bluuebunny/crossref_metadata_2025 huggingface dataset:
Relativistic theories of dissipative fluids
Authors: Geroch Robert
Published: July 2002

The simple Navier–Stokes equations for dissipative fluids, translated into relativity, form a parabolic—and hence mathematically nonviable—system. There have been formulated numerous alternative theories, consisting instead of hyperbolic equations—theories that necessarily involve more dynamical variables and more free functions than does the simple Navier–Stokes theory. It is argued that, these mathematical differences notwithstanding, the physical content of these hyperbolic theories is in most cases precisely the same as that of Navier–Stokes.
Boson mapping of symplectic algebras with Abelian subalgebra mapped as coordinates
Authors: Hess P. O. , López J. C.
Published: July 2002

An extended Dyson and Holstein-Primakoff boson mapping is constructed for coordinate systems. Only functions which depend on even powers in the coordinates are considered. It is shown that the Holstein-Primakoff boson mapping for coordinate systems is different from the one using creation and annihilation operators, with some advantages in application. As an example the mapping is applied to the schematic model of constant gauge fields in Quantum-Chromo-Dynamics with SU(2) for color. Other possible applications related to field theory are briefly discussed.
Local differential geometry as a representation of the supersymmetric oscillator
Authors: Thienel H.-P.
Published: July 2002

The choice of a coordinate chart on an analytical Rn(Rna) provides a representation of the n-dimensional supersymmetric oscillator. The 1-parameter group of dilations provides a Euclidean evolution moving the system through a sequence of charts, that at each instant supply a Hilbert space by Cartan’s exterior algebra endowed with a suitable scalar product. Stationary states and coherent states are eigenstates of the Lie derivatives generating the dilations and the translations, respectively.
A geometric formulation of the equivalence principle
Authors: Coleman Robert Alan , Schmidt Heinz-Jürgen
Published: July 2002

The principle of equivalence says that at any given space–time point, there exists a local coordinate system with respect to which the three-acceleration of a freely falling test body vanishes regardless of its three-velocity. In this article, a more intrinsic and geometric criterion for free fall motion is provided. The criterion is much simpler than a recently proposed criterion that is based on the Desargues property. For space–times of dimension greater than 2, the Desargues property is a theorem. It is shown that it suffices to require that a version of Pasch’s axiom is satisfied; that is, two paths in a plane intersect up to corrections of order ε3, where ε is the scale parameter of a shrinking process.
Skyrme models with self-dual limits: d=2,3
Authors: Arthur K. , Roche G. , Tchrakian D. H. , Yang Yisong
Published: July 2002

The most general Skyrme–Sigma models in two and three Euclidean dimensions described by O(3) and O(4) fields, respectively, are studied first by numerical methods, and analytic proofs of existence are subsequently given. Particular emphasis is given to the special cases of these models, where the topological inequalities can be saturated by self-duality equations. The O(d+1) models in d dimensions exhibit qualitatively similar features.
Canonical quantization of spontaneously broken topologically massive gauge theory
Authors: Chen Lusheng , Dunne Gerald , Haller Kurt , Lim-Lombridas Edwin
Published: July 2002

In this paper we investigate the canonical quantization of a non-Abelian topologically massive Chern–Simons theory in which the gauge fields are minimally coupled to a multiplet of scalar fields in such a way that the gauge symmetry is spontaneously broken. Such a model produces the Chern–Simons–Higgs mechanism in which the gauge excitations acquire mass both from the Chern–Simons term and from the Higgs–Kibble effect. The symmetry breaking is chosen to be only partially broken, in such a way that in the broken vacuum there remains a residual non-Abelian symmetry. We develop the canonical operator structure of this theory in the broken vacuum, with particular emphasis on the particle-content of the fields involved in the Chern–Simons–Higgs mechanism. We construct the Fock space and express the dynamical generators in terms of creation and annihilation operator modes. The canonical apparatus is used to obtain the propagators for this theory, and we use the Poincaré generators to demonstrate the effect of Lorentz boosts on the particle states.
Bicrossproduct Hopf superalgebras and D=4 κ-deformed Poincaré supergroup
Authors: Kosiński P. , Lukierski J. , Maślanka P. , Sobczyk J.
Published: July 2002

The general framework of bicrossproduct Hopf algebras given by Majid is extended to Z2-graded bicrossproduct Hopf superalgebras. As examples of bicrossproduct Hopf superalgebras we provide the graded algebras of functions on undeformed as well as κ-deformed D=4 Poincaré supergroups.
Marsden–Weinstein reduction on graded symplectic manifolds
Authors: Baguis P. , Stavracou T.
Published: July 2002

We extend the Marsden–Weinstein reduction of Hamiltonian systems with symmetry to the category of graded manifolds. We define free, proper, and symplectic actions in the graded setting; especially for the symplectic actions of graded Lie groups, it is possible to speak about momentum mappings. We also examine the reduction of the graded Hamiltonian derivations which determines the dynamics on the reduced phase space for constrained supersystems with symmetry. We apply the general formalism to specific examples, thus constructing graded (complex) projective spaces, and proving that the coadjoint orbits of graded Lie groups are reduced graded symplectic manifolds.
Generalized Lie algebras of type An
Authors: Lyubashenko Volodymyr , Sudbery Anthony
Published: July 2002

