bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear saturation of ideal interchange modes in a sheared magnetic field
Authors: Beklemishev A. D.
Published: July 2002

Pressure-driven ideal modes cannot completely interchange flux tubes of a sheared magnetic field; instead, they saturate, forming new helical equilibria. These equilibria are studied both analytically and numerically with reduced magnetohydrodynamic equations in a flux-conserving Lagrangian representation. For unstable localized modes, the structure of the nonlinear layer generated around the resonant flux surface depends on the value of Mercier parameter DM. The shape of magnetic surfaces in the vicinity of resonance is changed significantly even close to the instability threshold. However, the radial width of the affected layer becomes exponentially small near the threshold. The appearance of sheet currents and islandlike structures along the resonant flux surface may be of interest for the description of forced reconnection in models with finite resistivity. This study also includes the case of ballooning instability by representing nonlocal driving terms through the matching parameter Δ′, which defines the outer boundary conditions for the interchange layer.
Equilibrium spectra and implications for a two-field turbulence model
Authors: Koniges A. E. , Crotinger J. A. , Dannevik W. P. , Carnevale G. F. , Diamond P. H. , Gang F. Y.
Published: July 2002

Analytic expressions are given for statistical mechanical equilibrium solutions of two-field turbulence model equations that are used in describing plasma drift waves and for passive scalar advection in a neutral fluid. These are compared with those previously proposed [Phys. Fluids B 1, 1331 (1989)], in particular regarding the role of the cross correlations between fields. Implications for two-point closure calculations are discussed.
Propagation and damping of mode converted ion-Bernstein waves in toroidal plasmas
Authors: Ram A. K. , Bers A.
Published: July 2002

In the heating of tokamak plasmas by waves in the ion-cyclotron range of frequencies, the fast Alfvén waves launched at the plasma edge can mode convert to the ion-Bernstein waves (IBW). The propagation and damping of these mode converted waves was studied using a ray tracing code that follows the fast phase and the amplitude of the electromagnetic field along the IBW ray trajectories in a toroidal plasma. A simple analytical model is developed that describes the numerically observed features of propagation and damping of the IBW’s. It is found that along the ray trajectory of the IBW there is an upshift of the poloidal mode numbers, which can lead to the electron Landau damping of the wave. This damping is dependent on the strength of the toroidal plasma current. From the properties of the upshift of the poloidal mode numbers, it is concluded that the mode converted ion-Bernstein waves are not suitable candidates for electron current drive.
Magnetic field strength of toroidal plasma equilibria
Authors: Garren D. A. , Boozer A. H.
Published: July 2002

The confinement and stability properties of toroidal plasma equilibria are largely determined by the strength of the magnetic field expressed in terms of Boozer coordinates. Constraints due to the toroidicity of the configuration and the divergence-free property of the magnetic field limit the freedom in the Taylor series expansion of the magnetic field strength. Such field strength constraints limit the variety of desirable three-dimensional plasma equilibria that are available to the fusion program.
Nondimensional transport scaling in the Tokamak Fusion Test Reactor: Is tokamak transport Bohm or gyro-Bohm?
Authors: Perkins F. W. , Barnes Cris W. , Johnson D. W. , Scott S. D. , Zarnstorff M. C. , Bell M. G. , Bell R. E. , Bush C. E. , Grek B. , Hill K. W. , Mansfield D. K. , Park H. , Ramsey A. T. , Schivell J. , Stratton B. C. , Synakowski E.
Published: July 2002

General plasma physics principles state that power flow Q(r) through a magnetic surface in a tokamak should scale as Q(r)= {32π2Rr3Te2c nea/[eB (a2−r2)2]} F(ρ*,β,ν*,r/a,q,s,r/R,...) where the arguments of F are local, nondimensional plasma parameters and nondimensional gradients. This paper reports an experimental determination of how F varies with normalized gyroradius ρ*≡(2TeMi)1/2c/eBa and collisionality ν*≡(R/r)3/2qRνe(me/ 2Te)1/2 for discharges prepared so that other nondimensional parameters remain close to constant. Tokamak Fusion Test Reactor (TFTR) [D. M. Meade et al., in Plasma Physics and Controlled Nuclear Fusion Research, 1990, Proceedings of the 13th International Conference, Washington (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 9] L-mode data show F to be independent of ρ* and numerically small, corresponding to Bohm scaling with a small multiplicative constant. By contrast, most theories predict gyro-Bohm scaling: F∝ρ*. Bohm scaling implies that the largest scale size for microinstability turbulence depends on machine size. Analysis of a collisionality scan finds Bohm-normalized power flow to be independent of collisionality. Implications for future theory, experiment, and reactor extrapolations are discussed.
A mean field Ohm’s law for collisionless plasmas
Authors: Biglari H. , Diamond P. H.
Published: July 2002

A mean field Ohm’s law valid for collisionless plasmas is derived kinetically. It is shown that contrary to conventional thinking, the resulting hyperresistivity is significantly smaller than its fluid counterpart due to the fact that the turbulent decorrelation rate is linked to the rapid electron ballistic motion rather than the slower nonlinear mixing time. Moreover, the off-diagonal contributions to the parallel electron momentum flux are shown to result in Ohm’s law renormalizations that dwarf the current diffusivity and break radial parity symmetry.
Field line stochasticity during the m=1 reconnection
Authors: Baty H. , Luciani J. F. , Bussac M. N.
Published: July 2002

