bluuebunny/crossref_metadata_2025 huggingface dataset:
Experimental investigation of the nonlinear spectral dynamics of planar jet transition
Authors: Thomas F. O. , Chu H. C.
Published: July 2002

An experimental investigation of the nonlinear spectral dynamics involved in the transition of an initially laminar planar jet shear layer at moderate Reynolds number is presented. Application of a two-point measurement technique allows the quadratic nonlinear transfer function characterizing the local spectral dynamics to be estimated from digitized time-series fluctuation data. This approach provides a measure of the efficiency of local nonlinear processes and allows the relevant local quadratic wave interactions characterizing the jet shear layer transition to be unambiguously detected and quantified. The results indicate that the jet shear layer shows a strong preference for difference mode interactions. These function initially to produce low frequency modes near the jet column frequency. The finite amplitude saturation of the fundamental is dominated by sum interactions which enrich the harmonic content of the spectrum. The subharmonic resonant interaction is found to be a weakly nonlinear phenomenon that involves a linear growth rate modification of the subharmonic due to its phase couple with the fundamental. Measurements indicate that the phase couple between the subharmonic and fundamental instabilities develops very near the nozzle lip. This resonant interaction between fundamental and subharmonic is found to dominate the global nonlinearity of the shear layer though it is overshadowed locally by stronger sum and difference wave interactions. Evidence is also presented which demonstrates resonant phase coupling between the disturbance sensitive region near the nozzle lip and vortex interaction events in the downstream flow, thereby indicating that a resonant feedback coupling exists between these two regions of the flow field.
Exact calculation of convection thresholds in rotating binary liquid mixtures
Authors: Ardron M. R. , Lucas P. G. J. , Stein N. D.
Published: July 2002

The exact sine series method of Stein [Phys. Rev. A 43, 768 (1991)] has been extended to allow the calculation of critical Rayleigh numbers and wave numbers for both stationary and oscillatory convection states of rotating binary mixtures in Rayleigh–Bénard geometry. Checks on the accuracy of the method against previous calculations yield good agreement, provided these are multimode. Single-mode methods seriously underestimate Rc when the convection state is rotation-induced oscillatory. The method is used to obtain a hydrodynamic phase diagram showing a codimension-three point for a hypothetical mixture with Prandtl number 0.2 and Lewis number 0.0266. Threshold state calculations for a realistic 3He–4He mixture show that observation of a codimension-three point is impractical through the Prandtl number being too high.
Structural evolution of intermittency and anisotropy at different scales analyzed using three-dimensional wavelet transforms
Authors: Brasseur James G. , Wang Qunzhen
Published: July 2002

The three-dimensional Mexican hat wavelet transform is used as a Fourier-spectral space filter to study (1) the process by which the nonlinearities in the equations of motion create intermittent regions of concentrated vorticity and (2) the process by which isotropic turbulence becomes anisotropic by mean shear. In the first study, the three-dimensional wavelet transform is applied to direct numerical simulations of the transition from Gaussian initial conditions to isotropic turbulence. During this transition, the initially noncoherent vorticity field is transformed by the Navier–Stokes nonlinearities into coherent regions of concentrated vorticity. Analysis of the wavelet-transformed enstrophy field suggests (a) that small scales are always more intermittent than large scales, (b) that the level of intermittency at the small scales grows more rapidly than at the large scales, and most importantly (c) that the structural development of turbulence at different scales is correlated both with the evolution of global statistical measures that dominate at those scales (energy and dissipation rate) and with the evolution of the energy and dissipation-rate (or enstrophy) spectra. In the second study, the three-dimensional wavelet transform is applied to simulations of the transition from isotropic to homogeneous but anisotropic shear-dominated turbulence. It is found that the effect of mean shear on large scales is very different from the effect of shear on small scales. Enstrophy structures rotate continuously to the mean flow direction with time at all scales, while the structures are elongated by mean strain rate dominantly in the principal strain-rate direction. Small scales elongate more rapidly than large scales. However, scales both smaller and larger than the enstrophy peak had lower inclination angles relative to the mean flow direction. Furthermore, the anisotropic structure of the enstrophy field at scales smaller than the peak in the enstrophy spectrum is dominantly ‘‘rodlike,’’ whereas large-scale structure is more ‘‘disklike.’’
Time-periodic thermal convection in Hele–Shaw slots: The diagonal oscillation
Authors: Graham Michael D. , Müller Ulrich , Steen Paul H.
Published: July 2002

Numerical simulations show that the diagonal oscillation, previously observed in Bénard convection experiments in Hele–Shaw slots, arises from an internal layer instability; an internal stagnation point is essential to the oscillation mechanism. This is contrasted with the more classical oscillation arising from a convected boundary-layer instability. From a dynamical systems viewpoint, the diagonal oscillation occurs in its purest form as a simultaneous temporal and spatial symmetry breaking (a Takens–Bogdanov bifurcation). Continuation methods yield the relevant bifurcation diagrams and show that the existence of the diagonal oscillation is robust with respect to modifications of the boundary conditions.
Cross-diffusion effects on the stability criteria in a triply diffusive system
Authors: Terrones Guillermo
Published: July 2002

