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

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S. T. Thoroddsen and K. Takehara

Phys. Fluids 12, 1265 (2000); http://dx.doi.org/10.1063/1.870380 (3 pages) | Cited 54 times

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When a drop is deposited gently onto the surface of a layer of the same liquid, it sits momentarily before coalescing into the bottom layer. High-speed video imaging reveals that the coalescence process is not instantaneous, but rather takes place in a cascade where each step generates a smaller drop. This cascade is self-similar and we have observed up to six steps. The time associated with each partial coalescence scales with the surface tension time scale. The cascade will, however, not proceed ad infinitum due to viscous effects, as the Reynolds number of the process is proportional to the square root of the drop diameter. Viscous effects will therefore begin to be important for the very smallest drops. This cascade is very similar to the one observed previously by Charles and Mason [J. Colloid Sci. 15, 105 (1960)] for two immiscible liquids, where one of the liquids replaces the air in our setup. © 2000 American Institute of Physics.

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68.03.Cd	Surface tension and related phenomena
47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.55.D-	Drops and bubbles

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Growth and collapse of a vapor bubble in a narrow tube

E. Ory, H. Yuan, A. Prosperetti, S. Popinet, and S. Zaleski

Phys. Fluids 12, 1268 (2000); http://dx.doi.org/10.1063/1.870381 (10 pages) | Cited 32 times

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The fluid mechanical aspects of the axisymmetric growth and collapse of a bubble in a narrow tube filled with a viscous liquid are studied numerically. The tube is open at both ends and connects two liquid reservoirs at constant pressure. The bubble is initially a small sphere and growth is triggered by a large internal pressure applied for a short time. After this initial phase, the motion proceeds by inertia. This model simulates the effect of an intense, localized, brief heating of the liquid which leads to the nucleation and growth of a bubble. The dimensionless parameters governing the problem are discussed and their effects illustrated with several examples. It is also shown that, when the bubble is not located at the midpoint of the tube, a net flow develops capable of pumping fluid from one reservoir to the other. The motivation for this work is offered by the possibility to use vapor bubbles as actuators in fluid-handling microdevices. © 2000 American Institute of Physics.

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47.55.D-	Drops and bubbles
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Fingering phenomena for driven coating films

M. H. Eres, L. W. Schwartz, and R. V. Roy

Phys. Fluids 12, 1278 (2000); http://dx.doi.org/10.1063/1.870382 (18 pages) | Cited 41 times

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A theoretical and numerical model is formulated to describe the instability and the long-time evolution of both gravity-driven and surface-shear-stress-driven thin coating films. A single evolution equation, of higher-order diffusive type, models the flow for either problem. It is derived using the lubrication approximation. For partially wetting systems, the effect of finite contact angle is incorporated in the equation using a particular disjoining pressure model. The base state, in each case, is a two-dimensional steadily propagating capillary front. Slight perturbations of the base state, applied along the front, initiate the fingering instability. Early-time results accurately reproduce the wavelengths of fastest growth and the corresponding eigenmodes as reported in published linear stability analyses. As time proceeds, depending on parameter values, various fingering patterns arise. For conditions of perfect wetting with the substrate downstream of the moving front covered with a thin precursor layer, predicted nonlinear finger evolution agrees well with published experiments. The ultimate pattern, in this case, is a steadily translating pattern of wedge-shaped fingers. Alternatively, for partially wetting systems that exhibit sufficiently large static contact angles, long straight-sided fingers or rivulets are formed. Finally, for larger contact angles, or at relatively low speeds, we predict that the flowing rivulets will become unstable and break up into strings of isolated droplets. © 2000 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
68.03.Cd	Surface tension and related phenomena
68.15.+e	Liquid thin films

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Extensional viscosity of dilute polystyrene solutions: Effect of concentration and molecular weight

Rahul K. Gupta, D. A. Nguyen, and T. Sridhar

Phys. Fluids 12, 1296 (2000); http://dx.doi.org/10.1063/1.870383 (23 pages) | Cited 27 times