A full three-dimensional nonlinear magnetohydrodynamic (MHD) simulation using a high number of modes supports a model of the m=1 asymmetric resistive reconnection in tokamaks. The current sheet associated with the internal kink mode exhibits a toroidal modulation mainly due to a finite toroidal pressure effect that leads to an asymmetric m=1 magnetic island. The main effect of the modulation is to drive the growth of (m±1,m) magnetic islands in the plasma on a time scale imposed by the m=1 reconnection process. As the reconnection proceeds, different magnetic island chains with m of order 10 overlap, leading to an annular stochastic region around the m=1 separatrix. The diffusion in this stochastic layer depends exponentially on the current state of the reconnection, and can reach a value high enough to expel the electronic temperature in less than about 100 μsec if the modulation is greater than about 1.0, that is, for low-shear and/or high-pressure gradient equilibrium values on the q=1 surface.
Particle diffusion in stochastic magnetic fields
Authors: Laval G.
Published: July 2002

Particle transport across braided magnetic surfaces is studied by using simple field and collision models. Diffusion along and across field lines is taken into account. A general variational principle is established. It provides a useful guide for numerical computations. In a special case an explicit formula for the diffusion coefficient is obtained. Several diffusion regimes are clearly identified, and their domain of validity is determined. A new form of the diffusion coefficient has to be introduced in the long-mean-free-path regime.
Analysis of thermal, sound, and shear waves according to a relativistic kinetic model
Authors: Cercignani Carlo , Majorana Armando
Published: July 2002

In this paper a kinetic model describing a relativistic gas is considered. The collision frequency is assumed to depend upon the particle speed in a way suggested in a previous paper by the authors. The new model has more satisfactory properties than one previously studied. Several results of both analytic and numerical character concerning the sound and heat waves with frequencies comparable to the intermolecular collision frequency are given.
Approximate treatment near resonance of backward and traveling wave tubes in the Compton regime
Authors: Swegle John A.
Published: July 2002

Backward and traveling wave tubes are devices in which the kinetic energy of an electron beam is converted into electromagnetic radiation through interaction with a slow wave structure. In the low-current, or Compton, regime of operation, the linear instability leading to microwave generation is the result of a three-wave process involving the two space-charge waves on the beam and a normal mode of the slow wave structure. The three-wave character of this resonance is explored qualitatively and quantitatively by deriving an approximate, cubic dispersion relation valid near the resonance. Although the approximate dispersion relation is derived from the full relation for a specific system, the method of analysis is quite general and can easily be applied to other configurations. The approximate dispersion relation is employed to find expressions for the growth rates in these devices, to place this electromagnetic analysis into correspondence with Pierce’s circuit analysis, and to arrive at a proof that the instability in the backward wave device is absolute, while that in the traveling wave tube is convective.
The Stokes drag on a horizontal cylinder falling toward a horizontal plane
Authors: Trahan Jeffrey F. , Hussey R. G.
Published: July 2002

Measurements have been made of the Stokes drag on a cylinder of length 2l and diameter 2r falling with its axis horizontal toward a horizontal plane boundary. The distance from the cylinder axis to the plane is h. For l>2.48r and h>3r, the results agree well with the slender body theory of de Mestre and Russel [J. Eng. Math. 9, 81 (1975)]. For l>19r and h<0.5l, the theory of Jeffrey and Onishi [Q. J. Mech. Appl. Math. 34, 129 (1981)] for a cylinder of infinite length is in good agreement with the experimental results; this theory also agrees well with the results for cylinders as short as l=0.89r in the region h<2r. Measurements with tori indicate that the theory of Jeffrey and Onishi is not sensitive to curvature of the cylinder centerline in the horizontal plane. For h>2l and for all of the cylinders used (98r≥l≥0.89r) the data confirm the general boundary effect expression of Brenner [J. Fluid Mech. 12, 35 (1962)]; and are in better agreement with Brenner’s expression than with the modified form proposed by Williams [J. Fluid Mech. 24, 285 (1966)]. For l>5r, the deceleration of the cylinder is observed to be constant when the cylinder velocity is between 0.4 and 0.15 of its value far from the wall, but the deceleration tends to zero as the velocity approaches zero.
Global magnetic fluctuations in spheromak plasmas and relaxation toward a minimum-energy state
Authors: Janos A. , Hart G. W. , Nam C. H. , Yamada M.
Published: July 2002

Globally coherent modes have been observed during formation in the S-1 Spheromak plasma [Plasma Physics and Controlled Nuclear Fusion 1984 (IAEA, Vienna, Austria, 1985), Vol. 2, p. 535] by analysis of magnetic field fluctuations measured from outside the plasma. The modes are of low n number (2≤n≤5), where n is defined by the functional dependence einφ of the fluctuation on toroidal angle φ. These modes are shown to be related to flux conversion and plasma relaxation toward a minimum-energy state during the spheromak formation. The modes are active while the q profile is rapidly changing, with q on axis, q0, rising to 0.7. A significant finding is the temporal progression through the n=5, 4, 3, 2; m=1 mode sequence as q rises through rational fractions m/n. During formation, peak amplitudes of the n=2, 3, 4 modes relative to the unperturbed field have been observed as high as 20%, while more typical amplitudes are below 5%.
Plasma kinetic theory without the Markovian approximation: I
Authors: Pocobelli G.
Published: July 2002

