pages) | Cited 90 times

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Dynamics of formation of a drop of a Newtonian liquid from a capillary tube into an ambient gas phase is studied computationally and experimentally. While this problem has previously been studied computationally either (a) using a set of one-dimensional equations or (b) treating the dynamics as that of irrotational flow of an inviscid fluid or creeping flow, here the full nonlinear, transient Navier–Stokes system subject to appropriate initial and boundary conditions is solved in two dimensions to analyze the dynamics at finite Reynolds numbers. The success of the computations rests on a finite element algorithm incorporating a multiregion mesh which conforms to and evolves with the changing shape of the drop. The new algorithm is able to capture both the gross features of the phenomenon, such as the limiting length of a drop at breakup and the volume of the primary drop, and its fine features, such as a microthread that develops from a main thread or a neck in a viscous drop approaching breakup. The accuracy of the new calculations is verified by comparison of computed predictions to old and new experiments. With the new algorithm, it is shown for the first time that the interface of a viscous drop can overturn before the drop breaks. Calculations have also been carried out to determine the range of parameters over which algorithms that treat the drop liquid as inviscid and the flow inside it as irrotational can accurately predict the dynamics of formation of drops of low viscosity liquids. Limiting lengths of drops and primary drop volumes are computed over a wide range of the parameter space spanned by the relevant dimensionless groups. © 1999 American Institute of Physics.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.55.D-	Drops and bubbles
47.10.-g	General theory in fluid dynamics
47.50.-d	Non-Newtonian fluid flows
47.15.-x	Laminar flows

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Wake measurements for flow around a sphere in a viscoelastic fluid

Drazen Fabris, Susan J. Muller, and Dorian Liepmann

Phys. Fluids 11, 3599 (1999); http://dx.doi.org/10.1063/1.870225 (14 pages) | Cited 6 times

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The flow field around a sphere falling at its terminal velocity in a column of viscoelastic non-shear-thinning fluid is experimentally measured with digital particle image velocimetry. The working fluid is an extensively characterized, monodisperse, polystyrene based Boger fluid. The sphere radius relative to the radius of the column of fluid is small (a/r_c = 0.083). The Weissenberg number (λU_t/a) ranges from 0.5 to 14 over which the sphere experiences a drag increase up to 8 times that of the Newtonian flow. The flow field is investigated in detail for We 0.5 to 2.5. A length and width scale is defined for the wake. Over this range of We the wake is found to grow linearly with We and become self-similar in a transverse cross-section of the axial component of the velocity. Streamlines along with extension and rotation rates along those streamlines are also determined. © 1999 American Institute of Physics.

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47.55.Kf	Particle-laden flows
47.27.wb	Turbulent wakes
47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.50.-d	Non-Newtonian fluid flows

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Electrically driven convection in a thin annular film undergoing circular Couette flow

Zahir A. Daya, V. B. Deyirmenjian, and Stephen W. Morris

Phys. Fluids 11, 3613 (1999); http://dx.doi.org/10.1063/1.870226 (16 pages) | Cited 9 times

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We investigate the linear stability of a thin, suspended, annular film of conducting fluid with a voltage difference applied between its inner and outer edges. For a sufficiently large voltage, such a film is unstable to radially driven electroconvection due to charges which develop on its free surfaces. The film can also be subjected to a Couette shear by rotating its inner edge. This combination is experimentally realized using films of smectic A liquid crystals. In the absence of shear, the convective flow consists of a stationary, azimuthally one-dimensional (1D) pattern of symmetric, counter-rotating vortex pairs. When Couette flow is applied, an azimuthally traveling pattern results. When viewed in a co-rotating frame, the traveling pattern consists of pairs of asymmetric vortices. We calculate the neutral stability boundary for arbitrary radius ratio α and Reynolds number Re of the shear flow, and obtain the critical control parameter R_c(α,Re) and the critical azimuthal mode number m_c(α,Re). The Couette flow suppresses the onset of electroconvection, so that R_c(α,Re)>R_c(α,0). The calculated suppression is compared with experiments performed at α=0.56 and 0⩽Re⩽0.22. © 1999 American Institute of Physics.