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This paper reports a detailed investigation of the steady shear and extensional properties of mono-disperse polystyrene solutions for a range of molecular weights from 1.95 to 20 million and a range of concentrations from 69 ppm to 777 ppm. The steady shear and dynamic properties are reasonably well described by the Zimm model. The relaxation time and polymer viscosity evaluated using the Zimm model exhibit the expected scaling with concentration and molecular weight for theta solutions. In an extensional flow, these solutions show strain hardening and need about 5.5 to 6 strain units to reach steady state. The stress growth depends both on strain rate and strain. However, at moderate values of strain and when the Weissenberg number exceeds 6, the extensional stress growth depends only on total strain. The steady state extensional viscosity for each fluid was observed to depend on the magnitude of Weissenberg number (Wi). For Wi<6, the steady state extensional viscosity was observed to be an increasing function of the strain rate. At a Wi ∼ 10, the steady state extensional viscosity exhibits a maximum and surprisingly, for Wi>10, the steady state extensional viscosity is a decreasing function of the strain rate. The results indicate that even dilute solutions, with concentrations as low as 0.21 times the critical concentration, do show extension thinning under certain conditions. The transient and steady state extensional viscosities are found to be proportional to molecular weight (M_w) and concentration (c). This result is rather unexpected as the Zimm model would predict a scaling with c and Mw0.5 for the transient viscosity and scaling with c and Mw1.5 for the steady state viscosity. On the other hand, the Rouse model predicts a scaling with c and M_w (for transient extensional viscosity) and with c and Mw2 (for steady state extensional viscosity). Hence the data appear to follow a Rouse-like behavior for the transient viscosity. This implies that the advent of the stretching reduces the hydrodynamic interaction and a free draining behavior is obtained. As a result, predictions using the Zimm model parameters, estimated from shear data, are unable to predict the transient extensional viscosity. The data are analyzed using a constitutive equation that incorporates an anisotropic drag coefficient along with a Rouse spectrum of relaxation time. Such a model captures the extensional behavior of the solutions. © 2000 American Institute of Physics.

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61.25.H-	Macromolecular and polymers solutions; polymer melts
47.50.-d	Non-Newtonian fluid flows
66.20.-d	Viscosity of liquids; diffusive momentum transport

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Stability of two-dimensional strip casting processes

Peter Plaschko and Uwe Schaflinger

Phys. Fluids 12, 1319 (2000); http://dx.doi.org/10.1063/1.870384 (8 pages)

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The solidification of molten materials is of great significance in modern metallurgical engineering. We study disturbances of a process that is characterized by three disparate lengths: the solidification length L, the wavelength Λ, and the depth of the slab δ_∝. The present analysis is motivated by the relation δ_∞<Λ≪L, which is always true in practical strip casting processes. This justifies the use of an asymptotic expansion based on shallow water equations for long waves to describe the linear stability of disturbances. The leading-order equations govern a quasiparallel flow. In this limit we found two different types of disturbances: a weakly damped stable mode that runs downstream and a strongly damped perturbation traveling upstream. We focus on the downstream moving mode and show that this disturbance is strongly frequency dependent. Although the velocity disturbances are damped, there is a regime of parameters where the perturbations of the displacement grow in the horizontal direction. In our analyses we found a region of preferred frequencies. The displacement grows at these frequencies faster than for neighboring frequencies. The wavelengths of disturbances oscillating at these preferred frequencies are in qualitative agreement with the experimental observation of the wavelengths of harmonically varying grooves in the completely solidified material. © 2000 American Institute of Physics.

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64.70.D-	Solid-liquid transitions
81.30.Fb	Solidification

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Length scales of turbulence in stably stratified mixing layers

William D. Smyth and James N. Moum

Phys. Fluids 12, 1327 (2000); http://dx.doi.org/10.1063/1.870385 (16 pages) | Cited 57 times

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Turbulence resulting from Kelvin–Helmholtz instability in layers of localized stratification and shear is studied by means of direct numerical simulation. Our objective is to present a comprehensive description of the turbulence evolution in terms of simple, conceptual pictures of shear–buoyancy interaction that have been developed previously based on assumptions of spatially uniform stratification and shear. To this end, we examine the evolution of various length scales that are commonly used to characterize the physical state of a turbulent flow. Evolving layer thicknesses and overturning scales are described, as are the Ozmidov, Corrsin, and Kolmogorov scales. These considerations enable us to provide an enhanced understanding of the relationships between uniform-gradient and localized-gradient models for sheared, stratified turbulence. We show that the ratio of the Ozmidov scale to the Thorpe scale provides a useful indicator of the age of a turbulent event resulting from Kelvin–Helmholtz instability. © 2000 American Institute of Physics.

