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

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Characterization of vortex tubes and sheets

Mitsuru Tanaka and Shigeo Kida

Phys. Fluids A 5, 2079 (1993); http://dx.doi.org/10.1063/1.858546 (4 pages) | Cited 45 times

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Vortex structure is characterized in terms of the magnitude of the vorticity and strain rate. High vorticity with relatively low strain rate represents the vortex tube, and high vorticity with comparable strain rate the vortex sheet. The regions of high Laplacian of pressure and of high strain rate also represent the tubelike and sheetlike structures, respectively.

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47.10.-g	General theory in fluid dynamics
47.27.Ak	Fundamentals
47.32.C-	Vortex dynamics

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Eddy Rossby wave frequency in β‐plane turbulence

Boris Galperin, Semion Sukoriansky, and Ilya Staroselsky

Phys. Fluids A 5, 2083 (1993); http://dx.doi.org/10.1063/1.858547 (3 pages) | Cited 1 time

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The concept of eddy viscosity is generalized to include an ‘‘eddy β‐term’’ that accounts for the effect of unresolved turbulence and Rossby waves on the resolved modes in the subgrid‐scale representation of β‐plane turbulence.

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92.10.Lq	Turbulence, diffusion, and mixing processes in oceanography
47.32.-y	Vortex dynamics; rotating fluids
47.27.E-	Turbulence simulation and modeling

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Some asymmetric Stokes flows that are structurally similar

A. M. J. Davis

Phys. Fluids A 5, 2086 (1993); http://dx.doi.org/10.1063/1.858548 (9 pages) | Cited 5 times

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This paper considers the creeping flows generated by a disk moving edgewise parallel to a rigid wall or free surface, a disk oscillating edgewise in unbounded fluid and a hole in the rigid plane that bounds a shear flow excited by a parallel moving plane. The analyses for the three cases follow a similar pattern and several simplifying strategies are introduced to obtain significant improvements on the presentations suggested by previous work on such flows. Indeed, the resulting integral equations for the first disk problem are similar to those solved for the corresponding broadside motion. The drag force is shown to slowly approach its limit value as the disk is placed nearer to the free surface. The oscillatory hydrodynamic force is shown to have only Stokes and Basset components. The error in previously assuming the shear flow to extend to infinity is shown to be of order H⁻³, where H is the separation distance between the bounding planes.

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47.15.G-

Low-Reynolds-number (creeping) flows

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A hydrodynamic model of the oscillating screen viscometer

A. M. J. Davis

Phys. Fluids A 5, 2095 (1993); http://dx.doi.org/10.1063/1.858549 (9 pages) | Cited 3 times

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The viscometer consists of an oscillating screen immersed in a fluid and free to rotate about an axis in its plane. The viscosity can be determined from the measured ratio of the periodic driving force to the screen motion when an adequate hydrodynamical model of the immersed oscillator is available. The screen is formed by a square mesh of thin wire whose dimensions invite comparison with asymptotic results for narrow hollow bodies translating in Stokes flow. These indicate that the closed hole structure of the grid plays an important role in determining its motion. It is shown that this role diminishes as the frequency increases. The computed results, obtained from a system of linear equations, are consistent with experimental values over the appropriate range of frequency.

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47.15.G-	Low-Reynolds-number (creeping) flows
47.80.-v	Instrumentation and measurement methods in fluid dynamics
83.85.Jn	Viscosity measurements

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The force on a bubble, drop, or particle in arbitrary time‐dependent motion at small Reynolds number

Phillip M. Lovalenti and John F. Brady

Phys. Fluids A 5, 2104 (1993); http://dx.doi.org/10.1063/1.858550 (13 pages) | Cited 26 times

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The hydrodynamic force on a body that undergoes translational acceleration in an unbounded fluid at low Reynolds number is considered. The results extend the prior analysis of Lovalenti and Brady [to appear in J. Fluid Mech. (1993)] for rigid particles to drops and bubbles. Similar behavior is shown in that, with the inclusion of convective inertia, the long‐time temporal decay of the force (or the approach to steady state) at finite Reynolds number is faster than the t^−1/2 predicted by the unsteady Stokes equations.