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.
A cascade interpretation of Lundgren’s stretched spiral vortex model for turbulent fine structure
Authors: Gilbert Andrew D.
Published: July 2002

Lundgren’s [Phys. Fluids 25, 2193 (1982)] model for turbulent fine structure comprises coherent vortices which wind up vorticity variations into spiral structures; simultaneously the vortices are stretched axially by a background strain field. The model predicts a k−5/3 energy spectrum and is remarkably robust to the form of the coherent vortices and the form of the vorticity variations. To understand this the present article introduces a simple cascade argument which illuminates how the dynamical processes of vortex stretching and reduction of scale conspire to give this Kolmogorov spectrum. Some generalizations are considered.
Experiments on the evolution of gravitational instability of an overturned, initially stably stratified fluid
Authors: Voropayev S. I. , Afanasyev Y. D. , van Heijst G. J. F.
Published: July 2002

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.
The interaction of a hollow cathode with the ionosphere
Authors: Iess L. , Dobrowolny M.
Published: July 2002

The expansion of the plasma emitted by a hollow cathode source and its interaction with an ambient ionospheric plasma are described in a spherically symmetric, stationary, fluid model, which includes anomalous collisions due to ion acoustic or Buneman instability. Currents and potential profiles are self-consistently computed for different densities and polarizations of the hollow cathode plasma. The model indicates that the region where the potential has suprathermal values is quite large and that hollow cathodes strongly enhance the charge collection of a polarized body from the ambient plasma. These results are significant to the problem of power generation via tethered systems in space.
Magnetized equilibrium of a two-dimensional ion plasma
Authors: Prasad S. A. , Morales G. J.
Published: July 2002

An analytic expression for the self-consistent charge density of a magnetically confined two-dimensional ion plasma is obtained. The two-dimensional analog of the Brillouin limit is found for such systems.
Reciprocity relations and the mode conversion-absorption equation with an inhomogeneous source term
Authors: Cho Suwon , Swanson D. G.
Published: July 2002

The fourth-order mode conversion equation is solved completely via the Green’s function to include an inhomogeneous source term. This Green’s function itself contains all the plasma responsive effects such as mode conversion and absorption, and can be used to describe the spontaneous emission. In the course of the analysis, the reciprocity relations between coupling parameters are proved.
Effect of a gradient in parallel current on field error profiles in a reversed-field pinch
Authors: Sidikman K. L. , Callen J. D. , Nebel R. A.
Published: July 2002

Magnetic perturbations caused by external field errors are an important consideration in both the current operation and future design of reversed-field pinch (RFP) devices. Recently, it has been shown that perturbation profiles calculated in the presence of a relaxed RFP equilibrium (J0 =λB0, λ=const) are amplified when compared to those calculated in vacuum. This work extends the approach to include a partially relaxed equilibrium [λ=λ(r)], which is experimentally realistic, and the effects of finite resistivity, viscosity, and flow. The finite gradient in λ produces an amplification of the radial magnetic field perturbation much larger than that predicted for constant λ. Physically, this is due to the presence of an additional perturbed current associated with the gradient in λ which alters the curvature of the perturbation. Finite resistivity, viscosity, and flow act to reduce this amplification.
Nonlinear behavior of the radiative condensation instability
Authors: McCarthy D. , Drake J. F.
Published: July 2002

An investigation of the nonlinear behavior of the radiative condensation instability is presented in a simple one-dimensional magnetized plasma. It is shown that the radiative condensation is typically a nonlinear instability—the growth of the instability is stronger once the disturbance reaches finite amplitude. Moreover, classical parallel thermal conduction is insufficient by itself to saturate the instability. Radiative collapse continues until the temperature in the high density condensation falls sufficiently to reduce the radiation rate.
q dependence of magnetic turbulence in a tokamak
Authors: Graessle D. E. , Prager S. C. , Dexter R. N.
Published: July 2002

Low-frequency (ω≪ωci) radial magnetic field turbulence has been measured over the full minor radius for discharges in the Tokapole II tokamak [Nucl. Fusion 9, 1509 (1979)], and scaled over the range of edge safety factor 0.6≤qa≤5.0. It was found that qa served as a control parameter for both the magnetic fluctuation amplitude and the global confinement time. As qa is reduced from 5 to 0.6 the turbulence level increases by a factor of 50 while the confinement time decreases by more than a factor of 10. At qa≤1, the full fluctuation amplitude is roughly large enough to account for the global confinement using simple estimates of collisionless stochastic magnetic transport. At high qa, the turbulence is too small to account for transport using these estimates. Frequency spectra have been obtained from 10 to 400 kHz. For all qa most of the fluctuation power appears below 100 kHz. This low-frequency structure changes as the safety factor is varied. Although broadband in frequency, the long radial coherence lengths at these frequencies indicate global modes. For f≥100 kHz, the spectra become featureless, with a power-law frequency decay. Radial, poloidal, and parallel correlation analyses have been done as well. The parallel correlation length is estimated to be 150±10 cm. Radial and poloidal coherence lengths are of the order of the machine dimensions for frequencies below 100 kHz for all qa. For f≥100 kHz, radial coherence lengths are 0.5–2.5 cm. Poloidal mode number spectral information is obtained from two-point phase shift measurements, radial decay of fluctuations beyond the separatrix, and poloidal coherence measurements. The m spectrum broadens as qa decreases. This might explain the increase in fluctuation amplitudes as qa decreases. It is suggested that the turbulence for all discharges is due to the same underlying cause or set of causes, and that the differences result from geometric effects associated with the variation in qa.
Mode structure and continuum damping of high-n toroidal Alfvén eigenmodes*
Authors: Rosenbluth M. N. , Berk H. L. , Van Dam J. W. , Lindberg D. M.
Published: July 2002

