bluuebunny/crossref_metadata_2025 huggingface dataset:
Symplectic Dirac–Kähler fields
Authors: Reuter M.
Published: July 2002

For the description of space–time fermions, Dirac–Kähler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similar concept within the symplectic geometry of phase spaces. Rather than on space–time, symplectic Dirac–Kähler fields can be defined on the classical phase space of any Hamiltonian system. They are equivalent to an infinite family of metaplectic spinor fields, i.e., spinors of Sp(2N), in the same way an ordinary Dirac–Kähler field is equivalent to a (finite) multiplet of Dirac spinors. The results are interpreted in the framework of the gauge theory formulation of quantum mechanics which was proposed recently. An intriguing analogy is found between the lattice fermion problem (species doubling) and the problem of quantization in general.
Bethe Ansatz and thermodynamic limit of affine quantum group invariant extensions of the t–J model
Authors: Ambjo/rn J. , Avakyan A. , Hakobyan T. , Sedrakyan A.
Published: July 2002

We have constructed a one-dimensional exactly solvable model, which is based on the t–J model of strongly correlated electrons, but which has additional quantum group symmetry, ensuring the degeneration of states. We use Bethe Ansatz technique to investigate this model. The thermodynamic limit of the model is considered and equations for different density functions written down. These equations demonstrate that the additional color degrees of freedom of the model behave as in a gauge theory, namely, an arbitrary distribution of color indices over particles leave invariant the energy of the ground state and the excitations. The S-matrix of the model is shown to be the product of the ordinary t–J model S-matrix and the unity matrix in the color space.
Galilean wavelets: Coherent states of the affine Galilei group
Authors: Antoine J.-P. , Mahara I.
Published: July 2002

We derive Galilean wavelets, by which we mean coherent states of the affine Galilei group, that is, the Galilei group extended by independent space and time dilations. The construction follows a general method based on square integrable group representations, possibly modulo a subgroup, i.e., on a homogeneous space of the underlying group. We also examine the restriction to the Schrödinger subgroup, which contains only dilations that leave invariant the Schrödinger and the heat equations.
Functional determinants from Wronski Green functions
Authors: Kleinert H. , Chervyakov A.
Published: July 2002

A general technique is developed for calculating functional determinants of second-order differential operators with Dirichlet, periodic, and antiperiodic boundary conditions, without the knowledge of spectral properties. As an example, we give explicit formulas for a harmonic oscillator with an arbitrary time-dependent frequency, where our result is a generalization of the Gel’fand–Yaglom famous formula for Dirichlet boundary conditions. Our technique is based on the Wronski’s construction of Green functions, which does not require spectral knowledge. Our final formula expresses the ratios of functional determinants in terms of an ordinary 2×2 determinant of a constant matrix constructed from two linearly independent solutions of the homogeneous differential equations associated with second-order differential operators. For ratios of determinants encountered in semiclassical fluctuations around a classical solution, the result can further be expressed in terms of the classical solution. Special properties of operators with a zero mode are exhibited.
The inhomogeneous quantum groups from differential calculi with classical dimension
Authors: Lagraa M. , Touhami N.
Published: July 2002

From the bicovariant first-order differential calculus on inhomogeneous Hopf algebra ℬ we construct the set of right-invariant Maurer–Cartan one-forms considered as a right-invariant basis of a bicovariant ℬ-bimodule over which we develop the Woronowicz general theory of differential calculus on quantum groups. In this formalism, we introduce suitable functionals on ℬ which control the inhomogeneous commutation rules. In particular, we find that the homogeneous part of commutation rules between the translations and those between the generators of the homogeneous part of ℬ and translations are controlled by different R-matrices satisfying characteristic equations.
Lie–Poisson structure for the homogeneous motion of self-gravitating compressible fluids
Authors: San Miguel A.
Published: July 2002

In this paper we apply the theory developed by Marsden, Ratiu, and Weinstein for the reduction of a Hamiltonian system defined on the cotangent bundle of a Lie group to a Hamiltonian system in the coalgebra of a semidirect product to study the motion of a self-gravitating homogeneous compressible ideal fluid with a variable ellipsoidal boundary, assuming that the motions are given by invertible linear transformations. The relation between the Lie–Poisson equations obtained and the classical Dyson equations is discussed, and the Hamiltonian structure for the homogeneous expansion of a free nonrotating ellipsoid is derived.
Gravoelectric dual of the Kerr solution
Authors: Dadhich Naresh , Patel L. K.
Published: July 2002