In a homogeneous plasma with no external fields, an equation of evolution for the space-averaged distribution f̄ (v,t) is derived without making use of the Markovian approximation. The Vlasov equation is integrated for a limited, albeit arbitrary, time interval along analytical particle orbits. Orbit failure is avoided by considering a sequence of initial value problems. A Markovian limit is identified, in which quasilinear, resonance broadening, and mode coupling theories are recovered. Under non-Markovian conditions, the quasilinear wave–particle resonance is broadened at order E2.
A generalized reduced fluid model with finite ion-gyroradius effects
Authors: Hsu C. T. , Hazeltine R. D. , Morrison P. J.
Published: July 2002

Reduced fluid models have become important tools for studying the nonlinear dynamics of plasma in a large aspect-ratio tokamak. A self-consistent nonlinear reduced fluid model, with finite ion-gyroradius effects is presented. The model is distinctive in being correct to O(( ρi/a)2) and in satisfying an exact, relatively simple energy conservation law.
Stability analysis on the convection of a variable viscosity fluid in an infinite vertical slot
Authors: Thangam S. , Chen C. F.
Published: July 2002

Stability of convective motion in a variable-viscosity fluid contained in an infinite vertical slot generated by a lateral temperature difference was studied by means of linear stability analysis. The viscosity of the fluid was assumed to be an exponential function of the temperature. The undisturbed steady-state motion was assumed to consist of purely vertical motion with a linear temperature distribution across the slot. The linear stability equations were solved by the Galerkin method. The results show that (i) the onset of instability is in the oscillatory, or traveling wave, mode in fluids whose mean Prandtl number is greater than 25, and (ii) the variable-viscosity fluid is less stable than the constant-viscosity fluid at the same mean Prandtl number when it exceeds 100.
Density fluctuations induced by nonlinear Alfvén waves
Authors: Spangler Steven R.
Published: July 2002

The generation of plasma density fluctuations by nonlinear Alfvén waves is considered. Of particular interest is the modification to the ‘‘static approximation,’’ describing the relationship between wave intensity and plasma density, when the Alfvén wave packet is rapidly steepening. The study concentrates on a forced wave equation for the plasma density, which yields the static approximation in a select approximation. An analytic solution to this equation is obtained for a reasonable model of a steeping wave packet. The principal results are (a) the static approximation should give a surprisingly robust description of the coupling between Alfvén wave intensity and plasma density, (b) departures of the plasma density perturbation from the static approximation result are determined by a parameter that is a simple function of the wave amplitude and plasma β, (c) for rapidly evolving wave packets, the position of maximum density change is displaced from that of maximum wave intensity, and (d) the magnitude of the density fluctuation will not be much different than the static approximation estimate of (b2/B20)n0.
Eigenvalues associated with relaxed states of toroidal plasmas
Authors: Gimblett C. G. , Hall P. J. , Taylor J. B. , Turner M. F.
Published: July 2002

In the theory of relaxed states of toroidal plasmas certain eigenvalues of the equation ∇×B=μB play a crucial role. These eigenvalues are associated with vanishing toroidal flux and determine the onset of current limitation in a toroidal discharge. In axisymmetric systems there are both periodic and axisymmetric eigenfunctions and it is important to know whether the eigenmode associated with the lowest eigenvalue is periodic or axisymmetric. This depends on the shape of the poloidal cross section and determines the nature of the current-limited discharge. The eigenvalues of periodic and axisymmetric modes have been computed in rectangular and elliptical cross sections and in reentrant Multipinch-like cross sections. The reentrant case required new numerical techniques, which are described. It is found that in rectangular and elliptic cross sections the lowest mode is always periodic. However, in the Multipinch a transition occurs in which the lowest eigenmode changes from periodic to axisymmetric as the ‘‘waist’’ in the cross section is made narrower. The critical width is determined. These calculations suggest that in the GA Multipinch experiment [Nucl. Fusion 26, 255 (1986)] the current saturated discharge should be axisymmetric—unlike all other existing pinch experiments where it is periodic.
Nonlinear growth of fast reconnection in the long tearing-type field geometry
Authors: Ugai M.
Published: July 2002

Spontaneous growth of magnetic reconnection is numerically studied in the tearing-type field geometry. It is found that only in a sufficiently long system does magnetic reconnection fully couple to an anomalous resistivity and develop into the strong fast reconnection mechanism on nonlinear saturation. The supersonic plasma jet resulting from slow shocks causes a remarkable expansion of a magnetic island, and a fast shock stands at the interface between the plasma jet and the island.
Computer simulations of plasma expansion across a magnetic field
Authors: Galvez Miguel , Gary S. Peter , Barnes Christopher , Winske Dan
Published: July 2002