It is shown that the quantized enveloping algebra of sl(n) contains a generalized Lie algebra, defined by means of axioms similar to Woronowicz’s. This gives rise to Lie algebra-like generators and relations for the locally finite part of the quantized enveloping algebra, and suggests a canonical Poincaré–Birkhoff–Witt basis.
Local U(2,2) symmetry in relativistic quantum mechanics
Authors: Finster Felix
Published: July 2002

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory.
Symplectic-energy-momentum preserving variational integrators
Authors: Kane C. , Marsden J. E. , Ortiz M.
Published: July 2002

The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving. To do this, a space–time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy. Criteria for the solvability of the time steps and some numerical examples are given.
Time-dependent Schrödinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states
Authors: Nieto Michael Martin , Truax D. Rodney
Published: July 2002

Using the transformations from paper I, we show that the Schrödinger equations for (1) systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators all have isomorphic Lie space–time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is demonstrated.
A critical comparison of turbulence models for homogeneous shear flows in a rotating frame
Authors: Speziale Charles G. , Gatski Thomas B. , Mac Giolla Mhuiris Nessan
Published: July 2002

A variety of turbulence models, including five second-order closures and four two-equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates, in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range −0.1≤Ω/S≤0.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of their predictions.
Scattering of a capillary–gravity wave by a vertical cylinder
Authors: Mahdmina D. , Hocking L. M.
Published: July 2002

The scattering of a capillary–gravity wave by a surface-piercing obstacle depends on the condition applied at the contact line between the fluid and the obstacle. A model for this condition that incorporates the effect of dynamic contact-angle variation is used to determine the wave field close to the obstacle and at large distances from it. The solutions depend on the ratio between the wavelength of the incident wave and the radius of the obstacle, which is taken to be a circular cylinder, and on the relative size of the capillary and gravitational restoring forces. A third parameter is a constant of proportionality in the edge condition. Extreme values of this parameter relate to the special cases of orthogonal contact and of a fixed contact line. The strength of the scattered wave and the angular variation of its amplitude at large distances are calculated for a range of values of the parameters. The amplitude of the surface elevation on the boundary of the cylinder is also determined.
Nonlinear stability of a heated thin liquid film with variable viscosity
Authors: Reisfeld B. , Bankoff S. G.
Published: July 2002

The stability of a heated liquid film subjected to surface tension and van der Waals forces is explored in the case where the fluid viscosity is temperature dependent. The limits of very large and very small Biot numbers are examined, and in these cases it is found that the evolution equation can be rescaled to return the model equation developed by Williams and Davis [J. Colloid Interface Sci. 90, 220 (1982)] for an isothermal film. The effect of variable viscosity is deduced and is found to reduce the rupture time of the film relative to the constant-viscosity result.
Stokesian dynamics simulations of particle trajectories near a plane
Authors: Bossis G. , Meunier A. , Sherwood J. D.
Published: July 2002

The trajectories of spherical particles close to a plane in shear flow are computed, taking into account lubrication forces and many-body hydrodynamic interactions between spheres, and between spheres and the plane. It is shown that the relative motion of two particles may be reversed by the presence of the plane, and eddylike recirculation motions can occur. The resistance coefficient of a linear chain of N spheres is calculated as a function of the distance of the chain from the plane, and is shown to agree well with a simple model based on a screening coefficient derived from a single pair of spheres.
Influence of velocity slip and temperature difference on internal relaxation in diatomic–monatomic mixture free-jet expansion
Authors: Chidiac C. , Perrin M. Y. , Martin J. P.
Published: July 2002

The supersonic expansion of a mixture of a heavy gas and a light gas may result in a velocity slip and a temperature difference between light and heavy species. The purpose of this paper is to study the influence of these phenomena on the relaxation of internal degrees of freedom which takes place when one of the gases is a diatomic one. The model presented is based on the Wang–Chang–Uhlenbeck theory and on the assumption of a two-velocity and two-temperature model to represent the velocity distributions. The model incorporates the internal degrees of freedom of the diatomic molecule and can be used to study the effect of velocity slip and temperature difference on the mechanism of internal energy transfer involved in a free-jet expansion. The hydrodynamical equations and the master kinetic equations are derived. The formalism is applied to the system I2–He, assuming that a rotational temperature and a relaxation equation to describe the rotational relaxation can be defined. The unexpected high rotational temperatures observed experimentally in I2–He expansions presenting a velocity slip are reproduced.
Surface waves on viscous magnetic fluid flow down an inclined plane
Authors: Shen M. C. , Sun S. M. , Meyer R. E.
Published: July 2002

