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

Select this Article

Brinkman screening and the covariance of the fluid velocity in fixed beds

Donald L. Koch, Reghan J. Hill, and Ashok S. Sangani

Phys. Fluids 10, 3035 (1998); http://dx.doi.org/10.1063/1.869830 (3 pages) | Cited 12 times

Show Abstract

The phenomenon of Brinkman screening, whereby the fluid velocity disturbance produced by each particle in a fixed bed is attenuated by the forces that the fluid exerts on surrounding particles, plays a crucial role in limiting the range of velocity correlations in porous media and fixed beds. Koch and Brady [J. Fluid Mech. 154, 399 (1985)] showed theoretically that Brinkman screening leads to a finite hydrodynamic diffusion coefficient for fluid phase tracers in dilute fixed beds. In this Letter, we present the results of two simulation techniques (lattice-Boltzmann method and a multipole method) confirming the screening of the fluid velocity covariance that underlies the Koch and Brady theory. © 1998 American Institute of Physics.

+

Show PACS

47.56.+r	Flows through porous media
47.11.-j	Computational methods in fluid dynamics

Select this Article

Marangoni instability of two liquids mixing at a free surface

E. Tan and S. T. Thoroddsen

Phys. Fluids 10, 3038 (1998); http://dx.doi.org/10.1063/1.869831 (3 pages) | Cited 5 times

Full Text: | Download PDF

+

Show Abstract

The impact of a water drop on a thin layer of glycerin leads to the formation of an intricate flower-like pattern. We show that these leaf-like forms are generated by a surface-tension instability at the air–liquid interface along which there exists variable concentration of glycerin and water. Spatial variations of surface tension drive intense vortices inside the water layer, which interact with the glycerin–water concentration at the surface. Horizontal bending of these vortices is reinforced by the resulting enhancement of the surface-tension gradients. © 1998 American Institute of Physics.

+

Show PACS

47.27.T-	Turbulent transport processes
47.20.-k	Flow instabilities
47.32.C-	Vortex dynamics

Select this Article

A dynamic model for subgrid-scale variance and dissipation rate of a conserved scalar

Charles D. Pierce and Parviz Moin

Phys. Fluids 10, 3041 (1998); http://dx.doi.org/10.1063/1.869832 (4 pages) | Cited 71 times

Full Text: | Download PDF

+

Show Abstract

The dynamic procedure is applied to the problem of modeling the subgrid-scale variance and dissipation rate of a conserved scalar in large eddy simulations of turbulent reacting flows. A simple scaling relation for the subgrid-scale variance is proposed, and the coefficient of the scaling law is obtained using the dynamic procedure. The variance dissipation rate is modeled by assuming equilibrium with the local variance production rate, which is obtained using a dynamic model. Example model predictions are obtained using actual large eddy simulation data, and the subgrid variance predicted by the dynamic model is compared to results obtained using a scale similarity model. Generalization of the approach to multiple scalars and nonconserved scalars is briefly discussed. © 1998 American Institute of Physics.

+

Show PACS

47.27.E-	Turbulence simulation and modeling
47.70.Fw	Chemically reactive flows
82.40.-g	Chemical kinetics and reactions: special regimes and techniques

Select this Article

Two-fluid Taylor–Couette flow: Experiments and linear theory for immiscible liquids between corotating cylinders

Gretchen Baier and Michael D. Graham

Phys. Fluids 10, 3045 (1998); http://dx.doi.org/10.1063/1.869833 (11 pages) | Cited 21 times

Full Text: | Download PDF

+

Show Abstract

We investigate the centrifugal instability of a pair of radially stratified immiscible liquids in the annular gap between concentric, corotating cylinders: two-fluid Taylor–Couette flow. Experiments show that a two-layer flow with a well-defined interface and Taylor vortices in each phase can be obtained. The experimental results are in good agreement with predictions of inviscid arguments based on a two-phase extension of Rayleigh’s criterion, as well as with detailed linear stability calculations. For a given geometry, the most stable configuration occurs for fluids of roughly (exactly in the inviscid limit) equal dynamic viscosities. For fluids with sufficiently low viscosity, we also experimentally observe another instability that is evidently the two-fluid analog of the instability of a thin film of liquid coating the inside of a rotating drum. © 1998 American Institute of Physics.