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47.27.T-	Turbulent transport processes
47.65.-d	Magnetohydrodynamics and electrohydrodynamics
47.32.C-	Vortex dynamics
47.20.-k	Flow instabilities

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A weakly nonlinear analysis of the dynamics of a viscous flow in a symmetric channel with a sudden expansion

Zvi Rusak and Takumi Hawa

Phys. Fluids 11, 3629 (1999); http://dx.doi.org/10.1063/1.870227 (8 pages) | Cited 6 times

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A weakly nonlinear analysis of the dynamics of a two-dimensional, laminar flow in a long channel with a sudden expansion and the transition from symmetric to asymmetric states is presented. The asymptotic analysis is based on a study of the unsteady Navier–Stokes equations around the critical Reynolds number, Re_c, where a bifurcation occurs. It explores the special nonlinear interactions between the unsteady, convective, and viscous effects. The analysis results in an ordinary, nonlinear, first-order differential equation (similar to the Landau equation) which describes the evolution of the perturbation’s amplitude as function of Re near Re_c. The analytical solution shows that when Re<Re_c the symmetric state is stable. However, when Re ≥ Re_c the symmetric state in the channel loses its stability and evolves into an asymmetric state. The flow evolution, as described by the nonlinear model, shows agreement with time history plots from simulations using the unsteady Navier–Stokes equations. The linear stability characteristics of both the symmetric and asymmetric states are also found from the nonlinear approach and match with the previous results. The analysis provides new insight into the previous experimental and numerical results and sheds light on the nonlinear transition of a viscous flow in an expanding channel. © 1999 American Institute of Physics.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.15.-x	Laminar flows
47.15.Fe	Stability of laminar flows
47.11.-j	Computational methods in fluid dynamics

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Velocity field for Taylor–Couette flow with an axial flow

Steven T. Wereley and Richard M. Lueptow

Phys. Fluids 11, 3637 (1999); http://dx.doi.org/10.1063/1.870228 (13 pages) | Cited 32 times

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The flow in the gap between an inner rotating cylinder concentric with an outer stationary cylinder with an imposed pressure-driven axial flow was studied experimentally using particle image velocimetry (PIV) in a meridional plane of the annulus. The radius ratio was η = 0.83 and the aspect ratio was Γ = 47. Velocity vector fields for nonwavy toroidal and helical vortices show the axial flow winding around vortices. When the axially averaged axial velocity profile is removed from the velocity field in a meridional plane, the velocity field looks much like it would with no imposed axial flow except that the vortices translate axially and the distortion of the azimuthal velocity contours in meridional plane related to the vortices is shifted axially by the axial flow. The velocity vector fields for wavy vortices also show axial flow winding around the vortices. Again, removing the axial velocity profile results in a flow that appears similar to that with no axial flow. The path of the vortices is generally axial, but the vortices periodically move retrograde to the imposed axial flow due to the waviness of the vortices. The axial velocity of helical vortices, both nonwavy and wavy, is twice the rotational frequency of the inner cylinder indicating a coupling between the axial translation of the vortices and the cylinder rotation. Little fluid transport between vortices occurs for nonwavy vortices, but there is substantial transport between vortices for wavy vortex flow, much like supercritical cylindrical Couette flow with no axial flow. © 1999 American Institute of Physics.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.32.-y	Vortex dynamics; rotating fluids
47.15.-x	Laminar flows

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Secondary breakup of axisymmetric liquid drops. I. Acceleration by a constant body force

Jaehoon Han and Grétar Tryggvason

Phys. Fluids 11, 3650 (1999); http://dx.doi.org/10.1063/1.870229 (18 pages) | Cited 19 times

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The secondary breakup of liquid drops, accelerated by a constant body force, is examined for small density differences between the drops and the surrounding fluid. Two cases are examined in detail: a density ratio close to unity (ρ_d/ρ_o = 1.15, where the Boussinesq approximation is valid) and a density ratio of ten. A finite difference/front tracking numerical technique is used to solve the unsteady Navier–Stokes equations for both the drops and the surrounding fluid. The breakup is controlled by the Eötvös number (Eo), the Ohnesorge number (Oh), and the viscosity and density ratios. If viscous effects are small (small Oh), the Eötvös number is the main controlling parameter. In the Boussinesq limit, as Eo increases the drops break up in a backward facing bag, transient breakup, and a forward facing bag mode. At a density ratio of ten, similar breakup modes are observed, with the exception that the forward facing bag mode is replaced by a shear breakup mode. Similar breakup modes have been seen experimentally for much larger density ratios. Although a backward facing bag is seen at low Oh, where viscous effects are small, comparisons with simulations of inviscid flows show that the bag breakup is a viscous phenomenon, due to boundary layer separation and the formation of a wake. At higher Oh, where viscous effects modify the evolution, the simulations show that the main effect of increasing Oh is to move the boundary between the different breakup modes to higher Eo. The results are summarized by “breakup maps” where the different breakup modes are shown in the Eo–Oh plane for different values of the viscosity and the density ratios. © 1999 American Institute of Physics.