The objective of this paper is to study weakly nonlinear waves on a viscous magnetic fluid flow down an inclined plane under the influence of gravity and a constant magnetic field parallel to the plane. An approximate evolution equation is derived and a critical Reynolds number for the stability of three-dimensional long waves obtained. It is found that the component of the applied magnetic field aligned with the flow has a stabilizing effect but that the transverse component, however, has a destabilizing effect on the long waves. Stability regions of two-dimensional long waves at the critical Reynolds number and numerical results for the solution of a nonlinear ill-posed problem are presented. Several progressive-wave solutions are also given.
Large eddy simulation of turbulence-driven secondary flow in a square duct
Authors: Madabhushi Ravi K. , Vanka S. P.
Published: July 2002

The fully developed turbulent flow in a straight duct of square cross section has been simulated using the large eddy simulation (LES) technique. A mixed spectral-finite difference method has been used in conjunction with the Smagorinsky eddy-viscosity model for the subgrid scales. The simulation was performed for a Reynolds number of 360 based on friction velocity (5810 based on bulk velocity) and duct width. The simulation correctly predicted the existence of secondary flows and their effects on the mean flow and turbulence statistics. The results are in good qualitative agreement with the experimental data available at much higher Reynolds numbers. It is observed that both the Reynolds normal and shear stresses equally contribute to the production of mean streamwise vorticity.
The nonlinear Boltzmann equation including internal degrees of freedom
Authors: Schürrer F. , Griehsnig P. , Kügerl G.
Published: July 2002

A spatially homogeneous and isotropic gas, consisting of particles with internal degrees of freedom is considered. The corresponding extended Boltzmann equations are transformed into a system of scalar kinetic equations. The elastic and inelastic collisions are described by means of a generalized Krook–Wu model. The principle of microscopic reversibility is taken into account. A closed analytic form has been found for the resulting scalar scattering kernels. Their symmetries are sufficient to prove energy conservation and an H theorem.
Turbulent wakes of linearly stratified flow past a sphere
Authors: Lin Qiang , Boyer D. L. , Fernando H. J. S.
Published: July 2002

Experimental observations and associated scaling analyses are presented for the flow of a linearly stratified fluid past a sphere for conditions under which the wake is fully turbulent. It is shown that for internal Froude numbers Fi≲2, the turbulent wake is suppressed by stratification in the immediate lee of the sphere. For Fi≳2, the normalized thickness δT/D grows as t1/3 before the wake height reaches its maximum (which takes place at Nt≊2.0), much the same as for wakes of spheres in homogeneous flow; here D is the sphere diameter, N is the buoyancy frequency, and t is the time. The normalized horizontal wake dimension γT/D, on the other hand, grows in the near wake as t1/3 for all Fi but, for Nt≳2.0, grows somewhat more rapidly as t1/2. The Strouhal number for the far-wake vortex street is measured and shown to be roughly a constant St≊0.18, independent of the Reynolds and Froude numbers. It is suggested that the frequency of the far-wake, quasi-two-dimensional vortices is established by the eddy shedding frequency of the near wake and thus is independent of stratification effects.
Comment on ‘‘Is intermittent motion of outer flow in the turbulent boundary layer deterministic chaos?’’ [Phys. Fluids A 3, 1941 (1991)]
Authors: Meneveau Charles
Published: July 2002

Recently, Tsuji et al. [Phys. Fluids A 3, 1941 (1991)] presented measurements of the probability density of sizes of laminar regions in the upper portion of a turbulent boundary layer. This size distribution was shown to have a power-law decay exponent close to −4/3, and it was shown that certain one-dimensional chaotic maps have the same property. Here, it is argued that the experimental observations can also be explained by two different paradigms for the interface separating turbulent from irrotational fluid. The first is that of a globally self-similar fractal surface of Hausdorff dimension DH=7/3. The second is that of a power-law spiral sheet with a box dimension of the same value. Both are consistent with other experimental evidence to date, as well as with the Kolmogorov scaling of turbulent velocity fluctuations.
Stability of high-speed compressible rotating Couette flow
Authors: Hatay F. F. , Biringen S. , Erlebacher G. , Zorumski W. E.
Published: July 2002

In this study, the linear stability of high-speed, rotating Couette flow to two- and three-dimensional disturbances in finite-gap spacings, including the full effects of compressibility and viscosity, is considered. Particularly, the combined effects of Mach number, Reynolds number, radial heating, and gap spacing are investigated. For a stationary outer cylinder, the primary instability is an axisymmetric mode independent of the Mach number. Increasing Mach numbers have a destabilizing effect for wide gaps, and a stabilizing effect for narrow gaps. For a sufficiently fast, counter-rotating outer cylinder, the primary instability becomes a three-dimensional traveling wave. Compressibility has a stabilizing effect on these modes regardless of the gap width; also, heating at the outer cylinder stabilizes the flow. Bicritical points for the primary instability corresponding to the crossover of the azimuthal wave numbers are determined for cylinders counter-rotating with equal angular speed.
Stochastic forcing of the linearized Navier–Stokes equations
Authors: Farrell Brian F. , Ioannou Petros J.
Published: July 2002

