Phys. Fluids A (1989-1993) - Physics of Fluids

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Erosion of the basin of stability of a floating body as caused by dam breaking

E. Infeld, T. Lenkowska, and J. M. T. Thompson

Phys. Fluids A 5, 2315 (1993); http://dx.doi.org/10.1063/1.858794 (2 pages) | Cited 1 time

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The dam breaking problem in terms of changing water levels behind and ahead of the dam, has been solved in the shallow water model. Here the effect of dam breaking on a symmetric downstream floating body is considered. A forced Duffing equation model, proposed by one of the authors, is used. The analysis has practical implications in terms of how far a marina should be situated from a large dam. Comparison with basin erosion, as caused by a water surface soliton, is instructive.

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47.20.-k

Flow instabilities

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The pressure moments for two rigid spheres in low‐Reynolds‐number flow

D. J. Jeffrey, J. F. Morris, and J. F. Brady

Phys. Fluids A 5, 2317 (1993); http://dx.doi.org/10.1063/1.858795 (9 pages) | Cited 21 times

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The pressure moment of a rigid particle is defined to be the trace of the first moment of the surface stress acting on the particle. A Faxén law for the pressure moment of one spherical particle in a general low‐Reynolds‐number flow is found in terms of the ambient pressure, and the pressure moments of two rigid spheres immersed in a linear ambient flow are calculated using multipole expansions and lubrication theory. The results are expressed in terms of resistance functions, following the practice established in other interaction studies. The osmotic pressure in a dilute colloidal suspension at small Péclet number is then calculated, to second order in particle volume fraction, using these resistance functions. In a second application of the pressure moment, the suspension or particle‐phase pressure, used in two‐phase flow modeling, is calculated using Stokesian dynamics and results for the suspension pressure for a sheared cubic lattice are reported.

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47.15.G-	Low-Reynolds-number (creeping) flows
47.15.-x	Laminar flows
47.55.Kf	Particle-laden flows

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On the motion of small spherical bubbles in two‐dimensional vortical flows

G. R. Ruetsch and E. Meiburg

Phys. Fluids A 5, 2326 (1993); http://dx.doi.org/10.1063/1.858750 (16 pages) | Cited 12 times

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The motion of small, spherical noninteracting bubbles in two‐dimensional vortical flows by means of numerical simulations is investigated. After a discussion concerning the various bubble equations, bubble trajectories are calculated in a solid‐body vortex, where it is found that the bubble motion can be described in terms of the location where the bubbles accumulate, or equilibrium points, and the rate of entrapment into these equilibrium points. Of importance here is that the rate of entrapment into the vortex has an optimum value for some value of the inertia parameter, or inverse Stokes number. The bubble motion in a temporally evolving shear layer is investigated, where it is found that the solid‐body vortex model predicts the trends in the growth in concentration about the vortex center for the case without gravity. For the case with gravity, not all bubbles are captured by the vortex, and the percentage of bubbles captured increases with decreasing inertia parameter. Also discussed is how these factors affect the generation of the interface between regions seeded and not seeded with bubbles.

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47.55.Kf	Particle-laden flows
47.27.tb	Turbulent diffusion

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On evolution equations for thin films flowing down solid surfaces

Alexander L. Frenkel

Phys. Fluids A 5, 2342 (1993); http://dx.doi.org/10.1063/1.858895 (6 pages) | Cited 7 times

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A wavy free‐surface flow of a viscous film down a cylinder is considered. It is shown that if the cylinder radius is large, as compared to the film thickness, the long‐wave perturbation approach yields a rather simple evolution equation. This nonlinear equation is similar to the well‐known Benney equation of planar films, and becomes exactly the latter in the limit of infinite radius. Thus it is the annular‐case analog—which was missing in the literature—of the Benney equation. It is argued that under conditions implicitly implied in their derivation, the Benney‐type equations are not uniformly valid for large times. However, both the new and Benney equations are important heuristically—as sources of other, simpler, equations which, in certain domains of system parameters, are valid for all time. Also, the new equation of annular films is important as a qualitative model incorporating all significant physical factors.