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47.55.D-	Drops and bubbles
47.10.-g	General theory in fluid dynamics
47.20.-k	Flow instabilities
47.11.-j	Computational methods in fluid dynamics

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Shape and stability of doubly connected axisymmetric free surfaces in a cylindrical container

Lev A. Slobozhanin, J. Iwan D. Alexander, and Alexandre I. Fedoseyev

Phys. Fluids 11, 3668 (1999); http://dx.doi.org/10.1063/1.870230 (10 pages) | Cited 3 times

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The equilibrium and stability of a liquid that partially fills a cylindrical container with planar ends are examined. It is assumed that the free surface is axisymmetric and does not cross the symmetry axis of the container. Particular attention is given to the case where gravity is parallel to the cylinder’s axis, and where the free surface has one contact line on the lateral cylindrical wall and the other on one of the planar ends. The equilibrium configuration of such a surface is determined by the wetting angle, α, the Bond number, B, and the relative volume, V, of the annular region bounded by the free surface and the solid container. Shapes of stable and critical surfaces have been analyzed, and the stability regions for arbitrary Bond numbers have been obtained in the α–V plane. The shape and stability problems for a zero gravity configuration with both contact lines on the lateral wall of the cylinder are also studied. In addition, the stability of a free surface with at least one contact line coinciding with the edge formed by the lateral wall and a planar end is discussed. © 1999 American Institute of Physics.

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47.20.-k	Flow instabilities
68.03.-g	Gas-liquid and vacuum-liquid interfaces
68.05.-n	Liquid-liquid interfaces
68.08.Bc	Wetting

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Thermal separation in near-axis boundary layers with intense swirl

M. A. Herrada, M. Pérez-Saborid, and A. Barrero

Phys. Fluids 11, 3678 (1999); http://dx.doi.org/10.1063/1.870231 (10 pages) | Cited 2 times

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Swirling flows have a wide range of applications and exhibit a variety of interesting features. Gas cooling near the axis in these flows, the so-called Ranque–Hilsch effect, is one of them. To gain insight into this phenomenon, we have analyzed the thermal, near-axis boundary layer of a gas jet driven by a class of conical inviscid quasi-incompressible flows whose axial and azimuthal velocity components, w and v, and stagnation temperature, T_t, behave near the axis as w = W₀r^m−2,v = LW₀r^m−2, and T_t−T_r = T₀r^2(m−2), where z and r are the axial and radial coordinates, L is the Squire number directly related to the swirl strength, m is any real number such as 1 ⩽ m<2, T_r is a reference temperature, and W₀ and T₀ are arbitrary dimensional constants; W₀ is assumed to be positive while T₀ may be either positive or negative. To simplify the boundary layer analysis, low Mach number flows with small relative variations in the gas density have been considered. Radial profiles of axial and azimuthal velocity components, and static and stagnation temperatures are found to depend on the Squire parameter L, the Prandtl number, Pr, and the rest of the parameters of the problem. Even for the case of inviscid vortices with positive values of T₀, for which the stagnation temperature increases towards the axis, is found that the stagnation temperature decreases substantially in the vortex core for some range of values of both L and Pr (Ranque–Hilsch effect) when the effect of both heat conduction and the work done by viscous forces are taken into account. It is also found that there exists an optimum value L_op for which the cooling effect reaches a sharp maximum and that small deviations of L from L_op reduce drastically the cooling effect. The appropriate tuning of L_op can be dramatically important for the efficient operation of Ranque–Hilsch tubes. The influence of the Prandtl number and the rest of the parameters of the problem has been also considered. © 1999 American Institute of Physics.

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47.15.Cb	Laminar boundary layers
47.32.Ff	Separated flows
47.27.nb	Boundary layer turbulence
47.32.-y	Vortex dynamics; rotating fluids
47.27.wg	Turbulent jets

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Fully nonlinear global modes in slowly varying flows

A. Couairon and J.-M. Chomaz

Phys. Fluids 11, 3688 (1999); http://dx.doi.org/10.1063/1.870232 (16 pages) | Cited 15 times

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We study the existence of nonlinear solutions of the real Ginzburg–Landau amplitude equation, with varying coefficients when the solution is subject to a boundary condition at x = 0. These solutions, called nonlinear global modes, are explicitly obtained from a matched asymptotic expansion when nonlinear effect dominates over the inhomogeneity. The dynamics of this model is believed to mimic the behavior of strongly nonlinear but weakly nonparallel basic flow (basic flow varying in the streamwise direction). For the model, we derive scaling laws for the amplitude of nonlinear global modes and for the position of the maximum that explain for the first time the experimental observations of Goujon-Durand et al. [Phys. Rev. E 50, 308 (1994)] and the numerical simulations of Zielinska and Wesfreid [Phys. Fluids 7, 1418 (1995)] of the wake behind bluff bodies. © 1999 American Institute of Physics.