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47.27.nb	Boundary layer turbulence
47.55.Hd	Stratified flows
47.27.E-	Turbulence simulation and modeling
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.20.Bp	Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.20.Ma	Interfacial instabilities (e.g., Rayleigh-Taylor)
47.11.-j	Computational methods in fluid dynamics
02.60.Cb	Numerical simulation; solution of equations

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Anisotropy of turbulence in stably stratified mixing layers

William D. Smyth and James N. Moum

Phys. Fluids 12, 1343 (2000); http://dx.doi.org/10.1063/1.870386 (20 pages) | Cited 42 times

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Direct numerical simulations of turbulence resulting from Kelvin–Helmholtz instability in stably stratified shear flow are used to study sources of anisotropy in various spectral ranges. The set of simulations includes various values of the initial Richardson and Reynolds numbers, as well as Prandtl numbers ranging from 1 to 7. We demonstrate that small-scale anisotropy is determined almost entirely by the spectral separation between the small scales and the larger scales on which background shear and stratification act, as quantified by the buoyancy Reynolds number. Extrapolation of our results suggests that the dissipation range becomes isotropic at buoyancy Reynolds numbers of order 10⁵, although we cannot rule out the possibility that small-scale anisotropy persists at arbitrarily high Reynolds numbers, as some investigators have suggested. Correlation-coefficient spectra reveal the existence of anisotropic flux reversals in the dissipation subrange whose magnitude decreases with increasing Reynolds number. The scalar concentration field tends to be more anisotropic than the velocity field. Estimates of the dissipation rates of kinetic energy and scalar variance based on the assumption of isotropy are shown to be accurate for buoyancy Reynolds numbers greater than O(10²). Such estimates are therefore reliable for use in the interpretation of most geophysical turbulence data, but may give misleading results when applied to smaller-scale flows. © 2000 American Institute of Physics.

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47.27.nb	Boundary layer turbulence
47.27.E-	Turbulence simulation and modeling
47.55.Hd	Stratified flows
47.11.-j	Computational methods in fluid dynamics
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
02.60.Cb	Numerical simulation; solution of equations

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Direct numerical simulation of the flow in a lid-driven cubical cavity

E. Leriche and S. Gavrilakis

Phys. Fluids 12, 1363 (2000); http://dx.doi.org/10.1063/1.870387 (14 pages) | Cited 28 times

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Direct numerical simulation of the flow in a lid-driven cubical cavity has been carried out at a Reynolds number above 10 000. Both transient and steady-in-the-mean states of the flow posses long time scales requiring long integration times. A large fraction of the total kinetic energy and dissipation is concentrated in the near-lid mean flow. The flow over most of the domain is laminar with distinct wall-jet profiles found in three of the walls. The high momentum fluid near the lid transmits its energy into a downflowing nonparallel wall jet which separates ahead of the bottom wall. From the collision of this separated layer against the bottom wall two wall jets emerge. In this process the energy lost to turbulence by the impingement is partly recovered by the emerging wall jets. © 2000 American Institute of Physics.