By decomposing the Riemann curvature into electric and magnetic parts, we define the gravoelectric duality transformation by interchange of active and passive electric parts which amounts to interchange of the Ricci and Einstein tensors. It turns out that the vacuum equation is duality invariant. We obtain solutions dual to the Kerr solution by writing an effective vacuum equation in such a way that it still admits the Kerr solution but is not duality invariant. The dual equation is then solved to obtain the dual-Kerr solution which can be interpreted as the Kerr black hole sitting in a string dust universe.
Companion equations for branes
Authors: Baker Linda , Fairlie David
Published: July 2002

The quantum mechanical transition between a free particle Lagrangian and the Klein–Gordon field description of a free particle (particle-wave duality) is conjectured to extend to an analogous construction of relativistically invariant wave equations associated with strings and branes. Electromagnetic interactions in the two systems are discussed. It is emphasized that all integrable free field theories, including those of Dirac–Born–Infeld type, are associated with Lagrangians equivalent to divergences on the space of solutions of the equations of motion.
Velocity slip and defect: Hard sphere gas
Authors: Loyalka S. K. , Hickey K. A.
Published: July 2002

The half-space problem of rarefied gas flow (the Kramers problem) is considered and use of the SN algorithm is outlined. Accurate numerical results for the velocity slip coefficient and velocity defect are obtained for a hard sphere gas and are compared with previously reported results and experimental data.
Supercritical free-surface flow with a stagnation point due to a submerged source
Authors: Mekias Hocine , Vanden-Broeck Jean-Marc
Published: July 2002

Two-dimensional free-surface flow produced by a submerged source in a fluid of finite depth is considered. It is assumed that there is a stagnation point on the free surface immediately above the source. The shape of the free surface and the flow of the fluid are determined numerically by series truncation for various values of the Froude number F. It is found that there is a flow for each value of F ≥1.22. In addition, a local solution is constructed to describe the flow near the stagnation point as F→∞.
Effect of a bulge on the subharmonic instability of boundary layers
Authors: Nayfeh Ali H. , Ragab Saad A. , Masad Jamal A.
Published: July 2002

The influence of a two-dimensional hump on the three-dimensional (3-D) subharmonic secondary instability on a flat plate is investigated. The mean flow is calculated by using interacting boundary layers, thereby accounting for the viscid/inviscid interaction. The primary wave is taken in the form of a two-dimensional (2-D) Tollmien–Schlichting (T–S) wave. The secondary wave is taken in the form of a 3-D subharmonic wave. The results show that increasing the hump height results in an increase in the amplification factors of the primary and subharmonic waves. When the hump causes separation, the growth rates of both the primary and subharmonic waves are considerably larger than those obtained in the case of no separation.
Subcritical flow with a stagnation point due to a source beneath a free surface
Authors: Mekias Hocine , Vanden-Broeck Jean-Marc
Published: July 2002

Two-dimensional free-surface flows produced by a submerged source in a fluid of finite depth are considered. Subcritical solutions are calculated numerically by a boundary-integral equation method. The solutions depend continuously on two parameters: the Froude number F and the dimensionless elevation b of the source above the bottom wall. It is found that there is a train of waves in the far field. For each value of b, solutions exist only for values of F smaller than a critical value at which the waves break. It is shown that the amplitude of the waves is exponentially small as F tends to zero.
Three-dimensional stability analysis of the periodic flow around a circular cylinder
Authors: Noack Bernd R. , König Michael , Eckelmann Helmut
Published: July 2002

The onset of three-dimensionality in the von Kármán vortex street behind a circular cylinder is investigated by carrying out the first global, nonparallel, three-dimensional stability analysis of the periodic flow. This flow is found to become unstable at a Reynolds number of 170 by a critical, three-dimensional Floquet mode with a spanwise wavelength of 1.8 diam. The spatial structure of this mode indicates that the onset of three-dimensionality is due to a near-wake instability and not caused by a stagnation-line or a boundary-layer instability.
A self-consistent equilibrium model of plasma–beam systems
Authors: Yoshida Zensho
Published: July 2002

Model equations have been derived for the analysis of mechanical equilibria of plasma–beam systems. The plasma has a thermal pressure, and the charged particle beam has effective inertial pressure. Self-consistent force-balance conditions are formulated by a set of nonlinear elliptic partial differential equations. Examples of explicit solutions have been given by numerical analyses.
A review of models for collisionless one-dimensional plasma flow to a boundary
Authors: Bissell R. C. , Johnson P. C. , Stangeby P. C.
Published: July 2002