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47.11.-j	Computational methods in fluid dynamics
47.20.-k	Flow instabilities
47.27.wb	Turbulent wakes

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Four-vortex motion with zero total circulation and impulse

Hassan Aref and Mark A. Stremler

Phys. Fluids 11, 3704 (1999); http://dx.doi.org/10.1063/1.870233 (12 pages) | Cited 12 times

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The problem of four interacting point vortices on the unbounded plane with vanishing total circulation and vanishing impulse is reduced to a three-body problem analogous to the three-vortex problem on the unbounded plane. A “phase plane analysis” using trilinear coordinates, similar to that used for the three-vortex problem, is presented and used to discuss details of the motion. The methodology and results complement earlier analyses of the same problem by Eckhardt and Rott. © 1999 American Institute of Physics.

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47.32.C-

Vortex dynamics

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Vortices in rotating systems: Centrifugal, elliptic and hyperbolic type instabilities

D. Sipp, E. Lauga, and L. Jacquin

Phys. Fluids 11, 3716 (1999); http://dx.doi.org/10.1063/1.870180 (13 pages) | Cited 13 times

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This paper is devoted to the effects of rotation on the linear dynamics of two-dimensional vortices. The asymmetric behavior of cyclones and anticyclones, a basic problem with respect to the dynamics of rotating flows, is particularly addressed. This problem is investigated by means of linear stability analyses of flattened Taylor–Green vortices in a rotating system. This flow constitutes an infinite array of contra-rotating one-signed nonaxisymmetric vorticity structures. We address the stability of this flow with respect to three-dimensional short-wave perturbations via both the geometrical optics method and via a classical normal mode analysis, based on a matrix eigenvalue method. From a physical point of view, we show that vortices are affected by elliptic, hyperbolic and centrifugal instabilities. A complete picture of the short-wave stability properties of the flow is given for various levels of the background rotation. For Taylor–Green cells with aspect ratio E = 2, we show that anticyclones undergo centrifugal instability if the Rossby number verifies Ro>1, elliptic instability for all values of Ro except 0.75<Ro<1.25 and hyperbolic instability. The Rossby number is here defined as the ratio of the maximum amplitude of vorticity to twice the background rotation. On the other hand, cyclones bear elliptic and hyperbolic instabilities whatever the Rossby number. Besides, depending on the Rossby number, rotation can either strengthen (anticyclonic vortices) or weaken elliptic instability. From a technical point of view, in this article we bring an assessment of the links between the short-wave asymptotics and the normal mode analysis. Normal modes are exhibited which are in complete agreement with the short-wave asymptotics both with respect to the amplification rate and with respect to the structure of the eigenmode. For example, we show centrifugal eigenmodes which are localized in the vicinity of closed streamlines in the anticyclones; elliptical eigenmodes which are concentrated in the center of the cyclones or anticyclones; hyperbolic eigenmodes which are localized in the neighborhood of closed streamlines in cyclones. © 1999 American Institute of Physics.

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47.32.C-	Vortex dynamics
47.20.-k	Flow instabilities

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Does the tracer gradient vector align with the strain eigenvectors in 2D turbulence?

G. Lapeyre, P. Klein, and B. L. Hua

Phys. Fluids 11, 3729 (1999); http://dx.doi.org/10.1063/1.870234 (9 pages) | Cited 39 times