+

Show PACS

47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.20.-k	Flow instabilities
47.32.C-	Vortex dynamics

Select this Article

A numerical study of periodic disturbances on two-layer Couette flow

Jie Li, Yuriko Y. Renardy, and Michael Renardy

Phys. Fluids 10, 3056 (1998); http://dx.doi.org/10.1063/1.869834 (16 pages) | Cited 29 times

Full Text: | Download PDF

+

Show Abstract

The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds numbers, and a second-order velocity interpolation. The code is validated against linear theory for the stability of two-layer Couette flow, and weakly nonlinear theory for a Hopf bifurcation. Examples of long-time wave saturation are shown. The formation of fingers for relatively small initial amplitudes as well as larger amplitudes are presented in two and three dimensions as initial-value problems. Fluids of different viscosity and density are considered, with an emphasis on the effect of the viscosity difference. Results at low Reynolds numbers show elongated fingers in two dimensions that break in three dimensions to form drops, while different topological changes take place at higher Reynolds numbers. © 1998 American Institute of Physics.

+

Show PACS

47.15.-x	Laminar flows
47.20.-k	Flow instabilities
05.45.-a	Nonlinear dynamics and chaos
47.55.Hd	Stratified flows
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
02.40.Pc	General topology

Select this Article

Silo hiccups: Dynamic effects of dilatancy in granular flow

Thierry Le Pennec, Knut Jørgen Måløy, Eirik G. Flekkøy, Jean Claude Messager, and Madani Ammi

Phys. Fluids 10, 3072 (1998); http://dx.doi.org/10.1063/1.869835 (8 pages) | Cited 8 times

Full Text: | Download PDF

+

Show Abstract

The granular flow through an open silo is investigated experimentally. A mechanism based both on the dilation of the granular medium and an interaction with the interstitial gas causes the flow to stop at regular intervals. The experiments are carried out at different surrounding pressures P₀, and it is found that the intermittent flow becomes continuous at sufficiently low P₀, showing that the intermittency is linked to the interaction the gas. The scaling of the average flow rate with particle size further supports our view of the gas-grain interaction. © 1998 American Institute of Physics.

+

Show PACS

47.55.Kf	Particle-laden flows
47.60.-i	Flow phenomena in quasi-one-dimensional systems

Select this Article

On equilibrium modes and their stability in the small-gap Taylor problem by a new method

P. M. Eagles

Phys. Fluids 10, 3080 (1998); http://dx.doi.org/10.1063/1.869836 (8 pages) | Cited 1 time

Full Text: | Download PDF

+

Show Abstract

We consider small disturbances to the steady viscous flow between concentric rotating circular cylinders. It is shown that as the dimensionless gap width δ approaches zero the terms from ∂/∂θ in the governing equations are O(δ^1/2) and so do not appear in the first approximation. This is in contrast to the classical small-gap approximation, in which terms from ∂/∂θ do appear in the first approximation. Here θ is the usual azimuthal angle. Let ϵ be a measure of the size of the small perturbation. In Sec. III it is argued that the asymptotic relation ϵ ∼ δ² is needed to obtain a correct approximation to weakly nonlinear axisymmetric (Taylor-vortex) equilibrium flow for small values of δ. We use this relation between ϵ and δ to obtain a unified amplitude equation to describe both axisymmetric modes and those with a general dependence on the azimuthal angle, taking into account weakly nonlinear effects. This allows a description of single-mode equilibrium states and of their stability. Some unexpected results are obtained about the stability of these modes. The mode with m = 0 is shown to be stable for all relevant values of the Taylor number T. This is to be expected under the particular limiting process used. However the modes with m = 1, 2, and 3 are shown to become stable for successively higher values of T. It is also shown that these nonaxisymmetric equilibrium states may be obtained by the solution of some initial value problems, thus leaving open the possibility of attaining wavy disturbances by a different method than the usual one of instability of Taylor vortices. © 1998 American Institute of Physics.