A two-dimensional electrostatic particle-in-cell code is used to simulate the thermal expansion of a cylindrical plasma across a uniform magnetic field. The simulations show that at early times (i.e., short compared to an ion gyroperiod), the plasma develops three characteristic regions: a charge neutral core surrounded by a negatively charged region (the electron charge layer), and an external halo composed only of ions (the ion charge layer). The radii of these non-neutral regions increase when either the electron plasma to electron cyclotron frequency ratio ωpe/‖Ωe‖ increases or when the electron to ion temperature ratio, Te/Ti, decreases. These simulations, which have been run with an ion-to-electron mass ratio of 100, show that the plasma develops structure as a result of the growth of a nonoscillatory instability in the electron charge layer. This structure exhibits growth times short compared to the ion gyroperiod, and wavelengths of the order of the ion gyroradius. The mode number of this structure increases with decreasing ωpe/‖Ωe‖, with increasing initial radius of the plasma relative to the electron Debye length, and with increasing Te/Ti. The linear theory of the lower hybrid drift instability, driven by the E×B and ∇n×B electron drift velocities, provides a good description of the parametric variation of the structure wavelength. It is therefore concluded that this instability is the most likely source of the structure observed in these simulations.
Primary instabilities and bicriticality in flow between counter-rotating cylinders
Authors: Langford W. F. , Tagg Randall , Kostelich Eric J. , Swinney Harry L. , Golubitsky Martin
Published: July 2002

The primary instabilities and bicritical curves for flow between counter-rotating cylinders have been computed numerically from the Navier–Stokes equations assuming axial periodicity. The computations provide values of the Reynolds numbers, wavenumbers, and wave speeds at the primary transition from Couette flow for radius ratios from 0.40–0.98. Particular attention has been focused on the bicritical curves that separate (as the magnitude of counter-rotation is increased) the transitions from Couette flow to flows with different azimuthal wavenumbers m and m+1. This lays the foundation for further analysis of nonlinear mode interactions and pattern formation occurring along the bicritical curves and serves as a benchmark for experimental studies. Preliminary experimental measurements of transition Reynolds numbers and wave speeds presented here agree well with the computations from the mathematical model.
Three-dimensional simulation of the Raman free-electron laser
Authors: Ganguly A. K. , Freund H. P.
Published: July 2002

The nonlinear evolution of the free-electron laser amplifier is investigated numerically in the collective Raman regime for a configuration in which a relativistic electron beam propagates through a loss-free cylindrical waveguide in the presence of a helical wiggler and an axial guide magnetic field. A set of coupled nonlinear differential equations is derived that governs the evolution of the TE waveguide modes, the beam space-charge mode, and the trajectories of an ensemble of electrons. Comparison with experiment shows good agreement for cases in which the intersection between the vacuum waveguide mode and the beam resonance line are near ‘‘grazing’’ (i.e., when the intersections are sufficiently close together to result in one broad gain bandwidth). For interactions in which two distinct gain bands occur, the numerical procedure tends to underestimate the beam–plasma frequency and results in a 15%–20% discrepancy with experiment.
Appearance of a square pattern in a Rayleigh–Bénard experiment
Authors: Le Gal P. , Croquette V.
Published: July 2002

In this work the experimental verification of the appearance of square patterns in Rayleigh–Bénard systems is described. Convective square cells are observed above the threshold of convection in a layer of water sandwiched between two Plexiglas plates. These experimental results agree with earlier theoretical predictions [J. Fluid Mech. 139, 461 (1984); 152, 113 (1985); 178, 491 (1987)], and provide, as far as can be determined, the very first direct observation of the stability of square patterns due to a hybrid thermal boundary condition on the top and bottom of the convecting fluid layer.
Time-dependent inviscid vortices in global self-similar expansion
Authors: Low B. C.
Published: July 2002

A family of time-dependent solutions is derived, which describe the self-similar motion of an inviscid γ=5/3 adiabatic fluid in arbitrary three-dimensional geometry. The derivation identifies a non-Galilean frame of reference in which the self-similar flows are observed to be steady, subject to a (fictitious) inertial force. This theory generalizes a primitive version, previously published, to allow for quite general velocity structures which are topologically no less complex than those belonging to the set of all steady flows. The existence of these self-similar flows stems from a compatibility between the conservation laws governing the internal energy of the γ=5/3 adiabatic gas and its angular momentum. Illustrative analytic solutions are presented for vortices of finite spatial extent isolated in a body of fluid undergoing purely radial expansion. These vortices consist of axisymmetric, closed meridional circulations, with or without swirls. A related set of self-similar, magnetohydrodynamic solutions for the γ=2 adiabatic fluid in the Cartesian plane are derived in the second of two appendices.
Symmetric interaction of developing horizontal jet in a stratified fluid with a vertical cylinder
Authors: Voropayev S. I. , Afanasyev Ya. D.
Published: July 2002

A self-similar planar vortex dipole, arising at the front of developing horizontal jet in a stratified fluid, collides with a small vertical cylinder. The primary vortical flow interacts with the secondary vorticity generated at the boundary of the cylinder and finally a new dipole of reduced intensity forms. The estimates for the reduction of the flow momentum and alteration of the overall propagation velocity and length scales of the newly formed dipole are given. The evolution of the real flow is also explained mathematically.
Evidence of local axisymmetry in the small scales of a turbulent planar jet
Authors: Hussein Hussein J.
Published: July 2002