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47.15.G-

Low-Reynolds-number (creeping) flows

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Taylor dispersion in porous media. Determination of the dispersion tensor

J. Salles, J.‐F. Thovert, R. Delannay, L. Prevors, J.‐L. Auriault, and P. M. Adler

Phys. Fluids A 5, 2348 (1993); http://dx.doi.org/10.1063/1.858751 (29 pages) | Cited 62 times

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In homogeneous porous media, the analytical expression of the dispersion tensor D∗ can be calculated by the method of moments and by a multiple scale expansion; the symmetric component of this tensor is identical in both cases. Numerically, D∗ can be computed by two methods, namely the B equation and random walks. The porous media are modeled as being spatially periodic; D∗ is determined as a function of the Péclet number for four types of unit cells: deterministic, fractal, random, and reconstructed. A systematic comparison is made with existing numerical and experimental data. The long time behavior, and its Gaussian limit, is documented.

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47.56.+r

Flows through porous media

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Numerical simulation and physical analysis of high Reynolds number recirculating flows behind sudden expansions

Yves Gagnon, André Giovannini, and Patrick Hébrard

Phys. Fluids A 5, 2377 (1993); http://dx.doi.org/10.1063/1.858752 (13 pages) | Cited 11 times

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This work presents the results of numerical simulations of unsteady recirculating flows at high Reynolds number. The two geometries investigated are a two‐dimensional channel that incorporates a sudden expansion in the form of a single backward‐facing step and a two‐dimensional channel that incorporates a sudden expansion in the form of a double symmetrical backward‐facing step. The random vortex method (RVM) is used in this study. This grid‐free Lagrangian method solves the unsteady, incompressible Navier–Stokes equations and the continuity equation, with the appropriate physical boundary conditions, using a formulation in vorticity variables. In order to show the ability of the RVM an extensive set of numerical results is presented and compared with experimental results from the literature. In particular, the dissymmetrical behavior of the flow in the double expansion channel, as observed experimentally, is simulated accurately. Frequency analyses and autocorrelation analyses show that the flows are characterized by dominant frequencies and turbulent length scales that are function of the position inside the channels. Those frequencies and turbulent length scales are related to the dynamics of the flow fields.

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47.60.-i

Flow phenomena in quasi-one-dimensional systems

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Hydrodynamic instability of a fluid layer flowing down a rotating cylinder

L. A. Dávalos‐Orozco and G. Ruiz‐Chavarría

Phys. Fluids A 5, 2390 (1993); http://dx.doi.org/10.1063/1.858753 (15 pages) | Cited 13 times

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In this paper the linear stability of a fluid layer flowing down the inside and outside of a rotating vertical cylinder is investigated. To this end, two approximations are made: the small wave number approximation and the small Reynolds number approximation. In the former, only the radial destabilizing effect of surface tension is important and may be counteracted by the centrifugal force at a critical value. In the latter, the analysis integrates the azimuthal modes different from m=0. It is shown that for flow outside the cylinder, the magnitude of centrifugal force and wave number may change the dominant mode of instability. For flow inside the cylinder, only the mode m=0 may be unstable. These results generalize those of Boudourides and Davis [Z. Angew. Math. Phys. 37, 597 (1986)] for swirling viscous flows.

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47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.32.-y	Vortex dynamics; rotating fluids

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Pulsatile flow in a rotating straight pipe: I. Analysis of the fluid motion inside a nutation fluid damper

U. Lei and C. F. Ho

Phys. Fluids A 5, 2405 (1993); http://dx.doi.org/10.1063/1.858754 (25 pages)

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Rigorous analysis shows that the spin synchronous mode fluid motion inside a nutation fluid damper on board of a spinning satellite can be modeled as an incompressible, laminar pulsatile flow in a circular straight pipe. The pipe rotates with constant angular velocity ω about an axis perpendicular to its own axis. The distance between the rotation axis and the pipe axis is much greater than a, the pipe’s radius. The flow is driven by a three‐dimensional harmonic oscillation of the pipe wall with frequency Ω and amplitude w^′₀, and is governed by three‐dimensionless parameters: R_Ω(=Ωa²/ν), Δ(=ω/Ω), and A( = w^′₀/Ωa), where ν is the kinematic viscosity of the fluid. Both the asymptotic analysis and the numerical calculation have been carried out for R_Ω=0.1–1000 and Δ=0–2 under A≪1. It is found that the rotating effect increases the energy dissipation significantly in comparison with the result of the pulsatile straight pipe flow in an inertia frame (the previous theory for the nutation damper). For Δ=1.5, the energy dissipation in a rotating pipe flow is 5.43 times that in a ‘‘stationary’’ pipe flow for large R_Ω, which agrees with the previous experiment. A steady stream is induced by the convective effect for finite values of A. Such steady motion is consisted of axial counter flows together with pairs of counter‐rotating vortices in the cross‐sectional plane.