+

Show PACS

47.20.-k	Flow instabilities
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.32.C-	Vortex dynamics

Select this Article

Stability analysis of a Taylor–Couette flow of insulating fluid subjected to radial unipolar injection of charge

Juan L. Lara, Francisco Pontiga, and Antonio Castellanos

Phys. Fluids 10, 3088 (1998); http://dx.doi.org/10.1063/1.869837 (11 pages) | Cited 1 time

Full Text: | Download PDF

+

Show Abstract

The linear stability of a dielectric fluid filling a cylindrical capacitor is analyzed. The outer or the inner cylinders forming the capacitor may rotate with fixed angular velocities, thus generating a Taylor-Couette flow inside the fluid. A weak, moderate or strong injection of charge is assumed to occur at the anode when a high voltage is applied to the electrodes. The physical mechanisms associated to the instability of the steady flow are discussed. Special attention is paid to the case when the mobility of ions is similar to or smaller than the hydrodynamic mobility of the fluid. © 1998 American Institute of Physics.

+

Show PACS

47.20.-k	Flow instabilities
47.15.-x	Laminar flows
41.20.Cv	Electrostatics; Poisson and Laplace equations, boundary-value problems
47.65.-d	Magnetohydrodynamics and electrohydrodynamics

Select this Article

On the interaction between two oppositely signed, shielded, monopolar vortices

M. R. Schmidt, M. Beckers, A. H. Nielsen, J. Juul Rasmussen, and G. J. F. van Heijst

Phys. Fluids 10, 3099 (1998); http://dx.doi.org/10.1063/1.869838 (12 pages) | Cited 4 times

Full Text: | Download PDF

+

Show Abstract

The formation two-dimensional dipolar vortices by the interaction between two shielded monopolar vortices with opposite vorticity, as shown in a numerical study by Couder and Basdevant, is investigated in detail, both experimentally, in a nonrotating stratified fluid and numerically by direct solutions of the two-dimensional Navier–Stokes equations. A comparative study between the laboratory experiments and numerical simulations is performed. The vorticity distribution measured in the early stage of the evolution in the laboratory is used as initial data for the simulations, and an additional damping term in the Navier–Stokes equations, that accounts for the vertical diffusion in the laboratory experiments, is used. The results show that, depending on the initial separation between the vortices, the shields of the monopoles are peeled off and indeed a compact dipole with a linear (ω,ψ)-relationship is formed, or when the monopoles are further apart the shields of the monopoles are perturbed and two tripoles are formed. The characteristics of the emerged dipole are analyzed and a dye visualization of the dipole formation is performed. A second, more general numerical study yields a relationship between the formation time of the dipole and the initial separation distance between the monopoles and it shows that the deshielding process can be explained by the domination of strain over vorticity. © 1998 American Institute of Physics.

+

Show PACS

47.32.C-

Vortex dynamics

Select this Article

Numerical study of the effective viscosity and pressure in perturbed turbulent flows

Jean-François Panis and Michel Pérault

Phys. Fluids 10, 3111 (1998); http://dx.doi.org/10.1063/1.869839 (15 pages) | Cited 3 times

Full Text: | Download PDF

+

Show Abstract

We present a numerical investigation of the linear response of a turbulent flow to a perturbation at large scale. In the incompressible case, we show that part of the small scale action corresponds to the standard turbulent viscosity, but that there are also other terms which are important for the system dynamics and which do not reduce to a simple turbulent viscous effect. In the compressible case, we show that the small scales of the turbulent flow create a turbulent pressure force which resists compression. An adiabatic index is estimated for this pressure and is found to decrease with time scale, from a strongly adiabatic behavior down to a subisothermal behavior. © 1998 American Institute of Physics.