An asymptotic theory is described for calculating the mode structure and continuum damping of short-wavelength toroidal Alfvén eigenmodes (TAE). The formalism somewhat resembles the treatment used for describing low-frequency toroidal modes with singular structure at a rational surface, where an inner solution, which for the TAE mode has toroidal coupling, is matched to an outer toroidally uncoupled solution. A three-term recursion relation among coupled poloidal harmonic amplitudes is obtained, whose solution gives the structure of the global wave function and the complex eigenfrequency, including continuum damping. Both analytic and numerical solutions are presented. The magnitude of the damping is essential for determining the thresholds for instability driven by the spatial gradients of energetic particles (e.g., neutral-beam-injected ions or fusion-product alpha particles) contained in a tokamak plasma.
Electron thermal confinement in the edge plasma of a field-reversed configuration
Authors: Steinhauer Loren C.
Published: July 2002

The electron energy loss rate along the open field lines in the edge layer of field-reversed configurations (FRC’s) can be inferred from experiments using a simple model. Since FRC edge layers resemble θ pinches a similar model can be applied to θ pinches. Collecting results from a large number of FRC and θ-pinch experiments, it is shown that the electron energy loss is convective, with 3–7kTe lost per electron escaping from the plasma. This stands in marked contradiction to the conclusions of two previous papers, which claimed that the electron energy loss could be explained by thermal conduction. Convective electron thermal loss is well established as the loss mechanism in low-collisionality plasmas such as mirrors. However, thermal conduction (a diffusive mechanism) was expected in the dense, collisional plasmas of typical FRC’s and θ pinches. The thermal conduction mechanism (which applies for sufficiently high collisionality) is shown here to fail at a higher level of collisionality than expected. Consequently, in collisionality ranges where thermal conduction applies, its rate is comparable to or less than the convective loss rate.
The exact and drift Hamiltonian in a toroidal magnetic field
Authors: Yao Qun , Boozer Allen H.
Published: July 2002

The exact Hamiltonian and the first-order corrections to the standard drift Hamiltonian are given in magnetic coordinates for a full static electromagnetic field with magnetic surfaces. The exact Hamiltonian depends on both the field strength and the shape of the magnetic surfaces (the metric of the magnetic coordinates) while the standard drift Hamiltonian depends on the field strength only. The first-order correction to the standard drift Hamiltonian, in gyroradius to system size, depends in a generic way on the metric of the magnetic coordinates, as does the exact Hamiltonian. The finite-Larmor-radius effect and the polarization drift are in the first-order corrections.
Ideal magnetohydrodynamics: Global mode analysis of three-dimensional plasma configurations
Authors: Schwab Carolin
Published: July 2002

The global magnetohydrodynamic (MHD) stability of three-dimensional (3-D) toroidal plasmas, investigated here by the ideal MHD energy principle formulated in magnetic coordinates, is studied by a Finite-Element-Fourier code, the C_ode for the A_nalysis of the S_tability of 3-D equilibria (CAS3D) [Theory of Fusion Plasmas, Varenna 1990 (Editrice Compositori, Bologna, 1990), p. 667]. A first survey of the stability properties of 3-D equilibria clarifies structural characteristics of global MHD modes, such as the existence of separable mode families and the possibility of annihilating all compression terms, i.e., the fluid and the field compression, for the minimizing perturbation.
Guiding-center theory for three-dimensional collisionless finite Larmor radius plasmas
Authors: Ilgisonis V. I.
Published: July 2002

The guiding-center theory appropriate for describing an arbitrary three-dimensional collisionless plasma system is developed. The generalization of the drift kinetic equation for the finite Larmor radius (FLR) case is derived by the Vlasov kinetic equation expansion in powers of inverse cyclotron frequency in terms of conventional magnetohydrodynamic (MHD) variables. It is shown that the first integrals of this equation analogous to energy and magnetic moment can also be found in the nonstationary case. It allows one to get a compact and physically clear form for the drift kinetic equation, including FLR corrections. The moment equations similar to MHD ones, but including the FLR corrections, are also derived. Some acceptable ways to truncate the moment equations series are considered. In particular the FLR generalization of Chew–Goldberger–Low equations is also developed. All results are given explicitly in invariant vector form. They can be used to extend the applicability and to optimize numerical codes as MHD as combined MHD kinetic ones, and should be considered rather as methodological ones.
The theory of the early nonlinear stage of m=1 reconnection in tokamaks*
Authors: Zakharov L. , Rogers B. , Migliuolo S.
Published: July 2002