The small-scale characteristics of turbulent flow resulting from a jet exhausting into a quiescent environment is investigated. The Reynolds number based on exit conditions is approximately 20 000. Second-order derivative moments are obtained using flying hot-wire techniques. The measured derivative moments are used to evaluate both deviations from the requirements of local isotropy and the conditions for turbulence that is locally invariant about a preferred direction. Results of the rate of dissipation of kinetic energy are presented.
Nonlocal theory of area-varying waves on axisymmetric vortex tubes
Authors: Leonard A.
Published: July 2002

Area and axial flow variations on rectilinear vortex tubes are considered. The state of the flow is characterized by two dependent variables, a core area, and an azimuthal circulation per unit length, which vary in time and in distance along the length of the tube. Nonlinear integrodifferential equations of motion for these variables are derived by taking certain integrals of the vorticity transport equation. The equations are argued to be valid for moderately short waves (on the order of a few core radii) as well as for long waves. Applications to vortex breakdown and other wave phenomena are considered.
Acoustic receptivity of a boundary layer to Tollmien–Schlichting waves resulting from a finite-height hump at finite Reynolds numbers
Authors: Nayfeh A. H. , Ashour O. N.
Published: July 2002

The acoustic receptivity of a boundary layer to Tollmien–Schlichting (T–S) waves resulting from a finite-height hump at finite Reynolds numbers is investigated. The steady flow is calculated using an interacting boundary-layer (IBL) scheme that accounts for viscous/inviscid interactions. The unsteady flow is written as the sum of a Stokes wave and a traveling wave generated due to the interaction of the Stokes flow with the steady disturbance resulting from the hump. The traveling wave is governed by a set of nonhomogeneous equations, which is a generalization of the Orr–Sommerfeld equation. The solution of these nonhomogeneous equations is projected onto the quasiparallel eigenmode using the quasiparallel adjoint. This leads to a nonhomogeneous equation with variable coefficients governing the amplitude and phase of the T–S wave. Results are presented for the amplitude variation and the receptivity at finite Reynolds numbers. The results are in good agreement with the experimental results of Saric, Hoos, and Radeztsky [Boundary Layer Stability and Transition to Turbulence (ASME, New York, 1991), FED No. 114, pp. 17–22] for all tested hump heights at the two-tested sound pressure levels. Application of this paper’s theory to small humps yields results that agree with those of Choudhari and Streett [Phys. Fluids A 4, 2495 (1992)], and Crouch [Phys. Fluids A 4, 1408 (1992)]. Application of suction is shown to reduce the receptivity resulting from the hump.
Spatial transport of Reynolds stresses by pressure fluctuations
Authors: Kim Soong Kee , Chung Myung Kyoon
Published: July 2002

The spatial transport of Reynolds stresses by the pressure fluctuations, the so-called pressure transport, is analyzed by investigating the potential flow equation for the fluctuating pressure. Adopting the convection velocity concept for the unsteady term in the Euler equation, and integrating over space, the pressure–velocity correlation vector is decomposed into a bulk convective transport term (rapid part) and a turbulent diffusion term (slow part). Subsequent modeling of the convection velocity in terms of the intensity of turbulence, skewness, and the velocity scale of large-scale eddies results in a new computational model for the pressure transport.
Transient growth in circular pipe flow. II. Nonlinear development
Authors: O’Sullivan P. L. , Breuer K. S.
Published: July 2002

The Navier–Stokes equations for circular pipe flow are integrated using direct numerical simulation for the case of transitional Reynolds number. Previous work on linear disturbances (reported in Part I) is exploited for the simulation of low to moderate amplitude disturbances where it is found that the transient growth mechanism persists in the nonlinear development with the evolution attributable to the linear mechanism remaining of considerable significance. A hypothesis of Trefethen et al. [Science 261, 578 (1993)] concerning the role of nonlinearity in the transition process and ultimately in turbulence is elucidated and given support. It is suggested that nonlinearity is essential in continually perturbing the eigenmodes of the flow in such a way that each mode is never permitted to relax to its least stable eigenstate (damped in the subcritical case). In this way, the linear growth mechanism can be regarded as an underpinning component of the general nonlinear feedback insofar as it is the only part which can extract energy from the mean flow and thus yield a net increase in disturbance energy. The physical aspects of the flow simulations are consistent with puff formation where, using a pair of helical waves as initial data, a sharp trailing front is formed naturally; axisymmetric ring vortices are generated and the general flow characteristics are in broad agreement with experiment.
Onset of Taylor vortices and chaos in viscoelastic fluids
Authors: Khayat Roger E.
Published: July 2002