Transient amplification of a particular set of favorably configured forcing functions in the stochastically driven Navier–Stokes equations linearized about a mean shear flow is shown to produce high levels of variance concentrated in a distinct set of response functions. The dominant forcing functions are found as solutions of a Lyapunov equation and the response functions are found as the distinct solutions of a related Lyapunov equation. Neither the forcing nor the response functions can be identified with the normal modes of the linearized dynamical operator. High variance levels are sustained in these systems under stochastic forcing, largely by transfer of energy from the mean flow to the perturbation field, despite the exponential stability of all normal modes of the system. From the perspective of modal analysis the explanation for this amplification of variance can be traced to the non-normality of the linearized dynamical operator. The great amplification of perturbation variance found for Couette and Poiseuille flow implies a mechanism for producing and sustaining high levels of variance in shear flows from relatively small intrinsic or extrinsic forcing disturbances.
Radial ion transport measurements in a nonaxisymmetric magnetic mirror
Authors: Goodman D. L. , Petty C. C. , Post R. S.
Published: July 2002

Experimental radial ion transport rates and diffusion coefficients are presented for the Constance-B magnetic mirror [Phys. Rev. Lett. 58, 1853 (1987)]. The transport experiments are performed by measuring steady state equilibrium radial profiles of plasma density, ionization source, end loss current, electric field, electron temperature, and ion temperature. A charge coupled device (CCD) camera system [Rev. Sci. Instrum. 60, 2835 (1989)] is used to measure the two-dimensional radial density, source, and electron temperature profiles. End loss diagnostics including movable Faraday cups, electrostatic end loss analyzers, and an ion time-of-flight analyzer [Rev. Sci. Instrum. 59, 601 (1988)] are used to measure radial profiles of potential and ion temperature. The ion confinement time perpendicular to the magnetic field is found to be an order of magnitude shorter than predicted by classical and neoclassical transport theories. The radial profiles of the perpendicular diffusion coefficient (D⊥) are presented for hydrogen, helium, and argon plasmas. The coefficients are a factor of 10 larger than the maximum classical and neoclassical coefficients in all three plasmas. Plasma fluctuations resulting from whistler mode microinstability [Phys. Rev. Lett. 59, 1821 (1987)] as well as nonaxisymmetric potentials are suggested as possible explanations for the experimentally measured radial transport rate.
Axisymmetric magnetohydrodynamic equations: Exact solutions for stationary incompressible flows
Authors: Bacciotti Francesca , Chiuderi Claudio
Published: July 2002

The paper describes a new set of exact analytical solutions of the axisymmetric magnetohydrodynamic (MHD) equations for stationary and incompressible flows. The magnetic and flow surfaces are assumed to form a regularly nested set to stress the physical character of the solutions. As a result, these show a self-similar radial behavior. A suitable choice of the reference system reduces the problem to a single differential equation equivalent to the generalized Grad–Shafranov equation. The proposed method leads to the explicit expressions of the magnetic and flow surfaces. The analytical form of all the physical quantities for each possible shape of the surfaces can then be obtained in terms of two arbitrary functions of the self-similar radial variable, one being the density. By comparison, standard treatments of the generalized Grad–Shafranov equation require the specification of up to five arbitrary functions.
Nonlinear theory of stable, efficient operation of a gyrotron at cyclotron harmonics
Authors: Saraph G. P. , Antonsen T. M. , Nusinovich G. S. , Levush B.
Published: July 2002

One of the main obstacles in achieving stable, efficient operation at the cyclotron harmonics in a gyrotron is mode competition with parasitic modes at the fundamental frequency. In this article, the nonlinear dynamics of mode interactions in such a system are studied using a multifrequency, time-dependent model. The results of numerical simulations for a second harmonic gyrotron are presented by considering two starting scenarios: (a) fast voltage rise or an instant turn-on case, and (b) slow voltage rise case. For the first case, it is demonstrated that for a certain range of operating parameters, the presence of a parasitic mode at the fundamental can be helpful in the excitation of the second harmonic operating mode. In the second case, it is found that the unstable operating region increases with the value of the rise time constant of the electrode voltages. Stable, efficient gyrotron operation at the second harmonic is demonstrated using the numerical study.
Long-wavelength negative mass instabilities in high current betatrons
Authors: Godfrey Brendan B. , Hughes T. P.
Published: July 2002

Growth rates of negative mass instabilities in conventional and modified betatrons are calculated by analytic methods and by performing three-dimensional particle simulations. In contrast to earlier work, toroidal corrections to the field equations are included in the analytic model. As a result, good agreement with numerical simulations is obtained. The simulations show that the nonlinear development of the instabilities can seriously disrupt the beam.
Particle simulation of drift waves in a sheared magnetic field
Authors: Sydora R. D. , Leboeuf J. N. , Tajima T.
Published: July 2002

Electrostatic properties of density gradient drift waves (the universal mode) in a sheared magnetic field are studied using a two-and-one-half dimensional (2 1/2 -D) particle code. For the case of a single rational surface, the drift waves are found to be stable with an eigenmode structure that matches the linear theoretical prediction as long as the ion resonance layer is well within the system. This applies to both even and odd parity modes with respect to the rational surface. The dependence on various parameters such as the shear length is examined.
Transverse oscillations of an electron beam propagating in the ion focused regime
Authors: Schneider R. F. , Smith J. R.
Published: July 2002