The theory of the early nonlinear stage of reconnection, when the plasma central core displacement ξ0 is still small with respect to the q=1 radius r1 but exceeds the characteristic width of the singular layer, is considered. The two-dimensional magnetic geometry of m=1 reconnection is determined by solving Waelbroeck’s equations [Phys. Fluids B 1, 2372 (1989)]. Fast nonlinear exponential growth of the mode in contemporary high-temperature experiments is explained on the basis of the nonlinear two-fluid magnetohydrodynamic theory. It is shown that the stabilization of the reconnecting m=1 mode by ω*-effects is in qualitative agreement with experimental observations. A nonlinear cancellation of the ω*-stabilization is proposed as explanation of the triggering of the sawtooth crash.
Formation and decay of a spheromak plasma
Authors: Chin-Fatt C. , DeSilva A. W. , Goldenbaum G. C. , Hess R. , Coté C. , Filuk A. , Gauvreau J.-L. , Hwang F. K.
Published: July 2002

The magnetic properties of the spheromak configuration produced by a combination of slow theta and Z discharges in the University of Maryland Spheromak experiment (MS) are reported. The magnetic structure of the plasma in MS has been mapped out by arrays of passive magnetic pickup coils. The Taylor relaxation process is observed during the formation phase. The magnetic profile evolves in such a way that the ratio of poloidal current Ip to poloidal flux ψ in the plasma approaches a constant value, where μ0Ip=kelψ. When the spheromak is formed, the magnetic field configuration is close to Taylor’s minimum energy state, μ0j=kB. This constant k is related to the size of the spheromak produced. A spheromak with 1.0 T maximum field, corresponding to 650 kA poloidal current, has been produced in MS. However, due to the high plasma density (6–8×1020 m−3) and the presence of low-Z impurities (mainly carbon and oxygen), the plasma is radiation dominated with electron temperature ≤15 eV. The magnetic field decays exponentially during the decay phase. Axisymmetric equilibrium states that could exist in the configuration are calculated with a Grad–Shafranov equilibrium code. Comparison of the numerical calculation with the experimental measurements indicates that the magnetic-field structure stays close to the equilibrium state as the plasma decays.
Chaotic electron trajectories in a free-electron laser with a linearly polarized wiggler
Authors: Michel-Lours L. , Bourdier A. , Buzzi J. M.
Published: July 2002

The motion of an electron in a linearly polarized wiggler with an axial guide field is found to be nonintegrable. There is evidence for chaos from numerical calculations of Poincaré maps and of nonzero Lyapunov exponents. Resonances can be predicted from a one-dimensional Hamiltonian perturbed by a small ‘‘time-dependent’’ quantity.
Theory of semicollisional drift-interchange modes in cylindrical plasmas
Authors: Hahm T. S. , Chen Liu
Published: July 2002

Resistive interchange instabilities in cylindrical plasmas are studied, including the effects of electron diamagnetic drift, perpendicular resistivity, and plasma compression. The analyses are pertinent to the semicollisional regime where the effective ion gyroradius is larger than the resistive layer width. Both analytical and numerical results show that the modes can be completely stabilized by the perpendicular plasma transport. Ion sound effects, meanwhile, are found to be negligible in the semicollisional regime.
Radio-frequency-induced current and transport in toroidal plasmas
Authors: Antonsen Thomas M. , Yoshioka K.
Published: July 2002

The theory of current generation and transport in toroidal geometry as a result of the absorption of high-frequency waves is developed. The radial particle and heat fluxes as well as the parallel current are given in terms of velocity moments of the rf-induced velocity space particle flux. The radial flux can be separated into classical and neoclassical parts. It is suggested that the absorption of rf can be used to control impurity transport.
Vapor condensation in the presence of a noncondensable gas
Authors: Pong Lichung , Moses Gregory A.
Published: July 2002

Kinetic theory principles are used to study one-dimensional steady-state vapor condensation phenomena in the presence of a noncondensable gas. The results have been fitted to an interpolation formula describing the condensation flux that reduces to the one obtained by Labuntsov and Kryukov [Int. J. Heat Mass Transfer 22, 989 (1979)] in the limit of no noncondensable gas.
Finite-β ion mixing mode in sheared magnetic geometry
Authors: Migliuolo Stefano
Published: July 2002