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

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Three‐dimensional oscillatory convection in a gravitationally modulated fluid layer

R. Clever, G. Schubert, and F. H. Busse

Phys. Fluids A 5, 2430 (1993); http://dx.doi.org/10.1063/1.858755 (8 pages) | Cited 12 times

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The equations for three‐dimensional, time‐dependent convection in a gravitationally modulated fluid layer heated from below are solved numerically using the Galerkin method in space and a Crank–Nicolson scheme in time. Nonlinear solutions are obtained for the Prandtl number of air (0.71) and for two Rayleigh numbers above the value for onset of oscillatory convection. Multiples of the fundamental frequency of oscillatory convection were chosen in order to study the effects of possible resonances of the frequency of gravitational modulation. Modulation causes a transition from traveling wave convection, which persists in the unmodulated case, to standing wave convection and phase locking occurs for moderate values of the amplitude of the dimensionless gravitational modulation (scaled with the standard acceleration of gravity) in the range 0 to 3. For larger values of the modulation amplitude, frequency locking breaks down and chaotic time dependence occurs.

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47.20.Bp	Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.27.T-	Turbulent transport processes
44.25.+f	Natural convection

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Experimental observations of an unsteady detached shear layer in enclosed corotating disk flow

J. A. C. Humphrey and D. Gor

Phys. Fluids A 5, 2438 (1993); http://dx.doi.org/10.1063/1.858756 (5 pages) | Cited 10 times

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The flow in the unobstructed space between a pair of disks corotating at high speed in a fixed cylindrical enclosure can be divided into five regions amenable to theoretical analysis [C. A. Schuler, Ph.D. Thesis, University of California at Berkeley (1990); C. A. Schuler et al., Phys. Fluids A 2, 1760 (1990)]. One of these, region III in Fig. 2, is an axially‐aligned detached shear layer predicted by the analysis to be located at r_III/R₂≊Γ^1/2 and of thickness δ_III/R₂≊(2 Re)^−1/4, where R₂ is the radius of the disks, Re is the Reynolds number based on R₂ and the tip speed of rotation of the disks (ωR₂), and Γ is an experimentally determined constant. Through viscous diffusion, the detached shear layer allows the transition that must take place between the bulk of the three‐dimensional flow in the interdisk space (region II) and the two‐dimensional flow in solid body rotation surrounding the hub that spins the disks (region IV). Present findings, based on flow visualization, confirm these hitherto untested theoretical expressions and reveal that beyond a critical value of the Reynolds number the detached shear layer oscillates in the cross‐stream (r‐z) plane of the flow. The unsteadiness appears to originate at the enclosure side wall where the disk Ekman layers collide as a result of being redirected from the radial into the axial direction. These observations agree with the direct numerical simulations of Schuler [Ph.D. Thesis, University of California at Berkeley (1990)] which also show that the onset of flow unsteadiness in the cross‐stream plane coincides with the appearance of an integer number of circumferentially‐periodic large‐scale flow structures with large component of axial vorticity, of the type found by Hide and Titman [J. Fluid Mech. 29, 39 (1967)] in a similar flow configuration as of a critical value of the Reynolds number.

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47.32.-y

Vortex dynamics; rotating fluids

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Pressure gradient effect in natural convection boundary layers

F. J. Higuera and A. Liñán

Phys. Fluids A 5, 2443 (1993); http://dx.doi.org/10.1063/1.858757 (11 pages) | Cited 2 times

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The high Grashof number laminar natural convection flow around the lower stagnation point of a symmetric bowl‐shaped heated body is analyzed. A region is identified where the direct effect on the flow of the component of the buoyancy force tangential to the body surface is comparable to the indirect effect of the component normal to the surface, which acts through the gradient of the nonuniform pressure that it induces in the boundary layer. Analysis of this region provides a description of the evolution of the flow from a pressure‐gradient dominated regime to a buoyancy dominated regime. Numerical results are presented for the flows above and below heated power‐law body shapes, and the upstream propagation of small perturbations to the stationary flow is discussed. An asymptotic analysis is carried out for the flow below nearly flat horizontal bodies, for which the change from pressure‐gradient‐driven to buoyancy‐driven flow occurs very rapidly in a short region. The influence of body edges located in the region of interest is also discussed.