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47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.27.wg	Turbulent jets

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Cross-channel advective–diffusive transport by a monochromatic traveling wave

Adam H. Sobel and Glenn R. Flierl

Phys. Fluids 12, 1377 (2000); http://dx.doi.org/10.1063/1.870388 (5 pages)

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The cross-channel tracer flux due to the combined effects of advection and diffusion is considered for two-dimensional incompressible flow in a channel, where the flow is that due to a monochromatic traveling wave and the boundary conditions at the walls are fixed tracer concentration. The tracer flux is computed numerically over a wide range of the parameters ϵ = U/c and δ = K/cL, with U the maximum fluid velocity, c the wave phase speed, K the tracer diffusivity, and L the channel width. Prior work has used analytical methods to obtain solutions for δ either infinite (stationary overturning cells) or small. In addition to the full numerical solutions, solutions obtained using mean field theory are presented, as well as a new asymptotic solution for small ϵ, and one for small δ due to Flierl and Dewar. The various approximations are compared with each other and with the numerical solutions, and the domain of validity of each is shown. Mean field theory is fairly accurate compared to the full numerical solutions for small δ, but tends to underpredict the tracer flux by 30–50% for larger δ. The asymptotic solution derived by Flierl and Dewar for small δ is found to break down when δ ∼ ϵ⁻² rather than when δ ∼ 1 as suggested by the original derivation, and a scaling argument is presented which explains this. © 2000 American Institute of Physics.

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05.60.-k	Transport processes
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.35.-i	Hydrodynamic waves

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Bragg scattering of surface waves over permeable rippled beds with current

Chao-Lung Ting, Ming-Chung Lin, and Chwen-Ling Kuo

Phys. Fluids 12, 1382 (2000); http://dx.doi.org/10.1063/1.870389 (7 pages) | Cited 3 times

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In this study we develop a time-dependent wave equation for waves propagating with a current over permeable rippled beds. As well known, Bragg resonance occurs when the incident wavelength is twice the wavelength of the bottom ripple undulation and no current is present. However, the current in the near-shore region changes the resonance condition. A one-dimensional wave field is solved numerically based on the derived equation to study the effect of current on the Bragg resonance condition. Nonlinear wave–wave resonant interaction theory provides an explanation of the effect on Bragg resonance. Numerical results also indicate that the maximum reflection coefficient increases as current velocity increases from a negative to a positive value. Furthermore, the velocity of the current affects the position of the maximum reflection coefficient. © 2000 American Institute of Physics.

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47.35.-i

Hydrodynamic waves

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Numerical simulation of pattern formation in the Bénard–Marangoni convection

Hirofumi Tomita and Kanji Abe

Phys. Fluids 12, 1389 (2000); http://dx.doi.org/10.1063/1.870390 (12 pages) | Cited 5 times

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The Bénard–Marangoni convection is numerically simulated using the full three-dimensional Navier–Stokes equation. It is shown that hexagonal convection appears when the surface-tension effect dominates over the buoyancy effect. When two effects are comparable to each other, a mixed type of roll and hexagonal convections is stably obtained. It is found that the kinetic energy production by buoyancy does not depend on the convection pattern, whereas that by surface-tension strongly depends on the convection pattern. When the surface-tension effect is dominant, the kinetic energy production by surface-tension in the hexagonal convection is larger than that in the roll convection. Hexagonal convection gives a vertical heat transfer larger than that of roll convection. © 2000 American Institute of Physics.

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47.27.T-	Turbulent transport processes
68.03.Cd	Surface tension and related phenomena
47.11.-j	Computational methods in fluid dynamics

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On the relationship of effective Reynolds number and Strouhal number for the laminar vortex shedding of a heated circular cylinder

An-Bang Wang, Zdenek Trávníček, and Kai-Chien Chia

Phys. Fluids 12, 1401 (2000); http://dx.doi.org/10.1063/1.870391 (10 pages) | Cited 34 times

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The laminar vortex shedding of airflow behind a circular cylinder with different heating temperatures was experimentally investigated with emphasis on the relationship of wake frequency and the Reynolds number. A new method to generate the two-dimensional parallel vortex shedding for the heated cylinder was developed and tested. An “effective Reynolds number” that employs a kinematic viscosity computed from an “effective temperature” is used to account for the temperature effects on the vortex shedding frequency. The present result shows that the frequency data could be successfully collapsed with the effective temperature computed by T_eff = T_∞+0.28(T_W−T_∞) for a wide range of cylinder temperatures, T_∞ and T_W being the free-stream temperature and cylinder surface temperature, respectively. Moreover, the relationship between Strouhal number and effective Reynolds number was found to be “universal.” The physical interpretation of T_eff and the applicable region of the St–Re_eff curve are discussed. © 2000 American Institute of Physics.