The theory of ion temperature gradient driven instabilities (ion mixing modes) is presented for finite-β plasmas in sheared magnetic fields. Specifically the strong instability of long wavelength modes (perpendicular wavelengths larger than the ion gyral radius) is considered and it is analytically shown that these modes cannot be stabilized at reasonable values of β, where shear Alfvén dynamics are the dominant electromagnetic effect. The strong instability, with ‖ω/k∥vTi‖>1, persists in the regime me/mi<β<1.
Comments on ‘‘A fluid theory of ion collection by probes in strong magnetic fields with plasma flow’’ [Phys. Fluids 3
, 3777 (1987)]
Authors: Stangeby P. C.
Published: July 2002

In a recently published probe theory Hutchinson argues that the cross-field viscosity coefficient n⊥≊ρD⊥, where ρ is the mass density and D⊥ is the diffusion coefficient. This argument is questioned.
Linear mode conversion and the operator theory of wave mechanics
Authors: Dendy R. O.
Published: July 2002

The linear mode conversion regime for the approximate dispersion relation [ω−ω1(x,k)][ω−ω2(x,k)]=η occurs near x=xc, k=kc such that ω1(xc,kc)=ω2(xc, kc). Cairns and Lashmore-Davies [Phys. Fluids 25, 1605 (1982); 26, 1268 (1983)] have recently expressed the associated energy flow in terms of a single parameter that involves η and the partial derivatives of ω1 and ω2. In this paper, a different, wave-mechanical approach is used to obtain the same result. The process of linear mode conversion is discussed using the system L̂Ψ=i ∂Ψ/∂t, where L̂ is a Hermitian operator. The degeneracy of plasma modes, and their coupling by warm plasma corrections in an inhomogeneous plasma, is dealt with using first-order perturbation theory. Simple coupled first-order differential equations for the wave amplitudes follow, which can be integrated directly. The calculated energy flow reproduces the expression that is obtained from the theory of Cairns and Lashmore-Davies.
Chaotic electron motion caused by sidebands in free electron lasers
Authors: Riyopoulos S. , Tang C. M.
Published: July 2002

The electron dynamics in a free electron laser (FEL) is studied in the case when the radiation field contains many modes. This situation arises when unstable modes (sidebands) are excited during operation. It is observed that when the strength of these sidebands exceeds certain levels the electron motion becomes chaotic. This may lead to extensive particle detrapping and loss of amplification for the FEL signal. The threshold for the onset of stochastic electron motion is computed. The evolution of the trapped electron distribution exhibits a diffusive behavior. The rate of particle detrapping is parametrized by the diffusion coefficient 𝔇 in action space. The e-folding length for the number of trapped electrons is parametrized by J2s/𝔇, where Js is the action at the separatrix. It is found that the diffusion rates are related to the type of the sideband spectrum. The diffusion coefficient is always proportional to the ratio of the sideband power in all frequencies to the power of the carrier signal. The coefficient of the proportionality, however, scales differently on the FEL parameters for each of the three spectral categories: a narrow, a broad discrete, and a broad continuous spectrum. The diffusion coefficient is computed analytically for the last two cases and is in good agreement with numerical results. The narrow spectrum yields the highest and the broad continuous the lowest diffusion rates under constant sideband power. It is also found that, in all cases, the diffusion length, measured in wiggler periods, is independent of the electron energy γ.
Wave structures in jets of arbitrary shape. III. Triangular jets
Authors: Koshigoe Shozo , Gutmark Ephraim , Schadow Klaus C. , Tubis Arnold
Published: July 2002

The generalized shooting method, previously developed for the analysis of spatial instability modes of arbitrary shape jets, is applied to incompressible jets with triangular core regions of constant flow. The instability modes of these jets are classified, and calculations are carried out for spatial growth rates, phase velocities, and velocity fluctuation eigenfunctions of three fundamental and two overtone modes. All of the calculated eigenfunctions show negligible velocity fluctuations at the triangle vertices, in good correlation with experimental findings.
Curvature effects on axisymmetric instability of conduction regime in a tall air-filled annulus
Authors: Pécheux J. , Le Quéré P. , Abcha F.
Published: July 2002

This paper numerically studies curvature effects on the instability of the conduction regime of natural convection in a tall air-filled differentially heated annulus of vertical aspect ratio 16 by integrating the two-dimensional axisymmetric Navier–Stokes equations in the Boussinesq approximation. The numerical algorithm combines a pseudospectral Chebyshev space discretization with a second-order time-stepping scheme. It is shown that, in contrast with linear stability analysis of the conduction solution, the time-periodic cross-roll instability does not take place in finite aspect ratio cavities for small values of the radius ratio. For all values of the radius ratio transition to unsteadiness occurs through supercritical Hopf bifurcations. Extensive computations show very complex behaviors of the unsteady solutions depending on the radius ratio. The nature of the reverse transition to steady state that occurs for increasing value of the Rayleigh number is also found to depend strongly on the value of the radius ratio.
Hydrodynamic stability of viscous flow between rotating porous cylinders with radial flow
Authors: Min Kyungyoon , Lueptow Richard M.
Published: July 2002