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47.10.-g	General theory in fluid dynamics
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 interpretation of phase measurements of oscillatory thermocapillary convection in liquid bridges

Hendrik C. Kuhlmann and Hans J. Rath

Phys. Fluids A 5, 2117 (1993); http://dx.doi.org/10.1063/1.858551 (4 pages) | Cited 7 times

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In their study of time‐dependent thermocapillary convection in cylindrical liquid bridges Velten et al. [Phys. Fluids A 3, 267 (1991)] determined the azimuthal flow structure by measuring the phase of the temperature oscillations at three different azimuthal angles. Their explanation of the data in terms of modes with wave number m=0 is not always compatible with the normal‐mode decomposition of the disturbances at the threshold. A new interpretation is given that explains the peculiar phase measurements in terms of pairs of m≠0 counterpropagating waves.

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47.20.-k	Flow instabilities
47.20.Dr	Surface-tension-driven instability
47.35.-i	Hydrodynamic waves

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Nonlinear dynamics of liquid columns: A comparative study

R. M. S. M. Schulkes

Phys. Fluids A 5, 2121 (1993); http://dx.doi.org/10.1063/1.858552 (10 pages) | Cited 23 times

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One‐dimensional models have been used extensively over the past decade to study liquid columns. While the range of validity of these models is well known in the linear limit, this is not the case when nonlinear effects are important. By comparing results of a number of one‐dimensional models with results based on a velocity‐potential model in which no approximations have been made, the present aim is to establish exactly when the one‐dimensional models are applicable. First of all it is shown how the Cosserat equations in the inviscid limit may be obtained formally from the Euler equations. Subsequently, a linearized form of the Cosserat equations is derived and results of this model are compared with results obtained by means of the well‐established inviscid‐slice model and results obtained by the velocity‐potential approach. It is found that the applicability of the inviscid‐slice model is limited by short‐wavelength effects rather than amplitude effects. The range of validity of the inviscid‐slice model can be extended by including radial momentum contributions. However, even with the inclusion of radial momentum effects the one‐dimensional models are not well suited to describe the behavior close to the bifurcation point.

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47.20.Dr	Surface-tension-driven instability
47.15.km	Potential flows

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A numerical study of the effect of surface tension and noise on an expanding Hele–Shaw bubble

Wei‐Shen Dai and Michael J. Shelley

Phys. Fluids A 5, 2131 (1993); http://dx.doi.org/10.1063/1.858553 (16 pages) | Cited 19 times

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In this paper, the dynamics of an interface under the influence of surface tension is studied numerically for flow in the Hele–Shaw cell, where the interface separates an expanding bubble of inviscid fluid from a displaced viscous fluid. Of special interest is the long–time behavior of the so‐called q‐pole initial data, whose motion is explicitly known and globally smooth for the zero surface tension flow. The numerical method is spectrally accurate and based upon a boundary integral formulation of the problem, together with a special choice for the frame of motion along the interface. In 64‐bit arithmetic, a transition from the formation of side branches to tip splitting is observed as the surface tension is decreased. The tip splitting occurs on a time scale that decreases with the surface tension. This is consistent with some experimental observations. However, by increasing the arithmetic precision to 128 bits, it is found that this transition occurs at a yet smaller surface tension. The tip splitting is associated with the growth of noise in the calculation at unstable scales allowed by the surface tension, and a simple linear model of this growth seems to agree well with the observed behavior. The robustness of the various observed structures to varying amounts of noise is also investigated numerically. It is found that the appearance of side branches seems to be the intrinsic effect of surface tension, and the time scales for their appearance increases as the surface tension decreases. These results suggest, with some qualification, that surface tension acts as a regular perturbation to evolution from this initial data, even for long times.

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47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.10.-g	General theory in fluid dynamics
47.15.km	Potential flows

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Chaotic mixing in a spatially periodic continuous mixer

F. H. Ling

Phys. Fluids A 5, 2147 (1993); http://dx.doi.org/10.1063/1.858554 (14 pages) | Cited 15 times

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Mixing in a spatially periodic continuous mixer, the partitioned pipe mixer, is studied using bifurcation analysis with the help of geometric construction of periodic orbits and a knowledge of the symmetry of the mixing system. Mixing windows, where motion in the mixer is nearly globally chaotic, are found in the parameter space. Uniform ultimate mixtures are expected in the mixing windows as verified with the Poincaré sections. The present analysis provides a better understanding of the existing experimental results.