+

Show PACS

47.27.-i

Turbulent flows

Select this Article

Intermittency in the two-dimensional inverse cascade of energy: Experimental observations

Jérôme Paret and Patrick Tabeling

Phys. Fluids 10, 3126 (1998); http://dx.doi.org/10.1063/1.869840 (11 pages) | Cited 81 times

Full Text: | Download PDF

+

Show Abstract

An extensive experimental study of the two-dimensional inverse energy cascade is presented. The experiments are performed in electromagnetically driven flows, using thin, stably-stratified layers. Complete instantaneous velocity fields are measured using particle imaging velocimetry techniques. Depending on the bottom-wall friction, two different regimes are observed: when the friction is low, the energy transferred from the forcing scale towards large scales accumulates in the lowest accessible mode, leading to a mean rotation of the flow and to an energy spectrum displaying a sharp peak at the minimum wave-number. This condensation is accompanied by the emergence of a very strong vortex around which the rotation is organized. At higher frictions, the inverse energy cascade conjectured by Kraichnan [Phys. Fluids 10, 1417 (1967)] is observed and is found to be stationary, homogeneous and isotropic, with a Kolmogorov constant consistent with numerical estimates. This inverse cascade does not appear to be characterized by the presence of strong coherent vortices. The characteristic size of the latter is of the order of the injection scale. Their statistical properties tend to show that the cascade is rather driven by a clustering mechanism involving same sign vortices rather than a sequence of merging events producing larger and larger vortices. Intermittency effects are also investigated for the inverse cascade range. It is found that, within experimental errors, there is no intermittency in the inverse cascade range of two-dimensional turbulence and that the statistics of velocity increments, either longitudinal or transverse, are close to Gaussian. These results constitute the first experimental study of intermittency in two-dimensional turbulence as well as the first observation of normal scaling in a field of research which has been increasingly concerned with anomalous exponents. © 1998 American Institute of Physics.

+

Show PACS

47.55.Hd	Stratified flows
47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.32.C-	Vortex dynamics
47.65.-d	Magnetohydrodynamics and electrohydrodynamics

Select this Article

Measurements of a confined jet

L. P. Chua and A. C. Lua

Phys. Fluids 10, 3137 (1998); http://dx.doi.org/10.1063/1.869841 (8 pages) | Cited 4 times

Full Text: | Download PDF

+

Show Abstract

In this paper we study the flow characteristics of an air jet issuing from a rectangular nozzle of aspect ratio 6.0 into a confined chamber. Hot-wire measurements of mean and root mean square velocities were made in the mixing layers and interaction region of the jet, at two Reynolds numbers. The results showed that the mean velocity profiles achieved approximate self-preservation almost immediately after the end of potential core. However, the self-similarity of root mean square velocity profiles was established only after a distance of 12 nozzle widths downstream of the nozzle exit. The decay rate of the confined jet was found to be almost three times less than that of square and circular free jets but was greater than that of plane free jets by 10–30% with laminar initial conditions and similar Reynolds number (<8000). The spreading rate of the confined jet was found to be quite similar to that of the plane free jets but higher than the circular and square free jets. It is deduced from the results obtained that although the confined jet is three-dimensional flow in nature, the decay rate of the confined jet follows more closely to that of a two-dimensional type of flow rather than that for a three-dimensional flow. © 1998 American Institute of Physics.

+

Show PACS

47.27.wg	Turbulent jets
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.80.-v	Instrumentation and measurement methods in fluid dynamics

Select this Article

Theory of attached and lifted diffusion flames

Indrek S. Wichman and Bassem Ramadan

Phys. Fluids 10, 3145 (1998); http://dx.doi.org/10.1063/1.869829 (10 pages) | Cited 14 times

Full Text: | Download PDF

+

Show Abstract

Diffusion flame (DF) attachment and liftoff are examined, leading to (1) explanations of the origins of previous, successful empirical correlations; (2) the discovery of multiple lifting regimes. The latter includes a very slow flow regime, a slow-to-moderate flow regime, and a moderate-to-fast flow regime. Formulas for liftoff height ( math

_g) and characteristic flame tip breadth ( math

_r) are developed from a combination of the differential and integral form of the conservation equations. These formulas are compared with numerical solutions of the same equations. © 1998 American Institute of Physics.