A linear stability analysis has been carried out for flow between porous concentric cylinders when radial flow is present. Several radius ratios with corotating and counter-rotating cylinders were considered. The radial Reynolds number, based on the radial velocity at the inner cylinder and the inner radius, was varied from −30 to 30. The stability equations form an eigenvalue problem that was solved using a numerical technique based on the Runge–Kutta method combined with a shooting procedure. The results reveal that the critical Taylor number at which Taylor vortices first appear decreases and then increases as the radial Reynolds number becomes more positive. The critical Taylor number increases as the radial Reynolds number becomes more negative. Thus, radially inward flow and strong outward flow have a stabilizing effect, while weak outward flow has a destabilizing effect on the Taylor vortex instability. Profiles of the relative amplitude of the perturbed velocities show that radially inward flow shifts the Taylor vortices toward the inner cylinder, while radially outward flow shifts the Taylor vortices toward the outer cylinder. The shift increases with the magnitude of the radial Reynolds number and as the annular gap widens.
The existence of critical Reynolds numbers in pipe entrance flows subjected to infinitesimal axisymmetric disturbances
Authors: Abbot A. H. , Moss E. A.
Published: July 2002

A modified Chebyshev operational Tau approach was implemented to establish temporal eigenvalues for the axisymmetric Sexl stability equation, transformed to remove the singularity at the origin. Its application to the pipe entrance flow stability problem resulted in the determination of a well-defined maximum axial position—relatively close to the pipe inlet—which possesses a critical Reynolds number of infinity. Thus for the first time a whole range of pipe entrance velocity profile shapes is established—of which the Hagen–Poiseuille limit is only one—for which critical Reynolds numbers do not exist. When combined with the fact that nonparallel effects disappear at the last linearly unstable station, this result is significant because it shows that the greater proportion of the pipe entrance requires finite amplitude disturbances to destabilize the flow.
Joint statistics between temperature and its dissipation rate components in a round jet
Authors: Mi J. , Antonia R. A. , Anselmet F.
Published: July 2002

The joint statistics between the temperature fluctuation θ and all three components of the temperature dissipation rate εθ are investigated in the self-preserving region of a slightly heated turbulent round jet. The main factors which determine the correlation between θ and εθ are the asymmetry of p(θ), the probability density function (PDF) of θ, and the anisotropy of the small-scale turbulence. The assumption of statistical independence between θ and εθ appears to be more closely approximated in this flow than in a turbulent plane jet. Relatedly, the assumption of local isotropy is also more closely satisfied in the round jet than in the plane jet. When θ is in the range ±2 standard deviations, the expectations of all components of εθ, conditioned on θ, are approximately equal in the fully turbulent part of the flow; the magnitude of the conditional expectation is consistent with the independence assumption.
Intermediate asymptotics for convergent viscous gravity currents
Authors: Angenent S. B. , Aronson D. G.
Published: July 2002

Recent experiments by Diez et al. [Phys. Fluids A 4, 1148 (1992)] have shown that converging flow of a very viscous liquid over a rigid horizontal surface, near the time of convergence, approximates a certain self-similar solution to the nonlinear diffusion equation governing the flow. This Brief Communication presents a rigorous mathematical theory of the flow considered by Diez et al., which justifies their observations.
On the three-dimensional instability of elliptical vortex subjected to stretching
Authors: Le Dizès S. , Rossi M. , Moffatt H. K.
Published: July 2002

It is known that two-dimensional vortices are subject to generic three-dimensional instabilities. This phenomenon is located near the core of vortices and depends on the eccentricity of their streamlines. In this paper we are concerned with the modification of this instability when stretching is applied to such vortices. We describe this instability by linearizing the Navier–Stokes equations around a basic state, which is an exact time-dependent solution. The complete system for the perturbations is reduced to a single equation for the perturbed velocity along the vortex span. In the limit of weak stretching, a perturbation theory can be performed and leads to a WKBJ approximation for the solution. This procedure demonstrates that a small amount of stretching is able to prevent the appearance of three-dimensional instabilities for vortices with a low enough eccentricity. Since most vortices are slightly elliptical in turbulent flows, the above computations are expected to cover a wide range of experimental cases. In particular, it is tentatively argued that this mechanism may explain recent experimental observations [Phys. Fluids 7, 630 (1995)].
Active control of Rayleigh–Bénard convection
Authors: Howle Laurens E.
Published: July 2002

We report on stabilizing the unstable no-motion state in a moderate aspect ratio one-dimensional Rayleigh–Bénard convection experiment. A linear proportional control algorithm uses shadowgraphic convection images to determine heat flux perturbations which are applied to the lower boundary by a network of local heaters. We show that simple linear control stabilizes the otherwise unstable no-motion (conduction) state over a substantial range of supercritical Rayleigh numbers.
Horizontal vortex ring motion in linearly stratified media
Authors: Johari H. , Fang H.
Published: July 2002