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47.27.T-

Turbulent transport processes

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Two‐dimensional jets falling from funnels and nozzles

Jongwoo Lee and Jean‐Marc Vanden‐Broeck

Phys. Fluids A 5, 2454 (1993); http://dx.doi.org/10.1063/1.858758 (7 pages) | Cited 8 times

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Two‐dimensional flow in a domain bounded on one side by an infinite rigid wall and on the other by a semi‐infinite rigid wall and a free surface is considered. Gravity is included in the free surface condition and surface tension is neglected. The flows are characterized by the parameters H=(Q²/gw³)^1/3 and the angles α and β between the walls and the horizontal. Here, Q is the total flux, g the acceleration of the gravity and w the distance between the separation point (the point of intersection of the free surface with the semi‐infinite wall) and the infinite wall. The configurations include, as particular cases, flows from nozzles and funnels, the Kirchhoff jet and the flow under a gate. Numerical solutions are computed by series truncation. It is shown that there are three distinct configurations at the separation point corresponding to contact angles 2π/3, π−α (horizontal free surface at the separation point), and π (free surface tangent to the rigid wall at the separation point). For given values of β and α≳π/3, there is a critical value H_c of the parameter H such that H=H_c for a contact angle of 2π/3, H≳H_c for a contact angle of π and H<H_c for a contact angle of π−α. On the other hand, for given values of β and α≤π/3, there is only one configuration with a contact angle of π. Free surface profiles are presented for various values of α, β, and H.

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47.15.km	Potential flows
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Experiments on the evolution of gravitational instability of an overturned, initially stably stratified fluid

S. I. Voropayev, Y. D. Afanasyev, and G. J. F. van Heijst

Phys. Fluids A 5, 2461 (1993); http://dx.doi.org/10.1063/1.858759 (6 pages) | Cited 14 times

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Unstable density stratifications were created in the laboratory by rapid overturning of a narrow tank containing an initially stable density structure. The experiments were carried out for two different initial density distributions: (i) a two‐layer (steplike) and (ii) a linear stratification. For the former case the depth of the mixing layer was found to increase linearly with time. The number of convective elements (thermal‐like flow structures) present at the front of the mixing layer was observed to decrease with time, through the mechanism of subsequent pairing. In the case of an initially linear stratification the flow evolution is characterized by a number of distinct stages: different modes of instability emerge subsequently through the entire fluid column, leading to the formation of horizontal layers, which finally break up into thermal‐like convective flow structures.

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47.20.Bp

Buoyancy-driven instabilities (e.g., Rayleigh-Benard)

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Differential diffusion of passive scalars in isotropic turbulence

P. K. Yeung and S. B. Pope

Phys. Fluids A 5, 2467 (1993); http://dx.doi.org/10.1063/1.858760 (12 pages) | Cited 30 times

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The differential diffusion of passive scalars of different molecular diffusivities is studied by performing direct numerical simulations of scalar fields in statistically stationary isotropic turbulence at Taylor‐scale Reynolds number 38. Starting from identical initial conditions, each scalar field eventually becomes self‐similar, with constant length scale and with its variance decaying exponentially with time. This decay rate depends weakly on the diffusivity. The correlation coefficient between two scalars initially decreases rapidly, but subsequently evolves much more slowly. The scalars ultimately become completely decorrelated at all scales. The scale dependency of correlation is studied through the coherency spectrum, which is affected only indirectly by the diffusivity difference. A Fourier‐spectral approach emphasizes the importance of interscale spectral transfer of multiple scalars due to turbulent advection. Small‐time behavior is compared with an analysis based on the diffusion equation.