Four models of collisionless one-dimensional plasma flow to a boundary are compared with regard to their predictions of particle and heat fluxes to the boundary for a given plasma density and temperature far from the boundary. The models include two kinetic treatments, that of Emmert et al. [Phys. Fluids 23, 803 (1980)], and that of Bissell and Johnson [Phys. Fluids 30, 779 (1987)], an isothermal fluid model, Self and Ewald [Phys. Fluids 9, 2486 (1966) and Stangeby, [Phys. Fluids 27, 2699 (1984)], and an adiabatic fluid model, Zawaideh, Najmabadi, and Conn [Phys. Fluids 29, 463 (1986)]. The fluid models do not explicitly include collisions; however, the adiabatic closure condition employed, namely, neglect of ion heat conduction, implies a degree of ion self-collisionality. It is found that the particle and heat fluxes to the boundary differ very little among the four models—spanning a range of about ±10%. It is therefore concluded that, with regard to modeling of such important practical quantities as outfluxes, a simple and convenient formulation, such as the isothermal fluid model, is adequate. Substantial differences among the models are found for certain other predicted quantities, namely, the spatial variation of ion temperature along the flow and the magnitude of the electric field near the boundary.
Orbit effects on impurity transport in a rotating tokamak plasma
Authors: Wong K. L. , Cheng C. Z.
Published: July 2002

Particle orbits in a rotating tokamak plasma are calculated from the equation of motion in the frame that rotates with the plasma. It is found that heavy particles in a rotating plasma can drift away from magnetic surfaces significantly faster with a higher bounce frequency, resulting in a diffusion coefficient much larger than that for a stationary plasma. Particle orbits near the surface of a rotating tokamak are also analyzed. Orbit effects indicate that more impurities can penetrate into a plasma rotating with counterbeam injection. Particle simulation is carried out with realistic experimental parameters and the results are in qualitative agreement with some experimental observations in the Tokamak Fusion Test Reactor (TFTR) [in Proceedings of the 14th European Conference on Controlled Fusion and Plasma Heating (European Physical Society, Brussels, 1987), p. 121].
Density fluctuations in strong Langmuir turbulence: Scalings, spectra, and statistics
Authors: Robinson P. A. , Newman D. L.
Published: July 2002

A recently developed two-component model of strong Langmuir turbulence is applied to determine the scalings, spectra, and statistics of the associated density fluctuations. The predictions are found to be in excellent agreement with extensive results from numerical solution of the Zakharov equations in two and three dimensions.
The resistive tearing instability for generalized resistivity models: Theory
Authors: Otto A.
Published: July 2002

In collision-dominated plasmas, as well as in plasma systems with anomalous dissipation, the resistivity, in general, depends on the local plasma parameters. Except for some special applications, this dependence is usually not taken into account for the resistive tearing mode. In this paper, a dispersion relation for the resistive tearing mode is derived in a closed analytical form, where generalized models for the resistivity are considered. Because of the dependence on electron temperature, e.g., for the Spitzer resistivity, a further transport equation for the electron temperature is assumed in the presented theory. For applications to more realistic systems, the equilibrium configuration is assumed to be weakly two dimensional. Thus the obtained dispersion relation represents a generalization, which includes a number of results of previous authors. In order to determine this dispersion relation, a constant Ψ approximation is not applied such that the parameter regime of maximum growth rate is covered by the presented theory.
Electron cyclotron damping in thermal and nonthermal plasma
Authors: Matsuda Kyoko , Hsu Jang-Yu
Published: July 2002

The relativistic dispersion relation including temperature anisotropy and a parallel drift has been derived for electron cyclotron waves of frequency up to third harmonics, and solved for a perpendicularly stratified plasma around the fundamental and second harmonic resonances. For quasiperpendicular propagation, damping of fundamental modes is much more sensitively affected by T∥ than by T⊥. This is also true for the ordinary mode of oblique propagation. The theory has been extended to a bulk thermal distribution with a two-temperature or three-temperature tail distribution by a simple summation of each contribution to the dispersion tensor. The effect of a tail distribution is relatively small if the tail is localized in the resonant layer for the bulk electrons. For a nonlocal tail distribution, the existence of a tail becomes important.
Ion divergence generated by nonuniform current density of intense ion beams
Authors: Slutz S. A.
Published: July 2002