A magnetic probe array is utilized to perform current centroid measurements of a 4 kA, 700 kV, 100 nsec electron beam propagating in the ion focused regime. Results with several filling gases all show transverse oscillation, which may be indicative of hose-type motions of the beam.
Measurements of amplification and phase shift (wave refractive index) in a free-electron laser
Authors: Fajans J. , Bekefi G.
Published: July 2002

Measurements of the amplification and phase shifts (wave refractive index) in a free-electron laser (FEL) are reported. The studies have been carried out at microwave frequencies (7–16 GHz) in a free-electron laser operating in the collective (Raman) regime, using a mildly relativistic electron beam with energy of ∼160 keV, and current of ∼5 A. The observations are found to be in excellent agreement with theoretical predictions based on the full three-dimensional FEL dispersion relation.
Optimization of gyroklystron efficiency
Authors: Tran T. M. , Danly B. G. , Kreischer K. E. , Schutkeker J. B. , Temkin R. J.
Published: July 2002

In this article, the optimization of gyroklystron efficiency is investigated by employing a two–step procedure. As a first step, the prebuncher is analyzed using a small signal approximation, since the cavity(ies) here serve mainly to modulate the velocities of the electrons slightly, which will be bunched in the field-free drift section(s). It is found that the electrons entering the energy extraction cavity can be characterized entirely by only two dimensionless parameters: a bunching parameter q and a relative phase ψ. The numerical simulation of the extraction cavity, based on the nonlinear pendulum equations describing the interaction between the electrons and the rf field, supplemented by the initial conditions specified by q and ψ, constitutes the second step. The final result of this two-step analysis is the efficiency, η⊥,opt optimized with respect to q, ψ, and the magnetic detuning parameter Δ. This efficiency depends only on the normalized cavity length μ and the normalized rf field F of the energy extraction section. The efficiency as well as the conditions required to attain this optimum (qopt,Δopt, and qopt) are presented as contour plots on the (F,μ) plane and can be used efficiently to design gyroklystrons of any frequency and output power.
A radio frequency current drive model and its comparison with experiments
Authors: Yoshioka K. , Okazaki T. , Leuterer F. , Fujisawa N.
Published: July 2002

A simple analytic model for the estimation of lower-hybrid-generated current in the presence of a dc electric field is derived. The model is based on a perturbation solution of the adjoint problem to the Fokker–Planck equation and includes the effect of the continuous wave spectrum. It indicates that the dependence of the current drive efficiency on the dc electric field is determined only by the wave accessibility condition. The model’s results are found to agree with the ASDEX tokamak lower-hybrid experimental data [Plasma Phys. Controlled Fusion 27, 1399 (1985)] as well as the newly developed two-dimensional Fokker–Planck code results. The predictions lie within an experimental scattering of about 20%.
Stochastic transition intermittency in pipe flows: Experiment and model
Authors: Zhang Jun , Stassinopoulos Dimitris , Alstro/m Preben , Levinsen Mogens T.
Published: July 2002

New experimental results at the onset of turbulence in a gravity-driven pipe flow are presented, and a simple phenomenological model is introduced to describe the intermittent behavior observed. In this model slugs are stochastically produced at the pipe inlet, and the decrease in velocity due to turbulent friction is taken into account. The present approach shows that stochastic arguments account well for several experimental observations at low intermittency factors. In particular, it is shown that special intermittency routes to chaos are not needed to explain the exponentially decaying inverse cumulative distribution of laminar times.
Viscous structure of plane waves in spatially developing shear flows
Authors: Le Dizès Stéphane , Monkewitz Peter A. , Huerre Patrick
Published: July 2002

This paper is concerned with the propagation of linear plane waves in incompressible, two-dimensional weakly nonparallel shear flows for large Reynolds numbers. Waves are analyzed for arbitrary complex frequency ω and local wave number k when nonparallel effects are assumed to be due to weak viscous diffusion. The inviscid approximation is shown to correctly describe, at leading order, the cross-stream variations of local plane waves at all stations where they are locally amplified in a frame of reference moving at the local phase speed ℜeω/ℜek, i.e., at stations where the temporal growth rate σ≡𝔉mω−𝔉mk ℜeω/ℜek remains positive. This result also holds as long as the local phase speed lies outside the range of values reached by the basic velocity profile. By contrast, the inviscid approximation fails to represent cross-stream variations in the critical layers when waves are locally neutral (σ=0), and in large viscous regions when they become damped (σ<0). Uniformly valid WKBJ approximations are derived in these regions and the results are applied to the description of forced spatial waves and self-excited global modes. © 1995 American Institute of Physics.
Evidence for transient disturbance growth in a 1961 pipe-flow experiment
Authors: Mayer Ernst W. , Reshotko Eli
Published: July 2002