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47.15.-x	Laminar flows
47.32.C-	Vortex dynamics

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Mixing of viscous polymer liquids

Jason R. Stokes and David V. Boger

Phys. Fluids 12, 1411 (2000); http://dx.doi.org/10.1063/1.870392 (6 pages) | Cited 13 times

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A torsionally driven cavity is proposed as a suitable mixing device for viscoelastic fluids. “Chaotic” behavior occurs in the secondary flow plane using polyacrylamide Boger fluids due to the inducement of elastic flow instabilities in situations where inertial forces are small. The torsionally driven cavity is also a suitable well-defined geometry for testing the ability of non-Newtonian constitutive models to describe the behavior of elastic fluids in three-dimensional flow as a prelude to solving more difficult mixing problems. © 2000 American Institute of Physics.

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47.50.-d	Non-Newtonian fluid flows
83.50.-v	Deformation and flow
64.75.-g	Phase equilibria
47.20.Gv	Viscous and viscoelastic instabilities
47.52.+j	Chaos in fluid dynamics

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Axisymmetric capillary waves on thin annular liquid sheets. I. Temporal stability

C. Mehring and W. A. Sirignano

Phys. Fluids 12, 1417 (2000); http://dx.doi.org/10.1063/1.870393 (23 pages) | Cited 12 times

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A reduced-dimension approach is employed to analyze the nonlinear distortion and disintegration of axisymmetric thin inviscid annular liquid sheets in a surrounding void with nonzero gas-core pressure at zero gravity. Linear and nonlinear solutions for the free motion of periodically disturbed infinite linearly stable and unstable sheets are obtained and compared in this first paper. (The forced motion of semi-infinite annular sheets exiting from a nozzle or atomizer is considered in the second paper.) Both sinuous and dilational modes are studied. Both modes are dispersive unlike the planar case where only the dilational mode is dispersive. These modes are coupled even in the linear representation although for sufficiently large annular radius, a pure dilational linear oscillation is found. The sinuous oscillation always excites the dilational mode. Nonlinear effects can modify the wave shapes substantially, causing an increase in breakup time for the dilational mode and a decrease in breakup time for the sinuous mode. The capillary sheet instability due to the nonlinear interaction of harmonic and subharmonic dilational disturbances, originally observed on planar sheets, is also observed and analyzed for the annular geometry. Parametric studies on the influence of annular radius, disturbance wavelengths, and their ratios are reported. © 2000 American Institute of Physics.

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47.35.-i	Hydrodynamic waves
68.15.+e	Liquid thin films
47.20.-k	Flow instabilities

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Axisymmetric capillary waves on thin annular liquid sheets. II. Spatial development

C. Mehring and W. A. Sirignano

Phys. Fluids 12, 1440 (2000); http://dx.doi.org/10.1063/1.870394 (21 pages) | Cited 6 times

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The forced motion of semi-infinite axisymmetric thin inviscid annular liquid sheets, exiting from a nozzle or atomizer into a surrounding void under zero gravity but with constant gas-core pressure is analyzed by means of the reduced-dimension approach described in C. Mehring and W. A. Sirignano [Phys. Fluids 12, 1417 (2000)]. Linear analytical time-dependent (“limit-cycle”) solutions to the pure boundary-value problem are presented as well as linear and nonlinear numerical (transient) solutions to the mixed boundary- and initial-value problem of initially undisturbed sheets harmonically forced at the orifice or nozzle exit. Group velocities for the six independent solutions to the linear boundary-value problem are used to determine the location of boundary conditions. Numerical simulations of the linear transient problem are employed to validate these predictions. Parameter studies on sheet breakup and collapse lengths as well as on breakup and collapse times are reported. The dependence on modulation frequency, modulated disturbance amplitude, Weber number, and annular radius is presented for various cases of the mixed problem, i.e., for linearly or nonlinearly stable and unstable, dilationally or sinusoidally forced sheets. Nonlinear effects often have significant effects on breakup times and lengths or on collapse times and lengths. Nonlinear wave forms can deviate substantially from linear predictions resulting in major impacts on the size of the rings and shells that will remain after breakup. © 2000 American Institute of Physics.