Large electric and magnetic fields are generated by the space charge and current of intense ion beams. These fields induce ion divergence if the beam current density is not uniform. Within the accelerating region the deflection of ions due to the electric fields is much larger than ion deflection from the self-magnetic fields. An analytic technique is presented to calculate the electric fields generated by the static nonuniform beam space charge and the resulting ion trajectories during beam acceleration. It is shown that modest nonuniformities in the ion current density can result in significant ion divergence. Downstream of the ion acceleration region, the ion space charge is neutralized by the presence of electrons. Consequently, the self-magnetic field of the beam dominates the ion trajectories in this region. Analytic estimates of the beam divergence produced by the self-magnetic fields indicate that significant ion divergence can be generated by this process as well. A distinguishing feature between these two mechanisms is that the space-charge-induced divergence is largest for perturbation scale lengths smaller than the acceleration gap, while the converse is true for the divergence generated by the self-magnetic field of the beam. Both of these effects place uniformity requirements on ion sources.
Theory and three-dimensional simulation of light filamentation in laser-produced plasma
Authors: Berger R. L. , Lasinski B. F. , Kaiser T. B. , Williams E. A. , Langdon A. B. , Cohen B. I.
Published: July 2002

A desire to interpret recent experiments on filamentation with and without beam-smoothing techniques led to the development of a three-dimensional fluid model that includes the effects of nonlocal electron transport and kinetic ion damping of the acoustic waves. The damping of the electron-temperature perturbations that drive thermal filamentation by nonlocal electron conduction, valid in the diffusive limit, is supplemented in the present model by electron Landau damping in the collisionless limit when the wavelength of the perturbation is much less than the electron–ion scattering mean-free path. In this collisionless limit, Landau damping of the ‘‘temperature’’ fluctuations makes ponderomotive forces universally more important than thermal forces. Simulations in plasmas of current interest illustrate the relative importance of thermal and ponderomotive forces for strongly modulated laser beams. Although thermal forces may initiate filamentation, the most intense filaments are associated with ponderomotive forces. The present simulations of filamentation model well the density perturbations observed in experiments [Young et al., Phys. Rev. Lett. 61, 2336 (1988)]. In addition, a simple criterion is obtained analytically and supported by simulations for stabilization of filamentation by laser beam-smoothing techniques such as induced spatial incoherence and random phase plates [Eq. (1)].
The ponderomotive force in an overdense, absorbing, dispersive plasma, caused by an intense laser–matter interaction
Authors: Gamaly E. G.
Published: July 2002

The ponderomotive force acting on an overdense, absorbing plasma with nonlocal electric properties is calculated from first principles. On the basis of the space–time dependence of the electric field and the electron distribution function which were calculated self-consistently, the conductivity, current, and force in the plasma are calculated. The possibility of acceleration of ions by an intense laser beam is demonstrated and the proper conditions for this to occur are pointed out.
Striations of the convective type and feedback in low-pressure mercury/noble-gas discharges
Authors: van den Heuvel F. C. , Vrehen Q. H. F.
Published: July 2002

Experiments indicate that ionization-diffusion instabilities (striations) of the convective type, present in low-pressure mercury/noble-gas lamps, are generated by current fluctuations in the inhomogeneous part at the cathode end of the discharge. Self-excitation of striations is made possible by feedback via the electrical supply circuit of the lamp. An experimental boundary condition is found at the point of excitation. A simple plasma model, with an extension that takes feedback into account, fully describes the laser-like phenomenon of mode selection and the influence of the discharge length.
Experimental results and theoretical analysis of the effect of wavelength on absorption and hot-electron generation in laser-plasma interaction
Authors: Garban-Labaune C. , Fabre Edouard , Max Claire , Amiranoff F. , Fabbro Rémy , Virmont J. , Mead W. C.
Published: July 2002

Recent experiments performed at École Polytechnique on the wavelength scaling of laser light absorption by flat plastic targets are presented and interpreted. The measurements show larger absorption fractions for shorter laser wavelengths, lower laser intensities, and longer laser pulse lengths. These experiments are analyzed using computer hydrodynamics codes, and show that there are two possible physics models consistent with the data: (1) Inhibited electron heat flow together with absorption rates higher than those predicted by resonance absorption and inverse bremsstrahlung. (2) Nearly classical heat flow, with no additional enhancement in the absorption rate.
Solitary wave of a relativistic magnetosonic wave propagating perpendicularly to a magnetic field
Authors: Ohsawa Yukiharu
Published: July 2002