+

Show PACS

47.70.Fw	Chemically reactive flows
82.33.Vx	Reactions in flames, combustion, and explosions
47.15.-x	Laminar flows
02.60.Cb	Numerical simulation; solution of equations
02.60.Lj	Ordinary and partial differential equations; boundary value problems

Select this Article

Experiments on homogeneous turbulence in an unstably stratified fluid

S. T. Thoroddsen, C. W. Van Atta, and J. S. Yampolsky

Phys. Fluids 10, 3155 (1998); http://dx.doi.org/10.1063/1.869842 (13 pages) | Cited 1 time

Full Text: | Download PDF

+

Show Abstract

We have studied experimentally the effects of an unstable linear density profile on the evolution of homogeneous grid-generated turbulence. The experiments were performed in a thermally stratified wind tunnel employing hot- and cold-wire anemometry. The unstably stratified air stream was passed through a biplanar grid and the down-stream evolution of the turbulence statistics were studied. Contrary to the stably stratified case, where vertical velocity fluctuations are inhibited, here the buoyancy forces feed energy into the vertical motions. This injection at the actively turbulent length scales continues up to a critical time at which large-scale overturning of the entire fluid volume occurs. This overturn is due to the Rayleigh–Benard-type instability, which is manifest in the mean temperature field by a large plume rising up from the tunnel floor at the centerline. During the viscous decay, downstream of the grid, the r.m.s. vertical velocity fluctuations are relatively enhanced becoming 1.45 times the stream-wise fluctuations, before this overturn. The normalized buoyancy flux is also enhanced by the destabilizing buoyancy forces, reaching values as large as 0.88, significantly larger than those observed in the passively stratified case. Spectral ratios identify the length scales most affected. Results for different grid mesh-sizes show that the statistics are Reynolds number independent over the range of values studied here, i.e., Re_λ between 21 and 66. The probability density functions of temperature and velocity remain Gaussian in the homogeneous region. As the large-scale overturn takes over the flow, the scalar and velocity fluctuations are enhanced dramatically and qualitative changes are observed in the pdf of the temperature fluctuations. © 1998 American Institute of Physics.

+

Show PACS

47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.55.Hd	Stratified flows
47.20.-k	Flow instabilities

Select this Article

Short-wavelength instabilities of waves in rotating stratified fluids

Takeshi Miyazaki and Kei Adachi

Phys. Fluids 10, 3168 (1998); http://dx.doi.org/10.1063/1.869843 (10 pages) | Cited 4 times

Full Text: | Download PDF

+

Show Abstract

Standing and propagating plane waves in a rigidly rotating stably stratified fluid are considered. Based on a WKB analysis, it is shown numerically that almost all of them are unstable with respect to three-dimensional short-wavelength perturbations. The waves whose wavenumber vector is parallel to the axis of rotation and stratification are stabilized as the Brunt-Väisälä frequency N (normalized by the angular velocity of rigid rotation) increases, whereas the inclined waves are unstable at any N. These instabilities are caused by parametric resonances of low order (first and second) and the instability growth rate is determined theoretically, when the wave amplitude is small. © 1998 American Institute of Physics.

+

Show PACS

47.35.-i	Hydrodynamic waves
47.20.-k	Flow instabilities
47.32.-y	Vortex dynamics; rotating fluids
47.55.Hd	Stratified flows

Select this Article

The breakdown of large-scale flows in rotating, stratified fluids

James C. McWilliams, Irad Yavneh, Michael J. P. Cullen, and Peter R. Gent

Phys. Fluids 10, 3178 (1998); http://dx.doi.org/10.1063/1.869844 (7 pages) | Cited 11 times