Evidence is presented for what appears to have been nonmodal disturbance growth in a pipe-flow experiment performed by Kaskel [Technical Report No. 32-138, Jet Propulsion Laboratory, California Institute of Technology, 1961], based on a comparison of the experimental traces of disturbance amplitude with predictions of transient amplitude growth calculated from the underlying linear stability operator. Owing to the geometry of the experimental disturbance generator, modes having azimuthal wavenumbers n=0, 6 and 12 are expected to contribute the bulk of the disturbance energy, and numerically predicted amplitude growth versus downstream distance is in good agreement with the experiment.
Linear stability analysis of plane quadratic flows in a rotating frame with applications to modeling
Authors: Salhi Abdelaziz , Cambon Claude , Speziale Charles G.
Published: July 2002

The linear response of turbulence to a distortion and simple rotation is investigated in this paper from a fundamental theoretical standpoint. Quadratic flows are a special case of planar flows with constant mean velocity gradients, which can be characterized by a constant rate of strain D and a constant spanwise (normal to the plane) vorticity component −W=2Ω0, with arbitrary values (here, we can take D>0 and W>0 without any loss of generality). According to the sign of D2−Ω02, streamlines are hyperbolic, rectilinear (pure shear flow) or elliptic. Since these flows can also be considered as mean flows, when superimposing a three-dimensional disturbance (or fluctuating turbulent) field which satisfies statistical homogeneity, the linearized analysis of the disturbance field is of interest both from the point of view of hydrodynamic stability (e.g., the elliptical flow instability) and from the point of view of homogeneous rapid distortion theory (RDT) including applications to the basic statistics. The case of quadratic flow in a rotating frame (with angular velocity Ω in the direction normal to the plane of the basic flow) is revisited in this paper, in order to complete—with the three parameters D, −W=2Ω0 and Ω—previous works on linear theory by Cambon et al. [J. Fluid Mech. 278, 175 (1994)] and Speziale, Abid, and Blaisdell [Phys. Fluids 8, 781 (1996)]. From a simplified “pressure-less” linear approach, a general stability criterion is derived based on the value of the modified Bradshaw number Br=[D2−(2Ω+Ω0)2]/S2 (S=D−Ω0), which coincides with the rotational Richardson number introduced by Bradshaw [J. Fluid Mech. 36, 177 (1969)] and denoted by B=2Ω(S−2Ω)/S2 (in particular, for the case of pure shear flow where D=W/2=−Ω0=S/2). It is shown that this criterion gives results identical to the “true” linear stability analysis (including the effect of the fluctuating pressure) if the absolute vorticity 2Ω+2Ω0 has a zero value. In addition, the relevance of this criterion is checked with respect to the true linear approach in distorted wave space and related RDT applications. For all of the cases, the maximum amplification for the three-dimensional disturbance field is found for zero tilting vorticity 2Ω+Ω0 and for pure spanwise modes (with wave vector normal to the plane of the quadratic flow), in accordance with the generalized Bradshaw criterion and other results in hydrodynamic stability. For other spectral directions, the agreement is not as complete except for the pure shear case, and this is particularly discussed looking at statistical RDT solutions, which involve a summation over all directions of the wave vector. Finally, the impact of the whole analysis on second-order, one-point modeling is discussed.
Motion of a finger with bubbles in a Hele-Shaw cell: An exact solution
Authors: Vasconcelos Giovani L.
Published: July 2002

Exact solutions are reported for the problem of a finger moving steadily with bubbles at the tip in a Hele-Shaw cell in the absence of surface tension.
Computational simulations of vorticity enhanced diffusion
Authors: Vold Erik L.
Published: July 2002

Computer simulations are used to investigate a phenomenon of vorticity enhanced diffusion (VED), a net transport and mixing of a passive scalar across a prescribed vortex flow field driven by a background gradient in the scalar quantity. The central issue under study here is the increase in scalar flux down the gradient and across the vortex field. The numerical scheme uses cylindrical coordinates centered with the vortex flow which allows an exact advective solution and 1D or 2D diffusion using simple numerical methods. In the results, the ratio of transport across a localized vortex region in the presence of the vortex flow over that expected for diffusion alone is evaluated as a measure of VED. This ratio is seen to increase dramatically while the absolute flux across the vortex decreases slowly as the diffusion coefficient is decreased. Similar results are found and compared for varying diffusion coefficient, D, or vortex rotation time, τv, for a constant background gradient in the transported scalar vs an interface in the transported quantity, and for vortex flow fields constant in time vs flow which evolves in time from an initial state and with a Schmidt number of order unity. A simple analysis shows that for a small diffusion coefficient, the flux ratio measure of VED scales as the vortex radius over the thickness for mass diffusion in a viscous shear layer within the vortex characterized by (Dτv)1/2. The phenomenon is linear as investigated here and suggests that a significant enhancement of mixing in fluids may be a relatively simple linear process. Discussion touches on how this vorticity enhanced diffusion may be related to mixing in nonlinear turbulent flows.
A new proof of Kolmogorov’s 4/5-law
Authors: Rasmussen H. O.
Published: July 2002