Laminar vortex rings propagating horizontally in linearly stratified media were investigated in a water tank using the laser-induced fluorescence flow visualization technique. The vortex rings were observed to develop an asymmetry where the upper part of the ring became larger in the cross-sectional area than the lower part. The asymmetry was a result of the instability of the interface on the upper portion of the ring; the upper half of the vortex was heavier than its immediate surroundings, whereas the lower half was lighter. When the circulation-based internal Froude number was smaller than 1.3, the vortex rings retained their overall geometry and continually decreased in size by leaving significant amounts of dyed fluid behind in their wake. At Froude numbers greater than 3.2, the asymmetry was more pronounced, both in the relative position of the upper and lower cores as well as their sizes, and the overall vertical extent of the rings did not decrease until some time after the vortex formation. These observations led to a two-level classification of the collapse process. The collapse time and distance increased with Froude number at any Reynolds number. For a given Froude number and discharge time, increasing the Reynolds number delayed the vortex ring collapse. The normalized collapse time and distance for the lower Froude number vortex rings in the present study were found to scale with the composite parameter Re Fr2/3.
On the effects of nonequilibrium on the subgrid-scale stresses
Authors: Piomelli Ugo , Coleman Gary N. , Kim John
Published: July 2002

An a priori study of the subgrid-scale (SGS) stresses and dissipation in two nonequilibrium, wall-bounded flows is carried out. The velocity fields were computed by direct simulations of two- and three-dimensional boundary layers obtained, respectively, by a sudden change in the Reynolds number and by an impulsive motion in the spanwise direction of the lower wall of a plane channel in fully developed turbulent flow conditions. Several realizations of the transient period of the flow were examined. The SGS stresses react to the imposition of the secondary shear more rapidly than the large-scale ones, and return to equilibrium before the resolved stresses do. In general, the subgrid scales are less sensitive than the large ones to the near-wall and nonequilibrium effects. Scale-similar and dynamic models appear well-suited to reproduce the correlation between resolved Reynolds stress production and events with significant production of SGS energy.
Stability of an isorotating liquid bridge in an axial gravity field
Authors: Slobozhanin Lev A. , Alexander J. Iwan D.
Published: July 2002

The stability problem for the axisymmetric equilibrium states of an isorotating liquid bridge between equidimensional circular disks in a constant axial gravity field is considered. In particular, we examine the stability of bridges satisfying two constraints that are typical for the floating zone method used for materials purification and single crystal growth. First we consider the constraint that the relative volume of the bridge, V, is equal to 1. Here, V is the ratio of the actual bridge volume to that of a cylinder pinned to the edges of disks. For this case, the critical values of the slenderness (Λ) (ratio of the disk separation to the diameter) and of the free surface slopes (β1,β2) at both disks have been determined for a wide range of the Bond (B) and Weber (W) numbers. The second constraint is that the surface slope β1 at one of the disks is prescribed. The chosen values are 90° and 75° and correspond to extremes in growth angle values encountered in floating zone crystal growth. For this case, the dependencies of critical Λ and V values B and W have been calculated. In addition, both axial gravity directions are considered separately and the values of the slope angle, β2, at the other disk are also analyzed for critical states. The solution of the stability problem for any liquid bridge is discussed in detail using the case for B=W=0.1 as an example. In particular, the relationship between the general boundary of the stability region and the stability of bridges subject to the constraints outlined above is examined.
Advances in PDF modeling for inhomogeneous turbulent flows
Authors: Van Slooten P. R. , Jayesh  , Pope S. B.
Published: July 2002

Probability density function (PDF) models which are based on an exact representation of rapidly distorting homogeneous turbulence are applied to a free shear flow, the temporal mixing layer. These velocity wave-vector models were constructed in a previous paper by Van Slooten and Pope [Phys. Fluids 9, 1085 (1997)], but were only tested in cases of homogeneous turbulence. At the edges of free shear flows both turbulent–nonturbulent intermittency and pressure transport are demonstrated to play a significant role in the behavior of the flow. A natural treatment of intermittency is obtained by extending the PDF formulation to include a model for the turbulent frequency following a fluid particle. A model for the pressure transport is also constructed via a scaling analysis. The resulting velocity wave-vector turbulent-frequency PDF model with the pressure transport model yields a good comparison with the available direct numerical simulation data for the temporal shear layer.
A dynamic similarity model for large eddy simulation of turbulent combustion
Authors: Jaberi F. A. , James S.
Published: July 2002

A dynamic similarity subgrid-scale (SGS) unmixedness model is presented for large eddy simulation (LES) of turbulent reacting flows. The model is assessed both a priori and a posteriori via data obtained by direct numerical simulations (DNS) of homogeneous compressible turbulent flows involving a single step Arrhenius reaction. The results of a priori analysis indicate that the local values of the SGS unmixedness are accurately predicted by the model. A posteriori results also indicate that the statistics of the resolved temperature and scalars as obtained by LES compare favorably with DNS values.
Effects of insoluble surfactants on the nonlinear deformation and breakup of stretching liquid bridges
Authors: Ambravaneswaran Bala , Basaran Osman A.
Published: July 2002