Full Text: | Download PDF

+

Show Abstract

Flows under the influences of environmental rotation and stable density stratification often exhibit an approximate force balance and a consequently slow rate of evolution at large Reynolds number. Such flows are typically anisotropic in their velocity field. This regime is relevant to large-scale motions in the Earth’s atmosphere and ocean, as well as many other planetary and astrophysical systems. The Balance Equations are usually an accurate approximate model for this regime. However, they have solvability limits associated with a change of type in their time-integration operator. In this paper we derive these limiting conditions for the conservative Balance Equations in isentropic coordinates, show that the least familiar of these conditions coincides with loss of convexity of the streamfunction for horizontal velocity in the inertial reference frame, and identify these conditions with the general conditions for symmetric loss of stability for circular and parallel flows as well as for the three-dimensional loss of stability for elliptical flows. We then conjecture that the identified limits of balance coincide generally with the boundary between the distinctive nonlinear dynamical behaviors (i.e., their turbulent cascade and dissipation rates) associated with the large- and small-scale regimes in geophysical and astrophysical flows. © 1998 American Institute of Physics.

+

Show PACS

47.32.-y	Vortex dynamics; rotating fluids
47.55.Hd	Stratified flows
47.20.-k	Flow instabilities
95.30.Lz	Hydrodynamics

Select this Article

On a possible mechanism of anomalous diffusion by Rossby waves

F. Dupont, R. I. McLachlan, and V. Zeitlin

Phys. Fluids 10, 3185 (1998); http://dx.doi.org/10.1063/1.869845 (9 pages) | Cited 4 times

Full Text: | Download PDF

+

Show Abstract

We study the advection of passive tracers by traveling plane Rossby waves of finite amplitude. In distinction with previous studies the nonlinearity of the wave field is taken into account in the first order of perturbation theory by considering the Lagrangian transport by resonant wave triads. Using the waves’ phases as new dynamical variables we reduce the problem to the study of a specific one-and-a-half degree of freedom Hamiltonian system with nonharmonic modulation. By using a symplectic integrator we study this system numerically and find an interesting series of bifurcations of its phase portrait as the nonlinearity increases. As is standard in the systems of this type we commonly see a chaotic sea with elliptic islands in the phase space, which means that in the physical space the resonant triads give rise to chaotic mixing and ballistic transport, respectively. The relevance of these results to the transport properties of β-plane turbulence is discussed. © 1998 American Institute of Physics.

+

Show PACS

47.35.-i	Hydrodynamic waves
05.60.-k	Transport processes

Select this Article

Three-dimensional instability of anticyclonic swirling flow in rotating fluid: Laboratory experiments and related theoretical predictions

Ya. D. Afanasyev and W. R. Peltier

Phys. Fluids 10, 3194 (1998); http://dx.doi.org/10.1063/1.869846 (9 pages) | Cited 8 times

Full Text: | Download PDF

+

Show Abstract

We present results from a new series of experiments on the geophysically important issue of the instability of anticyclonic columnar vortices in a rotating fluid in circumstances such that the Rossby number exeeds unity. The core of the vortex is modeled as a solid cylinder rotating in a fluid that is itself initially in a state of solid-body rotation. When the cylinder rotates cyclonically the flow induced by the differential rotation is stable except for a brief initial period. When the cylinder rotates anticyclonically, however, intense perturbations spontaneously appear and amplify in the flow. The experimental results demonstrate that secondary motions appear in an annular region of finite width surrounding the cylinder (in accord with the prediction of the generalized Rayleigh criterion) and are governed by the process of three-dimensional centrifugal instability. These motions are characterized by a definite wave number in the coordinate direction parallel to the axis of the cylinder. Both the width of the unstable annular region and the vertical wavelength of the motions induced by centrifugal instability are determined by the main nondimensional parameter of the flow—the Rossby number. The evolution of the secondary motions gives rise to the appearance of tertiary motions—which are Kelvin–Helmholtz-like (barotropic) vortices that develop at the periphery of the unstable annulus, thus leading to the formation of exceedingly complex dynamical structures. If the rotating cylinder is withdrawn vertically from the fluid, the instability rapidly destroys the core of the vortex. During its initial phase of development the flow evolves in a way that is strongly analogous to the cylindrical Couette case. An appropriate theory is employed to explain the results of the laboratory experiments. © 1998 American Institute of Physics.