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47.35.-i	Hydrodynamic waves
47.11.-j	Computational methods in fluid dynamics

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Interaction between Görtler vortices and two-dimensional Tollmien–Schlichting waves

M. T. Mendonça, P. J. Morris, and L. L. Pauley

Phys. Fluids 12, 1461 (2000); http://dx.doi.org/10.1063/1.870395 (11 pages) | Cited 2 times

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The nonlinear interaction between Görtler vortices and two-dimensional Tollmien–Schlichting (TS) waves is studied with a spatial, nonparallel model based on the parabolized stability equations. The effect of the TS waves on the development of the vortices is accounted for, showing that TS wave amplitudes of the same order of magnitude as the vortices result in significant nonlinear interaction. The range of governing parameters that has been studied so far is extended and the main effects of Görtler number, spanwise wave number, and initial amplitudes are identified. The study shows that the relative growth rates and initial amplitudes are the two most significant parameters. © 2000 American Institute of Physics.

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47.32.C-	Vortex dynamics
47.35.-i	Hydrodynamic waves
47.15.Cb	Laminar boundary layers

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A closure method for random advection of a passive scalar

James P. Gleeson

Phys. Fluids 12, 1472 (2000); http://dx.doi.org/10.1063/1.870396 (13 pages) | Cited 9 times

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A novel functional method is applied to calculate the statistics of a passive scalar in an isotropic turbulent velocity field. The method yields asymptotic series expansions for small velocity correlation time from which approximate closure equations are derived. The closure method admits a diagram expansion, and is implemented as a Mathematica program. Padé summation of the asymptotic series yields accurate values for the effective diffusivity and gives formulas expressing the Lagrangian correlation of the velocity in terms of the Eulerian correlation. The approximations compare very favorably with numerical simulations of advection by a Gaussian velocity field. © 2000 American Institute of Physics.

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47.27.-i	Turbulent flows
47.11.-j	Computational methods in fluid dynamics

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Using cavitation to measure statistics of low-pressure events in large-Reynolds-number turbulence

A. La Porta, Greg A. Voth, F. Moisy, and Eberhard Bodenschatz

Phys. Fluids 12, 1485 (2000); http://dx.doi.org/10.1063/1.870397 (12 pages) | Cited 19 times

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The structure of the pressure field of a turbulent water flow between counter-rotating disks is studied using cavitation. The flow is seeded with microscopic gas bubbles and the hydrostatic pressure is reduced until large negative pressure fluctuations trigger cavitation. Cavitation is detected via light scattering from cavitating bubbles. The spatial structure of the low-pressure events are visualized using a high-speed video system. A fast photo detector is used to measure the scaling of the cavitation statistics with the pressure. This data is used to determine the shape of the tail of the probability density function for the pressure. The tail is found to be exponential and scales more rapidly with Reynolds number than the standard deviation of the pressure. This may indicate the influence of internal intermittency. © 2000 American Institute of Physics.

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47.27.Jv	High-Reynolds-number turbulence
47.55.dp	Cavitation and boiling
47.55.D-	Drops and bubbles

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Temporal and spatial unmixedness downstream of a plate array

D. W. Guillaume and J. C. LaRue

Phys. Fluids 12, 1497 (2000); http://dx.doi.org/10.1063/1.870398 (12 pages)

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The effect of a plate array on a turbulent velocity and turbulent concentration field is determined. Profiles of mean and root-mean-square velocity and concentration, profiles of temporal and spatial unmixedness, and profiles of the variance of the gradient of velocity and the variance of the gradient of concentration are presented. Velocity and concentration integral length scales are compared. A biplane injection grid is used to produce the turbulent concentration and turbulent velocity field. Helium is injected through the jets at the grid nodes as air passes through the grid. The time-resolved velocity and concentration data are obtained using a two-sensor probe that consists of a hot wire and a TSI 1440-20 aspirating concentration probe. The addition of a plate array is shown to decrease the spatial unmixedness to a nearly zero value in about half the downstream distance observed without plates. Further, an increase in dissipation is shown with the array in place that reduces the temporal unmixedness to a value less than the value observed without the plates in about one-third the downstream distance. © 2000 American Institute of Physics.