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47.15.-x	Laminar flows
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.52.+j	Chaos in fluid dynamics

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Linear stability of shear profiles and relation to the secondary instability of the Dean flow

Cédric Le Cunff and Alessandro Bottaro

Phys. Fluids A 5, 2161 (1993); http://dx.doi.org/10.1063/1.858555 (11 pages) | Cited 4 times

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Solutions of the Navier–Stokes equations for flow in a curved channel have previously been computed [Bottaro, J. Fluid Mech. 251, 627 (1993)] and the spatial development of the Dean flow is available at different supercritical Reynolds number. In this work the viscous instability of local longitudinal vortex structures (obtained from the nonlinear simulations) is investigated, with a focus toward the secondary instability of Dean vortices. Such a secondary instability takes the form of streamwise traveling waves. High‐frequency waves are termed twisting waves, low frequency are defined undulating waves. Instead of performing analyses in which the basic flow in the cross section is two dimensional, significant shear profiles along y and z are considered as base flows at constant x before the establishment of a fully developed state. Thus one is able to discover that the twist instability is of shear type and is caused by inflectional spanwise profiles of the streamwise velocity component. Sinuous waves are always preferred to varicose waves, and the latter mode of instability is destabilized only at large Reynolds numbers. Undulating waves are related to normal profiles of the streamwise velocity; this type of secondary instability is of centrifugal origin. Results of the analyses for both types of waves are in good agreement with experiments.

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47.20.Ft

Instability of shear flows (e.g., Kelvin-Helmholtz)

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Cross‐diffusion effects on the stability criteria in a triply diffusive system

Guillermo Terrones

Phys. Fluids A 5, 2172 (1993); http://dx.doi.org/10.1063/1.858556 (11 pages) | Cited 4 times

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The effects of cross‐diffusion on the onset of convective instability in a horizontally unbounded, triply diffusive, and triply stratified fluid layer (triply cross‐diffusive fluid layer) are investigated. Analytical solutions are obtained for steady and oscillatory onset when imposed gradients of the stratifying agencies are constant and vertical. Numerical results are based on diffusivity data for the system water/potassium chloride/potassium phosphate/phosphoric acid solution. Depending on the magnitude of the stratifying agencies, linear stability analysis shows that cross‐diffusion can either stabilize or destabilize a fluid layer. The off‐diagonal elements of the diffusivity matrix, which arise naturally as a result of the coupling among the various stratifying agencies, may strongly affect boundaries of convective stability and neutral curves. Discrepancies in the linear stability criteria were observed for seemingly negligible off‐diagonal elements of the diffusivity matrix.

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47.20.Bp	Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.55.Hd	Stratified flows

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Hysteresis in a swirling jet as a model tornado

V. Shtern and F. Hussain

Phys. Fluids A 5, 2183 (1993); http://dx.doi.org/10.1063/1.858888 (13 pages) | Cited 18 times

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A swirling jet, emerging normal to a plane, serves as a model of a tornado and is characterized by its flow force and outer circulation. This model is examined here using the full Navier–Stokes equations. Three branches of solutions are found which form a hysteresis loop and a cusp catastrophe that means jump transitions between flow regimes. One of the jumps relates to vortex breakdown and the other relates to a new (opposite) effect: abrupt vortex consolidation. These results are compared with those of Long [J. Fluid Mech. 11, 611 (1961)], who considered a near‐axis jet in the boundary layer approximation. More detailed analysis made here for high circulation values allows discovery of two new types of asymptotic solutions corresponding to a near‐plane fan jet and a two‐cell flow. It was also found that the boundary layer approach for the near‐axis jet fails to accurately yield the total flow force because the outer flow contributes a share of the momentum flux of comparable magnitude to that of the inner flow. The prediction of the jump transitions between one‐ and two‐cell flow patterns agrees with observations of abrupt changes in tornado patterns in nature.

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47.15.-x	Laminar flows
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking

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Vortex dipoles impinging on circular cylinders

P. Orlandi

Phys. Fluids A 5, 2196 (1993); http://dx.doi.org/10.1063/1.858557 (11 pages) | Cited 4 times

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Vortex pairs interacting with a circular cylinder have been simulated by the numerical simulation of the two‐dimensional Navier–Stokes equation in the vorticity streamfunction formulation. The interaction with a cylinder with a diameter equal to the diameter of the dipole has been simulated in the inviscid case with free‐slip boundaries. This case has been considered as a way to perturb the initial dipole, which splits into two vortices that rejoin at a different location on the cylinder depending on the initial displacement of the cylinder from the centerline of the primary vortex pair. By the scatter plots it was shown that the Lamb dipole after the perturbation relaxes to its initial k²ψ functional relationship. The case of no‐slip interaction has been considered when the cylinder is two orders of magnitude smaller than the dipole. The same features observed in the experiment of Homa et al. [J. Fluid Mech. 197, 571 (1988)] are obtained by the numerical simulations, that is a thin vorticity layer is generated at the cylinder, it rolls up and forms dipolar and tripolar structures, depending on the initial displacement of the cylinder from the centerline of the incoming dipole. Scatter plots of the vortex pair formed by the primary and secondary vorticity show a linear distribution similar to that of the Lamb dipole. The dependence on the Reynolds number has been investigated.