+

Show PACS

47.20.-k	Flow instabilities
47.32.-y	Vortex dynamics; rotating fluids

Select this Article

Rarefied gas flow between two cylinders caused by the evaporation and condensation on their surfaces

Liliana M. Gramani Cumin, Felix M. Sharipov, and Gilberto M. Kremer

Phys. Fluids 10, 3203 (1998); http://dx.doi.org/10.1063/1.869847 (6 pages) | Cited 1 time

Full Text: | Download PDF

+

Show Abstract

The rarefied gas flow between two coaxial cylinders caused by the evaporation and condensation on their surfaces is investigated on the basis of the kinetic and hydrodynamical equations. It is assumed that the cylinders may rotate with equal angular velocity. The equilibrium is perturbed by the small density difference of evaporated particles on the inner cylinder. The hydrodynamical equation has been solved analytically and the kinetic equation has been solved by the discrete velocity method modified for the discontinuous distribution function. The fields of the density, the velocity and the temperature are presented for a wide range of the Knudsen number. An analysis of the influence of the rotation of the cylinders on the flow field is given. © 1998 American Institute of Physics.

+

Show PACS

47.45.-n	Rarefied gas dynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.32.-y	Vortex dynamics; rotating fluids
64.70.F-	Liquid-vapor transitions
51.10.+y	Kinetic and transport theory of gases
47.10.-g	General theory in fluid dynamics

Select this Article

Similarity of gravity current fronts

Jeffrey D. Parsons and Marcelo H. García

Phys. Fluids 10, 3209 (1998); http://dx.doi.org/10.1063/1.869848 (5 pages) | Cited 35 times

Full Text: | Download PDF

+

Show Abstract

Mixing processes in gravity current fronts have only recently been quantified due to their complex, unsteady nature. The similarity of the mixing processes in these pioneer works, however, has not been explored adequately. Experiments that explore a wide range of fronts have been performed. These experiments have used techniques that exhaustively sample the temporal (using a high-speed conductivity probe) and spatial (using planar laser-induced fluorescence) density field more thoroughly than any previous work. Both types of experiments have confirmed earlier research suggesting that low Reynolds number fronts mix differently and less than higher Reynolds number flows. Similarity appeared to be achieved for Re_q>1000, where Re_q is a Reynolds number based upon the cube root of the buoyancy flux into the front and the height of current. It appears that certain secondary mixing processes, seen by other researchers studying stratified mixed layers, are responsible for the earlier changes seen with Reynolds number and cause significant mixing at the front. © 1998 American Institute of Physics.

+

Show PACS

47.20.-k	Flow instabilities
47.55.Kf	Particle-laden flows

Select this Article

Moment realizability and the validity of the Navier–Stokes equations for rarefied gas dynamics

C. David Levermore, William J. Morokoff, and B. T. Nadiga

Phys. Fluids 10, 3214 (1998); http://dx.doi.org/10.1063/1.869849 (13 pages) | Cited 17 times

Full Text: | Download PDF

+

Show Abstract

We present criteria for monitoring the validity of the Navier–Stokes approximation during the simulation of a rarefied gas. Our approach is based on an underlying kinetic formulation through which one can construct nondimensional non-negative definite matrices from moments of the molecular distribution. We then identify one such 3×3 matrix that can be evaluated intrinsically in the Navier–Stokes approximation. Our criteria are based on deviations of the eigenvalues of this matrix from their equilibrium value of unity. Not being tied to a particular benchmark problem, the resulting criteria are portable and may be applied to any Navier–Stokes simulation. We study its utility here by comparing stationary planar shock profiles computed using the Navier–Stokes equations with those computed using Monte Carlo simulations. © 1998 American Institute of Physics.