This paper presents a proof of Kolmogorov’s 4/5-law that uses only elementary vector analysis and which thereby avoids the more intricate tensor analysis. From this proof, it is easily seen that the 4/5-law holds also for turbulence lacking reflectional symmetry. Ordinary tensor analysis is used in order to confirm this conclusion.
Modification of turbulent helical/nonhelical flows with small-scale energy input
Authors: Suzuki Yuji , Nagano Yasutaka
Published: July 2002

Modification of helical/nonhelical turbulence by adding small-scale turbulence is investigated with the aid of direct numerical simulations of isotropic turbulence. Detailed characteristics of the energy and helicity spectral transfer were examined. It is found that nonlocal energy cascade through isosceles triads toward the wave-number range of the energy input is markedly enhanced, thus the turbulent intensity is decreased faster than a flow field with no energy input. The optimum wave number for turbulence reduction depends only on the characteristic wave number of the energy-containing range, once the magnitude of the energy input is given. A model equation for isosceles triads derived from the EDQNM approximation indicates that the optimum wave number increases with increasing energy ratio between the energy input and the parent turbulence. For helical turbulence, the sign of helicity is crucial for the helicity and energy transfer as well as the decay rate. When the helicity of small-scale energy input has the same sign as that of the parent turbulence, enhancement of the energy cascade is notedly deteriorated. The mechanism of suppressing interaction between the parent helical turbulence and the small-scale energy input is also explained with the aid of the EDQNM approximation.
Optimization of fluid front dynamics in porous media using rate control. I. Equal mobility fluids
Authors: Sudaryanto Bagus , Yortsos Yannis C.
Published: July 2002

In applications involving the injection of a fluid in a porous medium to displace another fluid, a main objective is the maximization of the displacement efficiency. For a fixed arrangement of injection and production points (sources and sinks), such optimization is possible by controling the injection rate policy. Despite its practical relevance, however, this aspect has received scant attention in the literature. In this paper, we provide a fundamental approach based on optimal control theory, for the simplified case when the fluids are miscible, of equal viscosity, and in the absence of dispersion and gravity effects. Both homogeneous and heterogeneous porous media are considered. From a fluid dynamics viewpoint, this is a problem in the deformation of material lines in porous media, as a function of time-varying injection rates. It is shown that the optimal injection policy that maximizes the displacement efficiency, at the time of arrival of the injected fluid, is of the “bang–bang” type, in which the rates take their extreme values in the range allowed. This result applies to both homogeneous and heterogeneous media. Examples in simple geometries and for various constraints are shown, illustrating the efficiency improvement over the conventional approach of constant rate injection. In the heterogeneous case, the effect of the permeability heterogeneity, particularly its spatial correlation structure, on diverting the flow paths, is analyzed. It is shown that bang–bang injection remains the optimal approach, compared to constant rate, particularly if they were both designed under the assumption that the medium was homogeneous. Experiments in a homogeneous Hele-Shaw cell are found to be in good agreement with the theory.
Toroidal phase locking phenomena and nonaxisymmetric flux perturbations in the Extrap T1 reversed-field pinch
Authors: Mazur S.
Published: July 2002

The structure of the magnetic fluctuations in the Extrap T1 reversed-field pinch [Phys. Scr. 44, 358 (1991)] has been studied over the pinch parameter range 1.6<Θ=Bθ(a)/〈Bφ〉<2.2. It is found that nonaxisymmetric perturbations of the toroidal flux and edge field dominate the global dynamics at all Θ. These perturbations are formed by phase locking of the dominant m=1 modes and m=0 modes due to strong nonlinear interaction. This m=1/m=0 mode locking rotates toroidally in the electron drift direction, with an angular rotation velocity of typically 3.3×104 rad/s. The toroidal mode numbers of the m=0 modes are consistent with being nonlinearly driven by the m=1 modes. Evidence is found that the behavior of the leading m=1 mode governs the degree of phase locking. The role of this phenomenon in mean field maintenance is discussed.
On the stability of axisymmetric modes in straight tokamaks
Authors: Zeiler A.
Published: July 2002

Axisymmetric magnetohydrodynamic m=1 modes in plane plasma–vacuum equilibria, which reduce to rigid shifts in the cylindrically symmetric limit, are investigated. It is shown that in elliptically corrugated equilibria stability to a given shift depends crucially on the direction of the shift (leading to the well-known vertical-shift instability), whereas in triangular or even more highly corrugated equilibria the direction of the shift is of no importance. Additionally, stability of elliptically corrugated equilibria with vanishing total current (but nonvanishing current density) is investigated.
Collective excitations and optical bistability in partially ionized hydrogen plasmas due to high electric fields
Authors: Morawetz K. , Kremp D.
Published: July 2002

The influence of an external electric field on the quantum distribution function and, consequently, on the nonequilibrium susceptibility is investigated in random phase approximation. The dispersion relation becomes bistable for certain wave vectors in a limited field-density-temperature plane. An instable acoustic mode is observed between two optical stable branches. These modes arise due to the applied field and can be controlled by the field strength. They are an expression of the nonequilibrium situation, which is established by an applied electric field.
Impact of dissociation on the viscosity of gases
Authors: Kunc Joseph A.
Published: July 2002