The influence of fluid elasticity on the onset and stability of axisymmetric Taylor vortices is examined for the Taylor–Couette flow of an Oldroyd-B fluid. A truncated Fourier representation of the flow field and stress leads to a six-dimensional dynamical system that generalizes the three-dimensional system for a Newtonian fluid. The coherence of the model is established through comparison with existing linear stability analyses and finite-element calculations of the nonlinear dynamics of the transition to time-periodic (finite-amplitude) flow. The stability picture and flow are drastically altered by the presence of the nonlinear (upper convective) terms in the constitutive equation. It is found that the critical Reynolds number Rec at the onset of Taylor vortices decreases with increasing fluid elasticity or normal stress effects, and is strongly influenced by fluid retardation. For weakly elastic flows, there is an exchange of stability at Re=Rec through a supercritical bifurcation, similar to the one predicted by the Newtonian model. As the elasticity number exceeds a critical value, a subcritical bifurcation emerges at Rec similar to the one predicted by the Landau–Ginzburg equation. More importantly, it is shown that, if fluid elasticity is adequately accounted for, any small but nonvanishing amount of fluid elasticity can lead to the onset of chaos usually observed in experiments on the Taylor–Couette flow of supposedly Newtonian fluids. This is in sharp contrast to the Newtonian model, which does not predict the destabilization of the Taylor vortices, and therefore cannot account for the onset of periodic and chaotic motion.
Approximation of subgrid-scale energy transfer based on the dynamics of resolved scales of turbulence
Authors: Domaradzki J. Andrzej , Liu Wei
Published: July 2002

Previously established properties of subgrid-scale nonlinear interactions in turbulent flows at low Reynolds numbers are employed to approximate the subgrid-scale energy transfer in terms of the resolved scales for statistically stationary channel flow. The approximation is obtained by focusing on the dynamics of resolved scales in the vicinity of the cutoff wave number. Predicted plane-averaged transfer is in a good agreement with the exactly computed quantity. The modeled forward transfer and inverse transfer are comparable, similarly to the case of the exact transfer, but each is overestimated by the model. The exact and the modeled transfers exhibit only moderate pointwise correlation, which increases if conditional probabilities of forward and inverse transfers are considered. Probability distribution functions for modeled and exact transfers are in a good qualitative agreement. In all cases the results provided by the approximation are at least comparable to, and generally better than those provided by the classical Smagorinsky model.
On the entrainment process in plane turbulent wakes
Authors: Huang Z. , Kawall J. G. , Keffer J. F. , Ferré J. A.
Published: July 2002

An experimental investigation of the entrainment process in the near regions of two plane turbulent wakes, generated by a porous body and a solid body, has been performed by means of hot-wire anemometry, digital data acquisition, and a pattern recognition technique. A fine-scale turbulence-activity indicator function, based on the envelope of the second derivative of the velocities, is incorporated in the pattern recognition technique for the purpose of studying the entrainment process, and an isocontour map that serves to depict the latter is obtained. The results indicate that although the coherent structures pertaining to the two wake flows are qualitatively the same, the entrainment processes are fundamentally different. With respect to the solid-body wake, as has been widely accepted, the entrainment is due largely to the engulfment action of K ármán-like coherent structures; as a consequence, the entrainment per se is concentrated near the center of the wake. In contrast, with respect to the porous-body wake, the entrainment is due mainly to the action of small-scale eddies, with length scales that are significantly smaller than those of the Kármán-like structures, causing the entrainment to be concentrated near the edge of the flow.
Evidence of shocklets in a counterflow supersonic shear layer
Authors: Papamoschou Dimitri
Published: July 2002

In this Letter, experimental evidence of shocklets in a counterflow Mach 2 shear layer is presented. Schlieren photography reveals shock waves emanating from the turbulent structure; they are normal in the vicinity of the structure and weaken into Mach waves a short distance away from the shear layer. The slope of the Mach waves suggests that the turbulent structures are nonstationary, even though the shear layer is symmetric.
Space–time imaging of a turbulent near-wake by high-image-density particle image cinematography
Authors: Lin J.-C. , Vorobieff P. , Rockwell D.
Published: July 2002

A cinematographic system allows acquisition of high-image-density PIV images in the cross-flow plane of the near-wake of a cylinder at a Reynolds number of 10 000. Images were acquired at a temporal resolution corresponding to 1% of the period of formation of the large-scale spanwise (Kármán) vortices. Such a sequence of images leads to three-dimensional space–time representations, which show the relationship between the instantaneous concentrations of streamwise vorticity and the phase of formation of the large-scale Kármán vortices. The first spatial correlations of instantaneous streamwise vorticity, taken over the cross-flow plane, reveal that the predominant concentrations of streamwise vorticity maintain a spanwise wavelength of approximately one cylinder diameter.
The effects of viscosity on centre modes in the incompressible stability of a trailing line vortex
Authors: Duck Peter W.
Published: July 2002

The effects of viscosity on centre-modes of instability/stability are considered, with particular emphasis on the trailing line vortex. These effects are shown to be particularly significant when the axial wavenumber is within O(Re−1/(2+λ)) of the critical (inviscid) value, where Re is the Reynolds number, and λ is a (positive) parameter defined explicitly in the paper. Also examined are the critical (singular) layers that arise within the flow, which are shown to have thickness O(Re−2λ/3(4+2λ)). A number of numerical results are presented, and these show that viscosity seems to generally play a stabilising role on the stability of the flow. In the Appendix, wavenumbers somewhat closer to the critical inviscid value are examined, and the effects of viscosity are shown to substantially permeate outside of the critical layers, and lead to a system similar to that discussed by Stewartson, Ng and Brown [Philos. Trans. R. Soc. London Ser. A 324, 473 (1988)] in the context of swirling Poiseuille flow.
Scaling properties of the velocity increments correlation function
Authors: Camussi R. , Baudet C. , Benzi R. , Ciliberto S.
Published: July 2002