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47.27.-i	Turbulent flows
47.32.-y	Vortex dynamics; rotating fluids
47.70.Fw	Chemically reactive flows
47.80.-v	Instrumentation and measurement methods in fluid dynamics

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Second-order temperature and velocity structure functions: Reynolds number dependence

R. A. Antonia, T. Zhou, and G. Xu

Phys. Fluids 12, 1509 (2000); http://dx.doi.org/10.1063/1.870399 (9 pages) | Cited 9 times

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An interpolation relation is used to fit second-order moments of temperature and velocity fluctuation increments which have been measured in three types of flows (decaying grid turbulence, cylinder wake, and circular jet) for values of the Taylor microscale Reynolds number R_λ in the range 30 (grid turbulence) to about 500 (jet). Several checks confirm the analytical framework underpinning the fit. The magnitude of the resulting scaling exponents increases with R_λ, the longitudinal one being first to asymptote to a constant value. The scaling exponent for the temperature increment is generally smaller than that for the longitudinal velocity increment but larger than that for the transverse velocity increment when R_λ ⩽ 300. For R_λ>300, the magnitude of the scaling exponents of the temperature and transverse velocity increments are nearly equal. Within the framework of small-scale intermittency, the magnitude of the Obukhov–Corrsin “constant” increases at small R_λ in similar manner to that of the longitudinal and transverse velocity Kolmogorov constants. © 2000 American Institute of Physics.

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47.27.wb	Turbulent wakes
47.27.wg	Turbulent jets

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Lobe dynamics applied to barotropic Rossby-wave breaking

Tieh-Yong Koh and R. Alan Plumb

Phys. Fluids 12, 1518 (2000); http://dx.doi.org/10.1063/1.870400 (11 pages) | Cited 15 times

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We applied the methods of lobe dynamics to the problem of transport across the edge of a barotropic vortex patch. The model used captures the essential dynamics of filament shedding in the wintertime stratospheric polar vortex. Two approaches were adopted for the problem: (1) the dominant periodic component of the vortical flow was identified and conventional lobe dynamics methods for periodic dynamical systems were applied to it; (2) the full aperiodic, dynamically consistent flow was retained and a modified brand of lobe dynamics was used to quantify the transport. Our results show that in the periodic case, much reversible transport occurs across the lobe dynamical boundary due to overlapping intruding and extruding lobes. In the aperiodic case, a small amount of intrusion was noted, contrary to the well-established fact that potential vorticity shedding in barotropic vortices is uniquely outwards. In our discussion, we argue that while lobe dynamics provides a rigorous framework for quantifying transport across the lobe dynamical boundary, this boundary may not be appropriate for quantifying transport across internal transport barriers, such as the stratospheric polar vortex edge. © 2000 American Institute of Physics.

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92.60.Fm	Boundary layer structure and processes
92.60.hk	Convection, turbulence, and diffusion

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Statistics of wind direction and its increments

Eric van Doorn, Brindesh Dhruva, Katepalli R. Sreenivasan, and Victor Cassella

Phys. Fluids 12, 1529 (2000); http://dx.doi.org/10.1063/1.870401 (6 pages) | Cited 22 times

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We study some elementary statistics of wind direction fluctuations in the atmosphere for a wide range of time scales (10⁻⁴ sec to 1 h), and in both vertical and horizontal planes. In the plane parallel to the ground surface, the direction time series consists of two parts: a constant drift due to large weather systems moving with the mean wind speed, and fluctuations about this drift. The statistics of the direction fluctuations show a rough similarity to Brownian motion but depend, in detail, on the wind speed. This dependence manifests itself quite clearly in the statistics of wind-direction increments over various intervals of time. These increments are intermittent during periods of low wind speeds but Gaussian-like during periods of high wind speeds. © 2000 American Institute of Physics.