A relativistic theory for a nonlinear magnetosonic wave propagating perpendicularly to a magnetic field is developed. On the basis of a relativistic two-fluid cold plasma model, the structure of a stationary magnetosonic wave is studied. Relativistic effects become important for the parameter regime ωce/ωpe≳1, because the fluid electron velocity perpendicular to a magnetic field and parallel to the wave front takes values close to the speed of light for such plasma parameters. It is found that there exists a stationary solitary wave solution even in the relativistic model. Some properties of the solitary wave, such as the soliton width, are discussed.
Exact numerical results for Poiseuille and thermal creep flow in a cylindrical tube
Authors: Valougeorgis Dimitris , Thomas J. R.
Published: July 2002

The FN method is used, in the field of rarefied gas dynamics, to develop a complete solution for the cylindrical Poiseuille flow and thermal creep problems. The linearized Bhatnagar–Gross–Krook (BGK) model and purely diffuse reflection at the surface are used to describe the physical problem. The derived set of singular integral equations is solved by polynomial expansion and collocation. By choosing suitable FN approximations, the solution of both problems under consideration is accomplished with a single matrix inversion, minimizing computational time and effort. The converged numerical results for the flow rates and the velocity profiles are correct to four significant figures, thus supporting the results of previous authors achieved by other methods.
Electron heating by ion acoustic turbulence in simulated low Mach number shocks
Authors: Tokar Robert L. , Gary S. Peter , Quest Kevin B.
Published: July 2002

Explicit and fully electromagnetic particle-in-cell simulations of perpendicular, collisionless, and nominally subcritical shocks are performed in one and two spatial dimensions using the code wave [Phys. Fluids 14, 830 (1971)]. Shock parameters are chosen to maximize the growth rates of the current driven ion acoustic instability in the shock. Electron heating by ion acoustic turbulence is observed at the shocks, at rates in agreement with second-order Vlasov theory predictions. However, the amount of resistive electron heating is small and ion reflection provides the major source of dissipation. Strictly resistive shocks do not exist for the parameters suitable for explicit particle codes running on today’s supercomputers, because the plasma convects through these shocks so quickly that current driven instabilities have little time to be amplified and to heat the electrons resistively. This effect is primarily a result of the relatively small values of ωpe/ωce that can be analyzed.
Nonlinear evolution of drift instabilities in the presence of collisions
Authors: Federici J. F. , Lee W. W. , Tang W. M.
Published: July 2002

Nonlinear evolution of drift instabilities in the presence of electron–ion collisions in a shear-free slab has been studied by using gyrokinetic particle simulation techniques as well as by solving, both numerically and analytically, model mode-coupling equations. The purpose of the investigation is to determine the mechanisms responsible for the nonlinear saturation of the instability and for the ensuing steady-state transport. Such an insight is very valuable for understanding drift-wave problems in more complicated geometries. The results indicate that the electron E×B convection is the dominant mechanism for saturation. It is also found that the saturation amplitude and the associated quasilinear diffusion are greatly enhanced over their collisionless values as a result of weak collisions. In the highly collisional (fluid) limit, there is an upper bound for saturation with eφ/Te≂(ωl/Ωi)/(k⊥  ρs)2. The associated quasilinear diffusion, which increases with collisionality, takes the form of Dql≂γl/k2⊥, where ωl and γl are the linear frequency and growth rate, respectively. In the steady state, the diffusion process becomes stochastic in nature. The relevant mechanisms here are related to the velocity-space nonlinearities and background fluctuations. The magnitude of the diffusion at this stage can be comparable to that of quasilinear diffusion in the presence of collisions, and it seems to remain finite even in the collisionless limit.
Stabilization of the diocotron instability in an annular plasma
Authors: Rosenthal G. , Dimonte G. , Wong A. Y.
Published: July 2002

The stabilization of the diocotron instability by an applied radial dc electric field in an annular magnetized pure electron plasma is investigated experimentally. The radial electric field E(r) from the annular plasma gives rise to a radially dependent azimuthal E(r)×Bz drift. The shear in this drift provides the free-energy source for the instability. A sufficiently large bias applied to a central conductor changes the rotation rates of the plasma and stabilizes the instability. The diocotron instability is experimentally identified by its dispersion relation. Its nonlinear saturation is explained in terms of the broadening of its radial extent and trapping of the azimuthally drifting electrons.
Finite-amplitude solitary waves at the interface between two homogeneous fluids
Authors: Pullin D. I. , Grimshaw R. H. J.
Published: July 2002