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47.15.-x

Laminar flows

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Navier–Stokes relaxation to sinh–Poisson states at finite Reynolds numbers

David Montgomery, Xiaowen Shan, and William H. Matthaeus

Phys. Fluids A 5, 2207 (1993); http://dx.doi.org/10.1063/1.858558 (10 pages) | Cited 30 times

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A mathematical framework is proposed in which it seems possible to justify the computationally‐observed relaxation of a two‐dimensional Navier–Stokes fluid to a ‘‘most probable,’’ or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher‐order ideal invariants such as enstrophy. A two‐fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean‐square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two‐fluid field variables.

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47.27.-i	Turbulent flows
05.70.Ln	Nonequilibrium and irreversible thermodynamics
47.90.+a	Other topics in fluid dynamics (restricted to new topics in section 47)

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Instability of a supersonic vortex sheet inside a circular duct

Chien‐Cheng Chang and Chih‐Yu Kuo

Phys. Fluids A 5, 2217 (1993); http://dx.doi.org/10.1063/1.858559 (12 pages)

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A theoretical study is carried out for investigating spatial instabilities of a supersonic vortex sheet inside a circular duct. The sheet is cylindrical in shape, separating the flow into an inner region and an outer one of uniform properties. It is found that there is one family of subsonic (Kelvin–Helmholtz) instability waves which are accompanied by two families of neutral modes. Two families of supersonic instability waves can be identified to be associated with two other families of neutral modes. A mathematical analogy indicates that instability modes at high frequencies bear resemblance to those obtained by Tam and Hu [J. Fluid. Mech. 203, 51 (1989).] for plane mixing layers inside a rectangular channel. Geometric effects of both the vortex sheet and the outer confinement are significant only at relatively low frequencies of disturbances. In addition, extensive parametric study reveals interesting features of the dependence of the instability waves on the density ratio, velocity ratio, radius ratio of the inner and outer regions, and three‐dimensional disturbances.

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47.20.-k	Flow instabilities
47.27.wg	Turbulent jets
47.40.Ki	Supersonic and hypersonic flows

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Nonexistence of Lyapunov functions and the instability of the von Kármán vortex streets

Chjan Lim

Phys. Fluids A 5, 2229 (1993); http://dx.doi.org/10.1063/1.858560 (5 pages) | Cited 1 time

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The instability of the von Kármán vortex streets and the existence of a global Lyapunov function at the special aspect ratio h/l=(1/π)sinh⁻¹(1), are some of the difficulties with the well‐known von Kármán model. By consistently applying the principle of genericity, its shown that a new family of near‐equilibrium periodic solutions of the von Kármán model for aspect ratios near 0.281... supplies numerous theoretical candidates for observed vortex trails. This set of solutions implies that there is no global Lyapunov functions when h/l≠(1/π)sinh⁻¹(1) which in turn leads to a rich variety of near‐equilibrium solutions for the model.

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47.15.ki	Inviscid flows with vorticity
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.27.wb	Turbulent wakes

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A note on the probability distribution of the dissipation rate in locally isotropic turbulence

Tianshu Liu

Phys. Fluids A 5, 2234 (1993); http://dx.doi.org/10.1063/1.858561 (5 pages) | Cited 1 time

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A nonlinear random differential equation describing the magnitude of vorticity is given for fine vortex tube in locally isotropic turbulence. From this vortex dynamics model, the asymptotic expressions of the probability density function of the dissipation rate in locally isotropic turbulence are obtained. In particular, several physical mechanisms behind turbulence statistics are explored.