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47.27.-i	Turbulent flows
47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.27.tb	Turbulent diffusion

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Chaotic scattering of two identical point vortex pairs

Tim Price

Phys. Fluids A 5, 2479 (1993); http://dx.doi.org/10.1063/1.858761 (5 pages) | Cited 2 times

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The scattering dynamics of two vortex pairs with equal circulations ±κ have hitherto been thought to be regular, in contrast to the case of nonidentical pairs where a hierarchy of resonant states gives rise to chaotic behavior. However, no rigorous explanation could be found for such regularity occurring in a nonintegrable Hamiltonian system. This was recently posed as an open problem [H. Aref et al., Fluid Dyn. Res. 3, 63 (1988)], and in this paper the problem is resolved by presenting a counter‐example mechanism which yields chaotic scattering dynamics when the initial pair spacings differ markedly. Alternative modes of scattering are characterized by symbolic sequences. These predictions are confirmed by numerical experiments which also show that the chaos persists even when the initial spacings are nearly equal, although the physical origin of the irregular scattering is less clear. Regular behavior is seen only in the integrable case of equal initial pair spacings.

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47.15.ki	Inviscid flows with vorticity
47.52.+j	Chaos in fluid dynamics
47.10.-g	General theory in fluid dynamics

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Statistical mechanics and correlation properties of a rotating two‐dimensional flow of like‐sign vortices

J. A. Viecelli

Phys. Fluids A 5, 2484 (1993); http://dx.doi.org/10.1063/1.858762 (18 pages) | Cited 11 times

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The Hamiltonian flow of a set of point vortices of like sign and strength has a low‐temperature phase consisting of a rotating triangular lattice of vortices, and a normal temperature turbulent phase consisting of random clusters of vorticity that orbit about a common center along random tracks. The mean‐field flow in the normal temperature phase has similarities with turbulent quasi‐two‐dimensional rotating laboratory and geophysical flows, whereas the low‐temperature phase displays effects associated with quantum fluids. In the normal temperature phase the vortices follow power‐law clustering distributions, while in the time domain random interval modulation of the vortex orbit radii fluctuations produces singular fractional exponent power‐law low‐frequency spectra corresponding to time autocorrelation functions with fractional exponent power‐law tails. Enhanced diffusion is present in the turbulent state, whereas in the solid‐body rotation state vortices thermally diffuse across the lattice. Over the entire temperature range the interaction energy of a single vortex in the field of the rest of the vortices follows positive temperature Fermi–Dirac statistics, with the zero temperature limit corresponding to the rotating crystal phase, and the infinite temperature limit corresponding to a Maxwellian distribution. Analyses of weather records dependent on the large‐scale quasi‐two‐dimensional atmospheric circulation suggest the presence of singular fractional exponent power‐law spectra and fractional exponent power‐law autocorrelation tails, consistent with the theory.

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47.32.C-	Vortex dynamics
05.20.Gg	Classical ensemble theory

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Structure of the velocity field associated with the spanwise vorticity in the wall region of a turbulent boundary layer

S. Rajagopalan and R. A. Antonia

Phys. Fluids A 5, 2502 (1993); http://dx.doi.org/10.1063/1.858763 (9 pages) | Cited 10 times

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Measurements of the spanwise vorticity fluctuation ω_z were made in a low Reynolds number turbulent boundary layer with a four‐hot‐wire probe. Measurements of the longitudinal velocity fluctuation u_p were also made with a single hot wire located at a fixed position near the edge of the viscous sublayer. The simultaneously sampled data are used to gain some insight into the vortical structure of the flow in the wall region. The large negative correlation coefficient between u_p and ω_z near the wall may be due partly to a sweeplike motion associated with negative ω_z and partly to the association between low‐speed fluid and positive ω_z. Spanwise vorticity fluctuations near the wall are, in general, negatively correlated with those in the outer part of the buffer region. This result is consistent with the effect of the wall on the velocity field induced by relatively strong vortices of the same sign as the mean shear. It is also consistent with the arrival in the wall region of eddies which rotate in the opposite direction to the mean shear. Conditional averages of the velocity field associated with both positive and negative ω_z detections are compared with those obtained from detections of various different features of the organized motion in the wall region. These averages support the conclusions inferred from the correlation between u_p and ω_z.