During the emission of single drops and the atomization of a liquid from a nozzle, threads of liquid are stretched and broken. A convenient setup for studying in a controlled manner the dynamics of liquid threads is the so-called liquid bridge, which is created by holding captive a volume of liquid between two solid disks and pulling apart the two disks at a constant velocity. Although the stability of static bridges and the dynamics of stretching bridges of pure liquids have been extensively studied, even a rudimentary understanding of the dynamics of the stretching and breakup of bridges of surfactant-laden liquids is lacking. In this work, the dynamics of a bridge of a Newtonian liquid containing an insoluble surfactant are analyzed by solving numerically a one-dimensional set of equations that results from a slender-jet approximation of the Navier–Stokes system that governs fluid flow and the convection-diffusion equation that governs surfactant transport. The computational technique is based on the method-of-lines, and uses finite elements for discretization in space and finite differences for discretization in time. The computational results reveal that the presence of an insoluble surfactant can drastically alter the physics of bridge deformation and breakup compared to the situation in which the bridge is surfactant free. They also make clear how the distribution of surfactant along the free surface varies with stretching velocity, bridge geometry, and bulk and surface properties of the liquid bridge. Gradients in surfactant concentration along the interface give rise to Marangoni stresses which can either retard or accelerate the breakup of the liquid bridge. For example, a high-viscosity bridge being stretched at a low velocity is stabilized by the presence of a surfactant of low surface diffusivity (high Peclet number) because of the favorable influence of Marangoni stresses on delaying the rupture of the bridge. This effect, however, can be lessened or even negated by increasing the stretching velocity. Large increases in the stretching velocity result in interesting changes in their own right regardless of whether surfactants are present or not. Namely, it is shown that whereas bridges being stretched at low velocities rupture near the bottom disk, those being stretched at high velocities rupture near the top disk.
Two-surface problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory
Authors: Takata Shigeru , Aoki Kazuo
Published: July 2002

The steady behavior of a multicomponent mixture of vapors and noncondensable gases between two parallel plane condensed phases for small Knudsen numbers, especially for the continuum limit (i.e., the limit as the Knudsen number vanishes), is investigated in the light of kinetic theory. By a systematic asymptotic analysis of the Boltzmann equation with kinetic boundary conditions, the flow due to evaporation and condensation on the condensed phases is shown to vanish in the continuum limit, and then the system of fluid-dynamic-type equations and their boundary conditions which describes the behavior in the limit is derived. On the basis of the system, it is shown that the vanishingly weak evaporation and condensation give a finite effect on the behavior of the mixture in the continuum limit. This is an example of the ghost effect discovered recently by Sone and co-workers [e.g., Y. Sone et al., Phys. Fluids 8, 628 and 3403 (1996); Y. Sone, in Rarefied Gas Dynamics, edited by C. Shen (Peking U.P., Beijing, 1997), p. 3]. Finally, for the case of a binary mixture of a vapor and a noncondensable gas, two typical problems, the simultaneous mass and heat transfer and the plane Couette flow, are considered to demonstrate the effect more concretely. The result is also compared with that obtained by the numerical analysis of the Boltzmann equation by the direct simulation Monte Carlo method.
Structure, density, and velocity fluctuations in quasi-two-dimensional non-Brownian suspensions of spheres
Authors: Rouyer F. , Lhuillier D. , Martin J. , Salin D.
Published: July 2002

Non-Brownian sedimenting suspensions exhibit density and velocity fluctuations. We have performed experiments on a quasi-two-dimensional counter-flow stabilized suspension of 2000 spherical particles, namely a liquid–solid fluidized bed in a Hele–Shaw cell. This two-dimensional suspension displays a uniform concentration but the particle radial distribution function and the fluctuations of the particle number in a subvolume of the suspension suggest that the microstructure is far from being random. We have also measured the velocity fluctuations of a test particle and the fluctuations of the mean particle velocity in a subvolume. It happens that the relation between velocity and concentration fluctuations in a subvolume can be deduced from a balance between buoyancy and parietal friction forces.
Fixed boundary dual liquid bridges in zero gravity
Authors: Lowry Brian J.
Published: July 2002

The equilibria and stability of fixed contact line dual liquid bridges are considered. The dual liquid bridges considered consist of two fixed length single bridges joined by an open channel so that both bridges are in pressure equilibrium. The system is simplified by requiring all bounds to be of equal radius, and also by neglecting gravity or other applied forces. The dual liquid bridge is found to be generally more stable than a single bridge of equal length in the fixed pressure case, but less stable in the fixed volume case. The maximum length of dual liquid bridge in the fixed pressure case is double that for a single bridge, 7.4547 times the radius. In the fixed volume case, a rupture of the stability envelope leads to ranges of boundary conditions for which there are no stable dual liquid bridges of any volume. One exception to fixed volume destabilization is the cylindrical dual bridge. The maximum length attainable for a cylinder is 8.9868 times the radius, which not coincidentally is also the secondary stability limit for a single fixed volume cylinder (beyond the classical limit of 2π times the radius). The results suggest that any application which pumps fluid through a series of cylindrical liquid bridges would be most favorable using a dual liquid bridge with pressure-constrained pumping.