Rigorous numerical analysis published in an earlier work [S. H. Kang and J. A. Kunc, Phys. Rev. A 44, 3596 (1991)] has shown that the viscosity–temperature dependence of dissociating iodine vapor can have a negative slope. In this work, a general and easy-to-use procedure is presented which allows the estimation of the range of physical conditions under which such a negative slope can occur in other dissociating diatomic gases.
Rarefaction waves, solitons, and holes in a pure electron plasma
Authors: Moody J. D. , Driscoll C. F.
Published: July 2002

The propagation of holes, solitons, and rarefaction waves along the axis of a magnetized pure electron plasma column is described. The time dependence of the radially averaged density perturbation produced by the nonlinear waves is measured at several locations along the plasma column for a wide range of plasma parameters. The rarefaction waves are studied by measuring the free expansion of the plasma into a vacuum. A new hydrodynamic theory is described that quantitatively predicts the free expansion measurements. The rarefaction is initially characterized by a self-similar plasma flow, resulting in a perturbed density and velocity without a characteristic length scale. The electron solitons show a small increase in propagation speed with increasing amplitude and exhibit electron bursts. The holes show a decrease in propagation speed with increasing amplitude. Collisions between holes and solitons show that these objects pass through each other undisturbed, except for a small offset.
One-dimensional Vlasov simulations of Langmuir solitons
Authors: Lin Ching-Huei , Chao J. K. , Cheng C. Z.
Published: July 2002

Interactions of Langmuir solitons with plasma are simulated using a one-dimensional electrostatic Vlasov code, including both electrons and ions. The Zakharov’s solutions are used as initial conditions. The wave is found to transfer energy into electrons during the heating process due to the interaction of resonant electrons with high-frequency electric fields. For Te≫Ti, the temporal evolution of the electron distribution function shows different heating behaviors depending on whether the electrons are interacting with a single soliton or many solitons. In single-soliton interactions, the final electron distribution function approaches an exponential form, f(v)∝exp(−6v/vte). However, for multisoliton interactions, the final stage of the heated electrons establishes a power-law distribution function, f(v)∝v−4, which agrees with that of Gorev and Kingsep [Sov. Phys. JETP 39, 1008 (1974)]. Simulation results for soliton motion show strong ion Landau damping, such that the solitons dissipated quickly when Ti=Te. Analyses indicate that nonlinear damping of Langmuir solitons by thermal ions for vg≤vti plays the most important role in slowing down the moving solitons. A double-hump structure was also found in the near-sonic soliton motion.
Resistive ballooning modes in scrape-off layer of tokamak plasmas
Authors: Novakovskii S. V. , Guzdar P. N. , Drake J. F. , Liu C. S.
Published: July 2002

Analytical and numerical study of the stability of the resistive ballooning modes (RBM) in the scrape-off layer (SOL) of a tokamak plasma is performed. It is shown that the stability of the RBM is controlled by the two parameters λ=(me/mi)1/2νeiqR/vTe—the ‘‘effective strength’’ of the Debye sheath current, and m̂=mL0/a the dimensionless poloidal number, where the characteristic scale L0 is given in the main text as a function of the basic plasma edge parameters. For λ≳1 the coupling to the sheath is unimportant and the unstable spectrum is virtually unchanged from that in the closed flux region. For λ<1 the sheath current has a strong destabilizing influence on long wavelength modes. The general case of arbitrary λ and m̂ is studied numerically and the spectrum of the unstable RBM is found. The influence of the diamagnetic effects is also investigated.
Screw dynamos of non-neutral beam–plasma systems in astrophysical jets
Authors: Ma Chun Yu , Wang De Yu
Published: July 2002

Astrophysical jets are composed of plasmas in which there are relativistic electrons and other cosmic ray particles generated by in situ reacceleration. The equilibrium analysis of a non-neutral beam–plasma system shows that the fluid components rotate around the cylindrical axis. When the relativistic electrons propagate through the background plasma of astrophysical jets, it is found that even very small non-neutrality will cause a differential rotation velocity large enough to amplify magnetic fields to a few microgausses on kiloparsec scales by the kinematic screw dynamo mechanism. The amplified magnetic field concentrates within a thin cylindrical shell, so it is beneficial for the confinement and collimation of jets.
Resonant enhancement for amplitude-modulated laser filament induced magnetic field in an inhomogeneous plasma
Authors: Annou R. , Tripathi V. K. , Srivastava M. P.
Published: July 2002

The Tripathi–Liu [Phys. Plasmas 1, 990 (1994)] model of magnetic-field generation due to an amplitude-modulated laser in a plasma is revisited. At plasma resonance, where modulation frequency equals the plasma frequency, significant enhancement in the magnetic field is seen. The magnetic field is found to scale directly with laser intensity and plasma frequency, while scaling inversely with laser spot size.