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This paper investigates the dynamics of tracer gradient for a two-dimensional flow. More precisely, the alignment of the tracer gradient vector with the eigenvectors of the strain-rate tensor is studied theoretically and numerically. We show that the basic mechanism of the gradient dynamics is the competition between the effects due to strain and an effective rotation due to both the vorticity and to the rotation of the principal axes of the strain-rate tensor. A nondimensional criterion is derived to partition the flow into different regimes: In the strain dominated regions, the tracer gradient vector aligns with a direction different from the strain axes and the gradient magnitude grows exponentially in time. In the strain-effective rotation compensated regions, the tracer gradient vector aligns with the bisector of the strain axes and its growth is only algebraic in time. In the effective rotation dominated regions, the tracer gradient vector is rotating but is often close to the bisector of the strain axes. A numerical simulation of 2D (two-dimensional) turbulence clearly confirms the theoretical preferential directions in strain and effective rotation dominated regions. Effective rotation can be dominated by the rotation rate of the strain axes, and moreover, proves to be larger than strain rate on the periphery of vortices. Taking into account this term allows us to improve significantly the Okubo–Weiss criterion. Our criterion gives the correct behavior of the growth of the tracer gradient norm for the case of axisymmetric vortices for which the Okubo–Weiss criterion fails. © 1999 American Institute of Physics.

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47.27.-i	Turbulent flows
02.10.Ud	Linear algebra
02.10.Xm	Multilinear algebra
47.11.-j	Computational methods in fluid dynamics

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Note on forced Burgers turbulence

Robert H. Kraichnan

Phys. Fluids 11, 3738 (1999); http://dx.doi.org/10.1063/1.870235 (5 pages) | Cited 9 times

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A putative powerlaw range of the probability density of velocity gradient in high-Reynolds-number forced Burgers turbulence is studied. In the absence of information about shock locations, elementary conservation and stationarity relations imply that the exponent −α in this range satisfies α ≥ 3, if dissipation within the power-law range is due to isolated shocks. A generalized model of shock birth and growth implies α = 7/2 if initial data and forcing are spatially homogeneous and obey Gaussian statistics. Arbitrary values α ≥ 3 can be realized by suitably constructed homogeneous, non-Gaussian initial data and forcing. © 1999 American Institute of Physics.

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47.27.Jv

High-Reynolds-number turbulence

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Calculations of longitudinal and transverse velocity structure functions using a vortex model of isotropic turbulence

Guowei He, Gary D. Doolen, and Shiyi Chen

Phys. Fluids 11, 3743 (1999); http://dx.doi.org/10.1063/1.870236 (6 pages) | Cited 5 times

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The longitudinal structure function (LSF) and the transverse structure function (TSF) in isotropic turbulence are calculated using a vortex model. The vortex model is composed of the Rankine and Burgers vortices which have the exponential distributions in the vortex Reynolds number and vortex radii. This model exhibits a power law in the inertial range and satisfies the minimal condition of isotropy that the second-order exponent of the LSF in the inertial range is equal to that of the TSF. Also observed are differences between longitudinal and transverse structure functions caused by intermittency. These differences are related to their scaling differences which have been previously observed in experiments and numerical simulations. © 1999 American Institute of Physics.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.32.C-	Vortex dynamics

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A nonlinear mechanism for receptivity of free-stream disturbances

S. Berlin and D. S. Henningson

Phys. Fluids 11, 3749 (1999); http://dx.doi.org/10.1063/1.870237 (12 pages) | Cited 11 times

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Numerical experiments on the interaction of simple vortical free-stream disturbances with a laminar boundary layer are presented. Both spatial and temporal direct numerical simulations (DNS) have been performed for two types of free-stream disturbances. A linear and a nonlinear receptivity mechanism were identified. The nonlinear mechanism was found to force streaks inside the boundary layer similar to those found in experiments on free-stream turbulence and it performed equally well for disturbances elongated in the streamwise direction as for and oblique free-stream disturbances. The boundary layer response caused by the nonlinear mechanism was, depending on the initial disturbance energy, comparable to that of the linear mechanism, which was only efficient for free-stream streamwise vortices. A parameter study revealed that the wall normal velocity component of the free-stream disturbances is more important for the investigated receptivity mechanisms than the streamwise component. The identified boundary layer receptivity mechanism, in which three-dimensional disturbances in the free-stream continuously force streaks inside the boundary layer, may explain differences between experimental results and previously suggested theories for the origin of streaks in boundary layers subjected to free-stream turbulence. © 1999 American Institute of Physics.