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47.27.N-	Wall-bounded shear flow turbulence
47.27.nb	Boundary layer turbulence

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Interacting scales and energy transfer in isotropic turbulence

Ye Zhou

Phys. Fluids A 5, 2511 (1993); http://dx.doi.org/10.1063/1.858764 (14 pages) | Cited 46 times

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The dependence of the energy transfer process on the disparity of the interacting scales is investigated in the inertial and far‐dissipation ranges of isotropic turbulence. The strategy for generating the simulated flow fields and the choice of a disparity parameter to characterize the scaling of the interactions is discussed. The inertial range is found to be dominated by relatively local interactions, in agreement with the Kolmogorov assumption. The far‐dissipation range is found to be dominated by relatively nonlocal interactions, supporting the classical notion that the far‐dissipation range is slaved to the Kolmogorov scales. The measured energy transfer is compared with the classical models of Heisenberg [Z. Phys. 124, 628 (1948)], Obukhov [Isv. Geogr. Geophys. Ser. 13, 58 (1949)] and the more detailed analysis of Tennekes and Lumley [The First Course of Turbulence (MIT Press, Cambridge, MA, 1972)]. The energy transfer statistics measured in the numerically simulated flows are found to be nearly self‐similar for wave numbers in the inertial range. Using the self‐similar form measured within the limited scale range of the simulation, an ‘‘ideal’’ energy transfer function and the corresponding energy flux rate for an inertial range of infinite extent are constructed. From this flux rate the Kolmogorov constant is calculated to be 1.5, in excellent agreement with experiments [A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. 2].

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47.27.Gs

Isotropic turbulence; homogeneous turbulence

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Skewed, exponential pressure distributions from Gaussian velocities

Mark Holzer and Eric Siggia

Phys. Fluids A 5, 2525 (1993); http://dx.doi.org/10.1063/1.858765 (8 pages) | Cited 12 times

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A simple analytical argument is given to show that the distribution function of the pressure and that of its gradient have exponential tails when the velocity is Gaussian. A calculation of moments implies a negative skewness for the pressure. Explicit analytical results are given for the case of the velocity being restricted to a shell in wave number. Numerical pressure distributions are presented for Gaussian velocities with realistic spectra. For real turbulent flows, one expects that the pressure distribution should retain exponential tails while the pressure gradients should develop stretched‐exponential distributions. In the context of the theory, available numerical and laboratory data are examined for the pressure, along with data for the wall shear stress in a boundary layer.

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47.27.Sd	Turbulence generated noise
47.27.Gs	Isotropic turbulence; homogeneous turbulence

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Further results on multifractality in shell models

D. Pisarenko, L. Biferale, D. Courvoisier, U. Frisch, and M. Vergassola

Phys. Fluids A 5, 2533 (1993); http://dx.doi.org/10.1063/1.858766 (6 pages) | Cited 52 times

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Very long integrations, involving hundreds of millions of time steps, have been performed for the Gledzer–Ohkitana–Yamada ‘‘shell model’’ of fully developed turbulence, thereby allowing the computation of essentially noise‐free structure functions at all inertial‐ and dissipation‐range scales. Previously reported results by Jensen et al. [Phys. Rev. A 43, 798 (1991)] on the multifractal behavior of this model are confirmed. Oscillations in the structure functions are found to be genuine. An exact relation for certain cubic moments, equivalent to Kolmogorov’s four‐fifth law, is derived and tested. The third‐order structure function, here defined in terms of the third moment of shell amplitudes, is not directly determined by this relation and need not have its exponent equal to one. Significant discrepancies are actually found when the ratio between successive shell wave numbers is less than two.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.52.+j	Chaos in fluid dynamics
47.53.+n	Fractals in fluid dynamics
02.60.Cb	Numerical simulation; solution of equations

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Turbulence amplification by a shock wave and rapid distortion theory

L. Jacquin, C. Cambon, and E. Blin

Phys. Fluids A 5, 2539 (1993); http://dx.doi.org/10.1063/1.858767 (12 pages) | Cited 19 times

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Amplification of turbulent kinetic energy in an axial compression is examined in the frame of homogeneous rapid distortion theory (RDT) by using the Craya–Herring formalism. By separating the turbulent field into solenoidal and dilatational modes (Helmholtz decomposition), one can show the dilatational mode is mediated by the parameter Δm₀=D₀/a₀k₀, which corresponds to the initial ratio between the acoustic time scale (a₀k₀)⁻¹ and the compression time scale D₀⁻¹, with D₀ the compression rate. It is shown here that amplification of total kinetic energy is then limited by two analytical solutions obtained for Δm₀=0 (purely solenoidal‐acoustical regime) and for Δm₀≫1 (‘‘pressure released’’ regime), respectively. The results of the theory are first compared to results of direct numerical simulations (DNS) on homogeneous axial compression. The applicability of this homogeneous approach to the shock wave turbulence interaction, is then discussed. Considering a shock‐induced compression at given Mach number, it is shown that the corresponding amplification factors predicted by homogeneous RDT largely differs from that obtained from Ribner’s linear interaction analysis and DNS on the shock problem.