+

Show PACS

47.45.-n	Rarefied gas dynamics
47.10.-g	General theory in fluid dynamics
47.11.-j	Computational methods in fluid dynamics

Select this Article

The decay of bubble oscillations

P. H. Roberts and C. C. Wu

Phys. Fluids 10, 3227 (1998); http://dx.doi.org/10.1063/1.869850 (3 pages) | Cited 5 times

Full Text: | Download PDF

+

Show Abstract

We study the initial value problem posed by the small amplitude free oscillations of a bubble in a viscous fluid. The solution consists of a linear combination of discrete normal modes and an integral over a continuous spectrum. The continuous spectrum dominates the solution for large times. As a result, the surface deformation ultimately decays algebraically and not as a modulated damped wave, as has sometimes been suggested. © 1998 American Institute of Physics.

+

Show PACS

47.55.D-	Drops and bubbles
47.35.-i	Hydrodynamic waves
02.30.-f	Function theory, analysis

Select this Article

The influence of interface profile on the onset of long-wavelength Marangoni convection

Ricardo Becerril, Stephen J. Van Hook, and J. B. Swift

Phys. Fluids 10, 3230 (1998); http://dx.doi.org/10.1063/1.869857 (3 pages) | Cited 5 times

Full Text: | Download PDF

+

Show Abstract

Recent experimental results [J. Fluid Mech. 345, 45 (1997)] for long-wavelength surface-tension-driven rupture of thin liquid layers (∼0.01 cm) found the onset for significantly smaller imposed temperature gradients than predicted by linear stability analyses that assume an initially flat interface with periodic boundary conditions. The presence of sidewalls and other aspects of the experiment, however, led to deformed interfaces even with no imposed temperature gradient. These sidewall effects were not due to a small system size since experiments with aspect ratios as large as 450 were significantly affected. The stability analysis presented here takes into account the effects of the deformed interface profile and shows that these effects account for some of the disagreement between experiment and theory. In addition, deviations from standard linear stability theory caused by these effects have the same qualitative behavior as the deviations seen in the experiments. © 1998 American Institute of Physics.

+

Show PACS

47.27.T-	Turbulent transport processes
47.20.-k	Flow instabilities

Select this Article

A new flow regime in a Taylor–Couette flow

T. T. Lim, Y. T. Chew, and Q. Xiao

Phys. Fluids 10, 3233 (1998); http://dx.doi.org/10.1063/1.869851 (3 pages) | Cited 15 times

Full Text: | Download PDF

+

Show Abstract

In this Brief Communication, we report a new finding on a Taylor–Couette flow in which the outer cylinder is stationary and the inner cylinder is accelerated linearly from rest to a desired speed. The results show that when the acceleration (dRe/dt) is higher than a critical value of about 2.2 s⁻¹, there exists a new flow regime in which the flow pattern shows remarkable resemblance to regular Taylor vortex flow but is of shorter wavelength. However, when the acceleration is lower than 2.2 s⁻¹, a wavy flow is found to occur for the same Reynolds number range. To our knowledge, this is probably the first time that such a phenomenon has been observed. For completeness, the case of a decelerating cylinder is also investigated, and the results are found to be almost the same. © 1998 American Institute of Physics.

+

Show PACS

47.20.-k	Flow instabilities
47.15.-x	Laminar flows
47.32.C-	Vortex dynamics

Select this Article

A model of heavy particle dispersion by organized vortex structures wrapped around a columnar vortex core

J. S. Marshall

Phys. Fluids 10, 3236 (1998); http://dx.doi.org/10.1063/1.869852 (3 pages) | Cited 4 times

Full Text: | Download PDF

+

Show Abstract

Dispersion of heavy particles from the core of a turbulent vortex with nonzero axial flow is investigated using an axisymmetric computational model, in which the coherent turbulent structures are modeled as periodic vortex rings wrapped around a columnar vortex. Two regimes of particle dispersion are distinguished, which are mapped in the space of two dimensionless parameters; the ratio L/R of vortex ring spacing to ring radius and the ratio Γ_R/Γ_C of ring strength to columnar vortex strength. In one regime, the outward particle drift is arrested by the ring vortices and the particles become trapped on a single wavy surface enclosing the columnar vortex core. In the other regime, the particles continue to move radially past the vortex rings and the particle dispersion is enhanced by the ring-induced velocity. © 1998 American Institute of Physics.

+

Show PACS