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47.20.Pc	Flow receptivity
47.15.Cb	Laminar boundary layers
47.32.C-	Vortex dynamics
47.27.-i	Turbulent flows

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Measurement of shock structure and shock–vortex interaction in underexpanded jets using Rayleigh scattering

J. Panda and R. G. Seasholtz

Phys. Fluids 11, 3761 (1999); http://dx.doi.org/10.1063/1.870247 (17 pages) | Cited 19 times

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The density field of underexpanded supersonic free jets issuing from a choked circular nozzle was measured using a Rayleigh scattering-based technique. This reliable and nonintrusive technique is particularly suitable for high-speed flows and is fundamentally superior to the intrusive probes and particle-based techniques such as laser Doppler velocimetry. A continuous wave laser and photon counting electronics were employed for time and phase-averaged density measurements. The use of dust-free air for the entrained flow allowed measurements in the shear layer region. The free jets were produced in the plenum to ambient pressure ratio range of 1.88–5.75, which corresponded to a fully expanded Mach number range of 0.99 ⩽ M_j ⩽ 1.8. A comparative study of schlieren photographs and time-averaged density data provided insight into the shock-cell structures. The radial profiles obtained at various axial stations covering a downstream distance of 10 jet diameters show the development of the jet shear layer and the decay of the shock–cells. The supersonic free jets produced screech sound. A phase-averaged photon counting technique, using the screech tone as the trigger source, was used to measure the unsteady density variation. The phase-averaged density data show the evolution of the large-scale turbulent vortices that are found to be modulated periodically along the flow direction. A comparison with previously obtained data showing near-field pressure fluctuation and convective speed of the organized vortices reveals many interesting dynamics. All quantities show regular spatial modulation. The locations of local maxima in density fluctuations are found to coincide with the high convective speed and the antinode points in the near-field pressure fluctuation. Interestingly, the periodicity of modulation is found to be somewhat different from the shock spacing. Instead it shows that the standing wave system, known to exist in the near-field pressure fluctuation, extends into the jet shear layer. The standing wave is formed between the downstream moving Kelvin–Helmholtz instability waves and the upstream propagating part of sound waves. A detailed field measurement of the unsteady density fluctuation was conducted for the M_j = 1.19 and 1.42 jets for which the near-field pressure fluctuation data were obtained previously. The phase-matched, combined plots of the density fluctuation present inside the jet flow, and the pressure fluctuation present just outside the jet boundary provide a charming insight into the shock–vortex interaction leading to the sound wave generation. © 1999 American Institute of Physics.

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47.27.wg	Turbulent jets
47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.40.Nm	Shock wave interactions and shock effects
47.32.C-	Vortex dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
43.28.Mw	Shock and blast waves, sonic boom
47.27.Sd	Turbulence generated noise
47.40.Ki	Supersonic and hypersonic flows

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Dynamic inverse modeling and its testing in large-eddy simulations of the mixing layer

J. G. M. Kuerten, B. J. Geurts, A. W. Vreman, and M. Germano

Phys. Fluids 11, 3778 (1999); http://dx.doi.org/10.1063/1.870238 (8 pages) | Cited 25 times

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We propose new identities for dynamic subgrid modeling in large-eddy simulation involving an explicit filter and its inverse. Exact defiltering of a class of numerical realizations of the top-hat filter is developed. The approach is applied to large-eddy simulation of the temporal mixing layer. Smagorinsky’s model is adopted as base model and the results are compared to the standard dynamic eddy-viscosity model as well as to filtered DNS (direct numerical simulation) results. The difference between the results of the two models for the present application is found to be quite small. This is explained by performing a sensitivity analysis with respect to the dynamic coefficient, which hints towards a “self-restoring” response underlying the observed robustness of the physical predictions. Using DNS data the validity of the assumption that the model coefficients are independent of filter width is tested and found to favor the inverse modeling procedure. The computational effort of the dynamic inverse model is 15% smaller than of the standard dynamic eddy-viscosity model. © 1999 American Institute of Physics.

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47.11.-j

Computational methods in fluid dynamics

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The subgrid-scale estimation model on nonuniform grids

Kuo-Chieh Loh and J. Andrzej Domaradzki

Phys. Fluids 11, 3786 (1999); http://dx.doi.org/10.1063/1.870239 (7 pages) | Cited 12 times

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The subgrid-scale estimation procedure developed previously using one-dimensional top hat filters on uniform grids is generalized to nonuniform grids. The method is evaluated in large eddy simulations of turbulent channel flow performed on a grid which is non-uniform in the wall-normal direction. © 1999 American Institute of Physics.