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47.10.-g	General theory in fluid dynamics
47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.40.Nm	Shock wave interactions and shock effects

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On the absence of motion in certain nonequilibrium states of gases and vapors in free‐molecular regime: General considerations and pipe flow

Carlo Cercignani, Aldo Frezzotti, and Mikhail N. Kogan

Phys. Fluids A 5, 2551 (1993); http://dx.doi.org/10.1063/1.858768 (6 pages) | Cited 3 times

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This paper is devoted to the discussion of certain nonequilibrium states of gases and vapors in the free‐molecular regime. In spite of the presence of temperature differences and, in some cases, of evaporation and condensation processes, the gas is shown to remain at rest. The case of a vapor in a tube of condensed phase, for which some numerical solutions are also given, is treated in some detail.

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47.45.Dt

Free molecular flows

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A lattice Boltzmann model for multiphase fluid flows

Daryl Grunau, Shiyi Chen, and Kenneth Eggert

Phys. Fluids A 5, 2557 (1993); http://dx.doi.org/10.1063/1.858769 (6 pages) | Cited 77 times

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A lattice Boltzmann equation method for simulating multiphase immiscible fluid flows with variation of density and viscosity, based on the model proposed by Gunstensen et al. for two‐component immiscible fluids [Phys. Rev. A 43, 4320 (1991)] is developed. The numerical measurements of surface tension and viscosity agree well with theoretical predictions. Several basic numerical tests, including spinodal decomposition, two‐phase fluid flows in two‐dimensional channels, and two‐phase viscous fingering, are shown in agreement of experiments and analytical solutions.

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47.55.Kf	Particle-laden flows
47.20.Dr	Surface-tension-driven instability

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Effective diffusion in time‐periodic linear planar flow

Alexandra Indeikina and Hsueh‐Chia Chang

Phys. Fluids A 5, 2563 (1993); http://dx.doi.org/10.1063/1.858770 (4 pages) | Cited 3 times

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It is shown that when a point source of solute is inserted into a time‐periodic, unbounded linear planar flow, the large‐time, time‐average transport of the solute can be described by classical anisotropic diffusion with constant effective diffusion tensors. For a given vorticity and forcing period, elongational flow is shown to be the most dispersive followed by simple shear and rotational flow. Large‐time diffusivity along the major axis of the time‐average concentration ellipse, whose alignment is predicted from the theory, is shown to increase with vorticity for all flows and decrease with increasing forcing frequency for elongational flow and simple shear. For the interesting case of rotational flow, there exist discrete resonant frequencies where the time‐average major diffusivity reaches local maxima equal to the time‐average steady flow case with zero forcing frequency.

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47.10.-g

General theory in fluid dynamics

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An interpretation of the translation of drops and bubbles at high Reynolds numbers in terms of the vorticity field

H. A. Stone

Phys. Fluids A 5, 2567 (1993); http://dx.doi.org/10.1063/1.858771 (3 pages) | Cited 8 times

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The steady translation of a drop is reconsidered in the high Reynolds number flow limit, R≫1. The standard approach for determining the drag on a spherical drop is to calculate the total energy dissipation in the fluid with the velocity field approximated using the potential flow solution outside the drop and Hill’s spherical vortex inside. Kang and Leal [Phys. Fluids 31, 233 (1988)] provide the first calculation of the drag for a spherical bubble by integrating the normal stresses over the bubble surface. Their detailed calculation shows that the drag coefficient up to O(R⁻¹) depends only on the O(1) vorticity distribution along the bubble surface and is independent of the vorticity distribution in the fluid. Here, this conclusion regarding the role of vorticity is extended to the case of any steady high Reynolds number bubble shape compatible with the steady translational speed; there is no restriction to sphericity. The results are demonstrated without explicit calculations and follow from the representation of the energy dissipation for translating drops in terms of the vorticity field.

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Show PACS

47.55.Kf	Particle-laden flows
47.15.Cb	Laminar boundary layers
47.15.ki	Inviscid flows with vorticity
47.10.-g	General theory in fluid dynamics

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Oct 1993

Volume 5, Issue 10, pp. 2315-2572

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