An experimental analysis of the scaling properties of the velocity increments correlation function is presented. It is found that the scaling behavior predicted by a shell model of turbulence, called the Gledzer-Ohkitani-Yamada (GOY) model, is in substantial agreement with present experimental results.
A mean field prediction of the asymptotic state of decaying 2D turbulence
Authors: Brands Hanna , Stulemeyer Jiri , Pasmanter Rubén A. , Schep Theo J.
Published: July 2002

We compare the quasi-stationary state obtained from a numerical integration of the two-dimensional Navier-Stokes equation, performed by Matthaeus et al. [Phys. Rev. Lett. 66, 2731 (1991)] with predictions of a mean field theory based on inviscid dynamics. We find that over a relatively short initial period, the theory does not apply, whereas at later stages its prediction for the quasi-stationary state is very good. We relate the failure and success of the inviscid theory to the relevance of viscous effects in the dynamics.
Experiments on the structure of baroclinic waves and zonal jets in an internally heated, rotating, cylinder of fluid
Authors: Bastin M. E. , Read P. L.
Published: July 2002

In this paper we report a laboratory investigation of the motion within a rotating cylinder of fluid subject to internal heating and to cooling at the outer cylindrical sidewall. The internal heating is supplied by ohmic dissipation as an electric current passes between the outer sidewall and an axial wire. The experiments focus on the formation of eddy features and the associated zonal jets. To identify how the flow regimes generated in this continuously forced system are modified by the presence of a radial depth gradient, experiments have been performed with both horizontal (f-plane) and oppositely sloping boundaries. Endwall configurations which cause the fluid depth (D) to increase with radius (∂D/∂r>0) and to decrease with radius (∂D/∂r<0) have been studied, as the former is applicable to the terrestrial atmosphere and oceans, while the latter may be relevant to deep atmospheres such as those of the giant planets and even planetary interiors. Stable, coherent, regular eddy features are observed over a wide range of rotation rates (Ω) in both horizontal and oppositely sloping endwall experiments. In the f-plane experiments regular modes with azimuthal wavenumbers m=1 and m=2 are observed. The regular wave regime of the ∂D/∂r>0 endwall experiments consists of modes with azimuthal wavenumbers m=1 to 5. Only the mode m=1 is seen in the regular wave regime of the ∂D/∂r<0 endwall experiments. The regular eddy structures produced in the ∂D/∂r>0 (∂D/∂r<0) endwall experiments are seen to be “vertically trapped” close to the bottom (top) boundary, whilst the amplitude of the f-plane modes is found not to vary substantially with depth. Further effects of the radial depth gradient are the observed reduction in the lateral scale of the eddy features in the ∂D/∂r>0 endwall experiments, which leads to the formation of between two and three independent trains of eddies within the lateral domain at sufficiently high values of Ω. Within the non-axisymmetric flow regimes of all three endwall configurations the number of zonal jets observed in the lateral domain of the experiment is larger than expected from the form of the background thermal forcing. The radial scale of the multiple zonal jets seen in the oppositely sloping boundary experiments is, however, much larger than a barotropic Rhines scale Lβ, suggesting that Lβ cannot be used to predict the radial wavenumber of the zonal mean flow in this continuously forced system.
Chaotic oscillations in a nearly inviscid, axisymmetric capillary bridge at 2:1 parametric resonance
Authors: Mancebo Francisco J. , Nicolás José A. , Vega José M.
Published: July 2002

We consider the 2:1 internal resonances (such that Ω1>0 and Ω2≃2Ω1 are natural frequencies) that appear in a nearly inviscid, axisymmetric capillary bridge when the slenderness Λ is such that 0<Λ<π (to avoid the Rayleigh instability) and only the first eight capillary modes are considered. A normal form is derived that gives the slow evolution (in the viscous time scale) of the complex amplitudes of the eigenmodes associated with Ω1 and Ω2, and consists of two complex ODEs that are balances of terms accounting for inertia, damping, detuning from resonance, quadratic nonlinearity, and forcing. In order to obtain quantitatively good results, a two-term approximation is used for the damping rate. The coefficients of quadratic terms are seen to be nonzero if and only if the eigenmode associated with Ω2 is even. In that case the quadratic normal form possesses steady states (which correspond to mono- or bichromatic oscillations of the liquid bridge) and more complex periodic or chaotic attractors (corresponding to periodically or chaotically modulated oscillations). For illustration, several bifurcation diagrams are analyzed in some detail for an internal resonance that appears at Λ≃2.23 and involves the fifth and eighth eigenmodes. If, instead, the eigenmode associated with Ω2 is odd, and only one of the eigenmodes associated with Ω1 and Ω2 is directly excited, then quadratic terms are absent in the normal form and the associated dynamics is seen to be fairly simple.
Taylor vortex instabilities induced by a rotating magnetic field: A numerical approach
Authors: Kaiser Th. , Benz K. W.
Published: July 2002