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92.60.Gn	Winds and their effects
05.40.Jc	Brownian motion
02.50.-r	Probability theory, stochastic processes, and statistics

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A model for the turbulent Hartmann layer

T. Alboussière and R. J. Lingwood

Phys. Fluids 12, 1535 (2000); http://dx.doi.org/10.1063/1.870402 (9 pages) | Cited 7 times

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Here we study the Hartmann layer, which forms at the boundary of any electrically-conducting fluid flow under a steady magnetic field at high Hartmann number provided the magnetic field is not parallel to the wall. The Hartmann layer has a well-known form when laminar. In this paper we develop a model for the turbulent Hartmann layer based on Prandtl’s mixing-length model without adding arbitrary parameters, other than those already included in the log-law. We find an exact expression for the displacement thickness of the turbulent Hartmann layer [also given by Tennekes, Phys. Fluids 9, 1876 (1966)], which supports our assertion that a fully-developed turbulent Hartmann layer of finite extent exists. Leading from this expression, we show that the interaction parameter is small compared with unity and that therefore the Lorentz force is negligible compared with inertia. Hence, we suggest that the turbulence present in the Hartmann layer is of classical type and not affected by the imposed magnetic field, so justifying use of a Prandtl model. A major result is a simple implicit relationship between the Reynolds number and the friction coefficient for the turbulent Hartmann layer in the limit of large Reynolds number. By considering the distance over which the stress decays, we find a condition for the two opposite Hartmann layers in duct flows to be isolated (nonoverlapping). © 2000 American Institute of Physics.

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47.27.-i	Turbulent flows
47.65.-d	Magnetohydrodynamics and electrohydrodynamics

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An experimental study of density waves in a hypersonic shock layer on a flat plate

S. G. Mironov and A. A. Maslov

Phys. Fluids 12, 1544 (2000); http://dx.doi.org/10.1063/1.870403 (10 pages) | Cited 8 times

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The characteristics of density waves in a shock layer on a flat plate have been measured by the method of electron beam fluorescence of nitrogen for the free-stream Mach number M_∞ = 21 and the local Reynolds number Re_x = 2×10⁴–3×10⁵. The measurements have been performed for natural perturbations. The data on spatial distribution of fluctuation spectra and phase velocities of the waves in the longitudinal and transverse directions have been obtained. The propagation angles and the increments of density waves have been determined. The characteristics of fluctuation coherence have been measured. The experimental equipment, techniques of measurements, and methods for the reconstruction of the mean density and density fluctuations are described in the paper. The limitations imposed upon the measurement method are discussed. © 2000 American Institute of Physics.

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47.40.Ki	Supersonic and hypersonic flows
47.40.Nm	Shock wave interactions and shock effects
47.15.Cb	Laminar boundary layers
47.27.Cn	Transition to turbulence
47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.27.nb	Boundary layer turbulence
47.15.Fe	Stability of laminar flows

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Development and calibration of algebraic nonlinear models for terms in the Reynolds stress transport equations

Torbjörn Sjögren and Arne V. Johansson

Phys. Fluids 12, 1554 (2000); http://dx.doi.org/10.1063/1.870404 (19 pages) | Cited 13 times

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A simple and straightforward method is presented for the derivation and calibration of algebraic nonlinear models for terms in Reynolds stress turbulence closures. The method extensively utilizes data from direct numerical simulations to allow an investigation of the model performance over the entire Reynolds stress anisotropy-invariant map. The model constants are determined from the condition of minimizing the mean square error over the invariant map, in order to give good model behavior for as wide a class as possible of flow situations. A low Reynolds number closure is proposed based on the most general form for closing the Reynolds stress transport equations in terms of Reynolds stresses and total dissipation rate. It is shown that forcing the closure to satisfy realizability in a strict sense leads to a good model behavior even for the complicated flow situation near a wall, without any use of ad-hoc wall damping functions in the closure. The model behavior in homogeneous turbulent flow is analyzed by formulating equations for invariant measures, yielding several quite general results for the behavior of the present and other existing models. A new approach to the modeling effects of rotation in the context of Reynolds stress closures is presented and tested for some different homogeneous flows subjected to rotation. © 2000 American Institute of Physics.

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47.27.E-

Turbulence simulation and modeling