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47.27.Gs

Isotropic turbulence; homogeneous turbulence

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The dynamics of shock accelerated light and heavy gas cylinders

J. W. Jacobs

Phys. Fluids A 5, 2239 (1993); http://dx.doi.org/10.1063/1.858562 (9 pages) | Cited 34 times

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Experiments have been carried out in which a cylindrical volume of a gas, that is either lighter or heavier than its surroundings, is impulsively accelerated by a weak shock wave. Laminar jets of helium or sulphur hexafluoride (SF₆) are used to produce the cylinders, and planar laser‐induced fluorescence is used to visualize the flow. It is found that the vorticity deposited on the boundary of the SF₆ cylinder by the interaction with the shock wave, separates from the heavy gas to form a pair of vortices, which subsequently wrap the SF₆ around them. This process is quite different from what is observed in the light gas experiments, which showed a small amount of helium to remain with the vorticity, eventually becoming part of the vortex cores. Centrifugal forces combined with differences in the rates of the diffusion of vorticity in the two gases are given as possible reasons for these differences. Measurement of the initial downstream velocity for a heavy gas cylinder is found to agree well with a theory based on two simple models. But, because diffusion causes the light gas jet density to be significantly greater than that of pure helium, the theory overpredicts the measured velocity of the light gas experiments. The final translational velocities for both light and heavy gas experiments are not accurately predicted by the model, and measurements of the vortex spacing are found to be significantly larger than those indicated by this theory. These differences are likely caused by the theory’s inability to accurately describe the viscous nonuniform flow.

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47.40.Nm	Shock wave interactions and shock effects
47.55.-t	Multiphase and stratified flows
47.32.-y	Vortex dynamics; rotating fluids

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On the variational method of closure in the theory of turbulence

S. V. Bazdenkov and N. N. Kukharkin

Phys. Fluids A 5, 2248 (1993); http://dx.doi.org/10.1063/1.858563 (7 pages) | Cited 5 times

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The variational approach to the closure problem of turbulence theory with particular attention to the perturbation–variation method of Qian [Phys. Fluids 26, 2098 (1983)] is studied. It is shown that although the method is based on a clear physical idea, it is not self‐consistent. The procedure to obtain the equation for the dynamic damping coefficient does contain arbitrariness, which leads to the dependence of this equation on the choice of variables. This ambiguity is illustrated by numerical evaluations of the Kolmogorov constant in two‐dimensional and three‐dimensional cases. The equation for the dynamic damping coefficient, which is invariant, with respect to the change of variables, is obtained and analyzed. The principal inevitability of arbitrariness in closure methods is discussed.

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47.27.-i

Turbulent flows

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Probability distributions and thermal transport in a turbulent grid flow

B. R. Lane, O. N. Mesquita, S. R. Meyers, and J. P. Gollub

Phys. Fluids A 5, 2255 (1993); http://dx.doi.org/10.1063/1.858564 (9 pages) | Cited 17 times

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Recent theoretical proposals concerning non‐Gaussian statistics of passive scalars in random velocity fields are tested experimentally, by measuring the probability distributions of fluctuating temperature in an oscillating grid flow across which a steady temperature gradient is maintained. Pronounced exponential tails occur at sufficiently high Reynolds number R, and predominantly Gaussian statistics at low R. When the extended tails are present for the passive scalar, the corresponding velocity power spectrum shows reasonable scaling, and the velocity distribution is not far from Gaussian. The present paper provides a more complete characterization of the flow field than an earlier brief report [Phys. Rev. Lett. 67, 3507 (1991)], and also contains a description of additional features, such as the skewness of the distributions. Finally, the effective or eddy diffusivity of both heat and a molecular impurity are measured and compared.

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47.27.tb	Turbulent diffusion
05.40.-a	Fluctuation phenomena, random processes, noise, and Brownian motion

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Statistics of an advected passive scalar

Yoshifumi Kimura and Robert H. Kraichnan

Phys. Fluids A 5, 2264 (1993); http://dx.doi.org/10.1063/1.858530 (14 pages) | Cited 32 times

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An elementary argument shows that non‐Gaussian fluctuations in the temperature at a point in space are induced by random advection of a passive temperature field that has a nonlinear mean gradient, whether or not there is molecular diffusion. This is corroborated by exact analysis for the nondiffusive case and by direct numerical simulation for diffusive cases. Eulerian mapping closure gives results close to the simulation data. Non‐Gaussian fluctuations of temperature at a point also are induced by a more subtle mechanism that requires both advection and molecular diffusion and is effective even when the statistics are strictly homogeneous. It operates through selectively strong dissipation of regions where intense temperature gradients have been induced by advective straining. This phenomenon is demonstrated by simulations and explored by means of an idealized analytical model.