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47.11.-j	Computational methods in fluid dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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A two-time-scale turbulence model for compressible flows: Turbulence dominated by mean deformation interaction

O. Grégoire, D. Souffland, S. Gauthier, and R. Schiestel

Phys. Fluids 11, 3793 (1999); http://dx.doi.org/10.1063/1.870222 (15 pages) | Cited 4 times

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The multiple-time-scale concept is applied to develop a turbulence model for compressible flows. Transport equations for the turbulent kinetic energies and the energy transfer rates are linked to each domain of the turbulent spectrum. The model coefficients are calibrated, with respect to simple flows, by using a new method which takes advantage of the spectral character of the model. One innovation of this method is to use, as a component, the CG model [V. M. Canuto and I. Goldman, Phys. Rev. Lett. 54, 430 (1985)] which gives the large scale spectrum as a function of the instability-generating turbulence. Then, the two-time-scale model, with its complete set of coefficients, has been successfully applied to the simulation of plane mixing layers and homogeneous shear flows. A significant issue of this work is the study of the behavior of the two-time-scale model when a shock wave interacts with a homogeneous turbulence. We first compare model results with experimental data for a 2.8 Mach number interaction [D. Alem, Ph.D. thesis, Université de Poitiers, 1995]. The decrease of the integral length scale, predicted by the linear analysis, is reproduced with the two-time-scale model, which, moreover, recovered the rate of reduction measured by Alem. The amplification of the turbulence level through the shock wave is also consistent with the measurements. Then, we confront our results with a direct numerical simulation of the shock–turbulence interaction at M = 1.2 [S. Lee et al., J. Fluid Mech. 251, 533 (1993)]. The spectrum of the turbulence injected in the inflow region of the direct numerical simulation appeared to be far from the freely decaying state. The two-time-scale model, which accounts for the spectral nonequilibrium effects, is able to recover the spatial decrease of turbulence in the inflow region whereas a single-time-scale model fails. Moreover, the profiles for the turbulent kinetic energy and its dissipation rate over all the calculation domain are much better reproduced with the two-time-scale model than with the primary k–ε model. © 1999 American Institute of Physics.

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47.40.-x	Compressible flows; shock waves
47.27.Gs	Isotropic turbulence; homogeneous turbulence

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Pattern recognition analysis of the turbulent flow past a backward facing step

F. Scarano, C. Benocci, and M. L. Riethmuller

Phys. Fluids 11, 3808 (1999); http://dx.doi.org/10.1063/1.870240 (11 pages) | Cited 18 times

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A pattern recognition technique for the investigation of large-scale coherent structures, is applied to analyze the turbulent separated flow over a backward facing step (BFS) at a Reynolds number Re_h = 5.0×10³. The instantaneous two-dimensional velocity distribution is obtained by means of digital particle image velocimetry (D-PIV) measurements. High spatial resolution (Δr/h = 1/25) is achieved with the application of an iterative window refinement image processing algorithm. The measurement plane is oriented in order to investigate spanwise aligned vortices footprints. The detection algorithm is based on velocity pattern spatial cross correlation. An additional isotropy condition is imposed to improve the detection of vortices and shear layer. The structure of the shear layer emanating from the step edge is examined emphasizing the role of coherent fluctuations with a length scale d ranging from 0.12 h to 0.44 h. A characteristic statistical spatial occurrence is found for the educed spanwise-aligned rollers: a quasi-linear spreading region extends from x/h = 0.8 up to x/h = 3.5. Within the same region the production of turbulent kinetic energy exhibits a maximum. At smaller scale, the vortices show a significant presence of counter-rotating structures inside the free shear layer suggesting that the spanwise rollers undergo early three dimensional instability and breakdown within a few step units. Conditional data averaging is also applied to the results and structural properties (coherent velocity, vorticity and turbulence production) are highlighted: close to the step edge the coherent vorticity distribution is strongly distorted showing an intense interaction between the rollers and the shear layer. A roughly circular pattern is recovered downstream x/h = 4.© 1999 American Institute of Physics.

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47.27.nb	Boundary layer turbulence
47.32.Ff	Separated flows
47.20.-k	Flow instabilities
47.32.C-	Vortex dynamics
05.40.-a	Fluctuation phenomena, random processes, noise, and Brownian motion
47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.54.-r	Pattern selection; pattern formation

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Propagation of acoustic waves in disordered flows composed of many vortices. I. General aspects

Denis Boyer, Maurizio Baffico, and Fernando Lund

Phys. Fluids 11, 3819 (1999); http://dx.doi.org/10.1063/1.870241 (10 pages) | Cited 5 times

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We study the coherent propagation of an acoustic wave through a disordered flow with zero mean velocity. The flow is modeled as an assembly of vortices randomly distributed. The source term of the linear wave equation satisfied by the acoustic pressure must be expanded up to terms of order Mach number of the background flow squared. The complex wave number of the coherent wave is calculated analytically and related to average properties of the flow using multiple scattering theory in a Bourret approximation. The perturbations induced by the fluid motion on the index of refraction and on the attenuation length of the wave are of order Mach number squared. The role of the finite compressibility of the fluid is considered in detail, as well as the need, or lack thereof, to consider widely different time scales for acoustic propagation and flow evolution. For a gas and for long wavelengths, the phase velocity of the coherent wave may become higher than in the fluid at rest. © 1999 American Institute of Physics.