Numerical stability analysis and general flow characterization were performed for the flow induced by transverse rotating magnetic fields in cylindrical containers. Starting from Richardson’s theoretical critical value for the generation of Taylor vortices in infinite cylinders, overstability in finite cylinders with different aspect ratios was investigated. Decreasing aspect ratio leads to a more stable configuration. For small cylinders and reasonable frequencies of the magnetic field, instabilities arise at low magnetic inductions, e.g., Bc≈0.5 mT [gallium as model liquid, with radius of the cylinder R=12.5 mm, aspect ratio (h/d)=2 and frequency f=50 Hz]. As a source of instabilities Taylor vortices have been identified. They are transported by the secondary flow, emerging in finite cylinders due to the imbalance of pressure gradient and centrifugal force close to the top and bottom, thus generating time-dependent flow. Their generation is statistical and manifests itself in, e.g., nonperiodic temperature oscillations with small amplitudes in a classical Bénard configuration. Furthermore the intensity of the secondary flow was investigated for the isothermal case to give hints on its general influence on the overall mass transport.
Drop formation due to turbulent primary breakup at the free surface of plane liquid wall jets
Authors: Dai Z. , Chou W.-H. , Faeth G. M.
Published: July 2002

An experimental study of turbulent primary breakup at the free surface of plane liquid wall jets along smooth walls in still air at normal temperature and pressure is described. The study seeks a better understanding of spray formation processes in marine environments, such as in bow sheets. The measurements involved initially nonturbulent annular liquid wall jets, to approximate plane liquid wall jets, with the growth of a turbulent boundary layer along the wall initiated by a trip wire. Pulsed shadowgraphy and holography were used to observe liquid surface properties as well as drop sizes and velocities after turbulent primary breakup. Test conditions included several liquids (water, glycerol mixtures and ethyl alcohol), liquid/gas density ratios of 680–980, wall jet Reynolds numbers of 17 000–840 000 and Weber numbers of 6 100–57 000, at conditions where direct effects of liquid viscosity were small. Measurements included the following: location of the onset of surface roughness, drop size and velocity distributions after breakup, flow properties at the onset of breakup, and mean drop sizes and velocities after breakup. In general, the measurements were correlated successfully based on phenomenological theories.
The viscous-convective subrange in nonstationary turbulence
Authors: Chasnov J. R.
Published: July 2002

The similarity form of the scalar-variance spectrum at high Schmidt numbers is investigated for nonstationary turbulence. Theoretical arguments show that Batchelor scaling may apply only at high Reynolds numbers. At low Reynolds numbers, Batchlor scaling is not possible unless the turbulence is stationary or the enstrophy decays asymptotically as t−2. When this latter condition is satisfied, it is shown from an analysis using both the Batchelor and Kraichnan models for the scalar-variance transfer spectrum that the k−1 power law in the viscous-convective subrange is modified. Results of direct numerical simulations of high Schmidt number passive scalar transport in stationary and decaying two-dimensional turbulence are compared to the theoretical analysis. For stationary turbulence, Batchelor scaling is shown to collapse the spectra at different Schmidt numbers and a k−1 viscous-convective subrange is observed. The Kraichnan model is shown to accurately predict the simulation spectrum. For nonstationary turbulence decaying at constant Reynolds number for which the enstrophy decays as t−2, scalar fields for different Schmidt numbers are simulated in situations with and without a uniform mean scalar gradient. The Kraichnan model is again shown to predict the spectra in these cases with different anomalous exponents in the viscous-convective subrange.
The compressible inviscid algebraic instability for streamwise independent disturbances
Authors: Hanifi Ardeshir , Henningson Dan S.
Published: July 2002

An inviscid algebraic instability for streamwise independent disturbances in compressible flow is found to be related to Ellingsen and Palm’s [Phys. Fluids 18, 487 (1975)] solution for incompressible flow. For compressible flow, the streamwise disturbance velocity, the density, as well as temperature perturbations grow linearly with time. The effect of viscosity on the inviscid algebraic growth is clarified using a rescaling of the viscous disturbance equations, showing the dependence of the viscous transient growth on the Reynolds number.
On the statistical solution of the Riemann equation and its implications for Burgers turbulence
Authors: E Weinan , Vanden Eijnden Eric
Published: July 2002

The statistics of the multivalued solutions of the forced Riemann equation, ut+uux=f, is considered. An exact equation for the signed probability density function of these solutions and their gradient ξ=ux is derived, and some properties of this equation are analyzed. It is shown in particular that the tails of the signed probability density function generally decay as |ξ|−3 for large |ξ|. Further considerations give bounds on the cumulative probability density function for the velocity gradient of the solution of Burgers equation.
Magnetic-field generation and turbulence suppression due to cross-helicity effects
Authors: Yokoi Nobumitsu
Published: July 2002

The regeneration mechanism of magnetic fields in turbulent motion is studied using a turbulent dynamo model, in which effects of global plasma rotation are incorporated through the turbulent cross helicity (velocity/magnetic-field correlation). The turbulent model consists of the mean-field equations and the transport equations for turbulent quantities such as the turbulent energy, its dissipation rate, and the turbulent cross helicity. Prominent properties of the cross-helicity effect, such as the direct linkage to the mean vortical motion, the alignment of the mean electric current and the mean vorticity, etc., are discussed in comparison with the helicity or α effect. This model is applied to simple plasma flows, such as a cylindrical pipe and an accretion disk. The numerical results show that the turbulence suppression and magnetic-field generation due to the cross-helicity effects occur in the presence of mean vortical motion. The possible cross-helicity production mechanisms are also discussed.