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47.27.T-	Turbulent transport processes
47.27.tb	Turbulent diffusion
47.27.Gs	Isotropic turbulence; homogeneous turbulence

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Relaxation of discrete rotational energy distributions using a Monte Carlo method

Iain D. Boyd

Phys. Fluids A 5, 2278 (1993); http://dx.doi.org/10.1063/1.858531 (9 pages) | Cited 16 times

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A new model is presented for simulating rotational energy relaxation in the direct simulation Monte Carlo method (DSMC) using discrete distributions. The method extends the phenomenological approach generally employed that simulates the distribution as a continuum. The discrete approach simulates the mechanics of relaxation for the rigid rotor model. The theory is developed and combined for use with an existing model for simulating the rate of rotational relaxation. A number of test problems are then considered. Each set of flow conditions is chosen because of the availability of experimental data. Some of the experimental measurements provide rotational energy distributions thus allowing detailed comparison with the numerical simulations. Generally, the comparisons are quite favorable, although it is indicated that more sophisticated models are required to simulate some of the detailed structure of the energy distributions observed experimentally.

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47.70.Nd	Nonequilibrium gas dynamics
02.70.Rr	General statistical methods
34.50.Ez	Rotational and vibrational energy transfer
47.40.Ki	Supersonic and hypersonic flows

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Transition from steady to periodic liquid‐metal magnetohydrodynamic flow in a sliding electrical contact

Gita Talmage, John S. Walker, Samuel H. Brown, and Neal A. Sondergaard

Phys. Fluids A 5, 2287 (1993); http://dx.doi.org/10.1063/1.858532 (8 pages)

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In homopolar motors and generators, large dc electric currents pass through the sliding electrical contacts between rotating copper disks (rotors) and static copper surfaces shrouding the rotor tips (stators). A liquid metal in the small radial gap between the rotor tip and concentric stator surface can provide a low‐resistance, low‐drag electrical contact. Since there is a strong magnetic field in the region of the electrical contacts, there are large electromagnetic body forces on the liquid metal. The primary, azimuthal motion consists of simple Couette flow, plus an electromagnetically driven flow with large extremes of the azimuthal velocity near the rotor corners. The secondary flow involves the radial and axial velocity components, is driven by the centrifugal force associated with the primary flow, and is opposed by the electromagnetic body force, so that the circulation varies inversely as the square of the magnetic‐field strength. Three flow regimes are identified as the angular velocity Ω of the rotor is increased. For small Ω, the primary flow is decoupled from the secondary flow. As Ω increases, the secondary flow begins to convect the azimuthal‐velocity peaks radially outward, which in turn changes the centrifugal force driving the secondary flow. At some critical value of Ω, the flow becomes periodic through the coupling of the primary and secondary flows. The azimuthal‐velocity peaks begin to move radially in and out with an accompanying oscillation in the secondary‐flow strength.

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47.65.-d

Magnetohydrodynamics and electrohydrodynamics

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The Green’s function for passive scalar diffusion in a homogeneously sheared continuum

J. D. Goddard

Phys. Fluids A 5, 2295 (1993); http://dx.doi.org/10.1063/1.858533 (3 pages) | Cited 3 times

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The impulsive‐source distribution or Green’s function for an unbounded n‐dimensional Euclidean space filled by a material medium which undergoes a time‐dependent homogeneous deformation and which is characterized by a time‐dependent anisotropic diffusion tensor is derived. The special case of time‐independent velocity gradients is considered (motions with constant stretch history), in which the anisotropic diffusivity is assumed to arise from the distortion of the otherwise isotropic medium supporting the diffusion process. Explicit reductions are given for steady simple‐shearing (viscometric) flows. Also, a brief discussion is given of the relevance to general linear Brownian dynamical systems and the associated Taylor dispersion processes.

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47.10.-g

General theory in fluid dynamics

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Perturbation growth in shear flow exhibits universality

Brian F. Farrell and Petros J. Ioannou

Phys. Fluids A 5, 2298 (1993); http://dx.doi.org/10.1063/1.858534 (3 pages) | Cited 14 times

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Disturbance structures that achieve maximum growth over a specified interval of time have recently been obtained for unbounded constant shear flow making use of closed‐form solutions. Optimal perturbations have also been obtained for the canonical bounded shear flows, the Couette, and plane Poiseuille flows, using numerical solution of the linearized Navier–Stokes equations. In this note it is shown that these optimal perturbations have similar spectra and structure indicating an underlying universality of shear flow dynamics that is not revealed by traditional methods based on modal analysis.

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47.10.-g	General theory in fluid dynamics
47.20.-k	Flow instabilities
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.27.Cn	Transition to turbulence

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