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47.32.C-	Vortex dynamics
43.20.El	Reflection, refraction, diffraction of acoustic waves

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Propagation of acoustic waves in disordered flows composed of many vortices. II. Examples

Denis Boyer and Fernando Lund

Phys. Fluids 11, 3829 (1999); http://dx.doi.org/10.1063/1.870242 (17 pages) | Cited 1 time

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The theory of acoustic wave propagation through systems of many vortices randomly distributed, developed in Part I, is applied to specific examples in two and three dimensions. Two classes of vortex blobs are considered; vortices with an axisymmetric distribution of vorticity, such as disks or tubes, and vortices with a nonvanishing dipolar moment such as dipoles or rings. The index of refraction and attenuation length are numerically computed as a function of wavelength for various values of vortex parameters. The asymptotic behavior of the dispersion relation for very short and very long wavelengths is also derived analytically. At short wavelengths λ the attenuation length scales as λ⁻² in all examples studied. At long wavelengths the scaling depends on the lowest nonvanishing multipole moment of the vorticity distribution; say, for vortex rings, it is λ⁻⁴ as in Thomson scattering. For an ideal gas, the phase velocity of the coherent acoustic wave is greater than in the undisturbed flow for long wavelengths and smaller than in the undisturbed flow for short wavelengths. This appears to be a robust feature. When properly normalized, the attenuation length does not depend very strongly on the ratio l/ϵ, where l is a vortex length scale and ϵ the thickness of the vorticity bearing region, both in two and three dimensions. The effective index of refraction, however, does depend on this ratio. The conditions of applicability of the results, which rely on a Born approximation scheme, are also determined. The expressions obtained in this paper for the scattering cross sections are used to discuss the properties of sound localization in two dimensional disordered flows. © 1999 American Institute of Physics.

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47.32.C-	Vortex dynamics
43.20.El	Reflection, refraction, diffraction of acoustic waves

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Nonlinear spectral dynamics of hypersonic laminar boundary layer flow

Ndaona Chokani

Phys. Fluids 11, 3846 (1999); http://dx.doi.org/10.1063/1.870243 (6 pages) | Cited 5 times

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The nonlinear interactions of the instability modes in a hypersonic laminar boundary layer undergoing natural transition are examined using bispectral analysis. The data are from an experiment of a boundary layer flow on a cooled-wall cone in a low-level free-stream disturbance hypersonic wind tunnel, and thus, the bispectral measurements are a good representation of the natural transition processes. The bispectral analysis shows that in the initial stages of transition the dominant nonlinear interaction is forcing by the fundamental to generate a harmonic. Subsequently, mutual forcing of the fundamental and harmonic yield a second harmonic. Difference interactions within the band of unstable disturbances centered on the fundamental and harmonic also generate a low frequency nonlinear interaction. At high amplitudes of the fundamental and harmonic a nonlinear interaction characterized by a low frequency modulation of the fundamental and harmonic then follows. This nonlinear interaction is then the most dominant and precedes the breakdown of the laminar flow. © 1999 American Institute of Physics.

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47.40.Ki	Supersonic and hypersonic flows
47.15.Cb	Laminar boundary layers
47.15.-x	Laminar flows
47.15.Fe	Stability of laminar flows
47.20.-k	Flow instabilities

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A model for Marangoni drying

A. Thess and W. Boos

Phys. Fluids 11, 3852 (1999); http://dx.doi.org/10.1063/1.870244 (4 pages) | Cited 10 times

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We propose a simple theoretical model for the movement of a thin liquid film on a flat plate that is vertically withdrawn from a large liquid reservoir in the presence of a surface tension gradient. This problem is relevant to Marangoni drying—a technique that is used in the semiconductor industry for the purpose of water removal from wafers. Due to the smallness of the capillary number the fluid flow can be described by the classical Landau–Levich equation with an additional term accounting for the Marangoni effect. A numerical solution of this equation shows that the thickness of the residual film is a monotonically decreasing function of the surface tension gradient, thereby providing an explanation of the Marangoni drying process. © 1999 American Institute of Physics.

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