Numerical solutions are presented for finite-amplitude interfacial waves. Only symmetric waves are calculated. Two cases are considered. In the first case the waves are free-surface solitary waves propagating on a basic flow with uniform vorticity. Large-amplitude waves of extreme form are calculated for a range of values of the basic vorticity. In the second case the waves are propagating on the interface between two homogeneous fluids of different densities, which are otherwise at rest. Again large-amplitude waves of extreme form are calculated for a range of values of the basic density ratio. In particular, in the Boussinesq limit when the density ratio is nearly unity, solitary waves of apparently unlimited amplitude can be found.
Anomalous absorption of high intensity subpicosecond laser pulses
Authors: Brunel F.
Published: July 2002

When very intense laser radiation is incident on a sharply bounded overdense plasma, strong energy absorption can be accounted for by the electrons that are drawn into the vacuum and sent back into the plasma with velocities on the order of the quiver velocity. The absorption process takes place on the time scale of the laser light cycle and no corona or underdense plasma need be present. The validity of this mechanism is confirmed through 2 1/2 -dimensional particle-in-cell (PIC) simulations in the case of a two-pump system. From these simulations the presence of strong average magnetic fields is also noted, even without the presence of a thermal gradient, because of the average current of electrons drawn from the overdense plasma.
Instability of the large Reynolds number flow of a Newtonian fluid over a viscoelastic fluid
Authors: Chen KangPing , Crighton D. G.
Published: July 2002

The stability of the large Reynolds number flow of a Newtonian fluid over a much more viscous viscoelastic fluid is studied via a linear analysis. The two fluids are confined within a channel and the flow is driven by the motion of the plate bounding the Newtonian fluid. Matched asymptotic expansions are used to derive the dispersion relation, and the flow is found to be always unstable to an interfacial mode due to the discontinuity in the fluid viscosities. It is shown that even a small amount of elasticity of the viscoelastic fluid can change the stability characteristics considerably.
The evolution of an isolated turbulent region in a two-layer fluid
Authors: Flór J. B. , Fernando H. J. S. , van Heijst G. J. F.
Published: July 2002

A turbulent region is generated by horizontal pulsed injection at the interface of a two-layer fluid. Flow visualization studies reveal the existence of three stages in the evolution of the vertical size of this region: growth, maximum height, and collapse. A scaling analysis for the height of the turbulent region is presented, which appears to be in good agreement with the measurements. Comparable results were obtained by Fernando, van Heijst, and Fonseka (submitted to J. Fluid Mech.) for similar experiments in a linearly stratified fluid. Thorpe-scale measurements of the turbulent region reveal that the ratio of the rms displacement Lt and the maximum displacement Ltmax remain constant with time. The eventual formation process of the dipolar vortices after the collapse and the influence of interfacial wave motions on these dipolar vortices are discussed.
Karhunen–Loéve expansion of the derivative of an inhomogeneous process
Authors: Sung H. J. , Adrian R. J.
Published: July 2002

The properties of the Karhunen–Loéve (KL) expansion of the derivative ux(x) of an inhomogeneous random process possessing viscous boundary-layer behavior are studied in relation to questions of efficient representation for numerical Galerkan schemes for computational simulation of turbulence. Eigenfunctions and eigenvalue spectra are calculated for the randomly forced one-dimensional Burgers’ model of turbulence. Convergence of the expansion of ux is much slower than convergence of the expansion of u(x), and direct expansion of ux is not significantly more efficient than differentiating the expansion of u. The ordered eigenvalue spectrum of ux is proportional to the square of the order parameter times the eigenvalue spectrum of u. The underlying cause of slow convergence is the earlier onset of locally sinusoidal behavior of the KL eigenfunctions when the expansion is performed over the entire domain of the solution.
A simple model of countergradient flow
Authors: Robson R. E. , Mayocchi C. L.
Published: July 2002

Countergradient flow is explained in terms of a nonlocal flux-gradient relationship, obtained through solution of the widely-used BGK or ‘‘relaxation time’’ model kinetic equation in one dimension for a layered source in an atmosphere with stationary turbulence. It is also pointed out that the classical formula derived by Taylor [Proc. London Math. Soc. Ser. A 20, 196 (1921)] for dispersion from a point source is fully recoverable from BGK theory.
A comparison study of conditional-sampling methods used to detect coherent structures in turbulent boundary layers
Authors: Yuan Y. M. , Mokhtarzadeh-Dehghan M. R.
Published: July 2002

The present work describes the results of an experimental study of coherent structures in a two-dimensional zero pressure gradient turbulent boundary layer by conditional sampling. The main aim of the work is to compare coherent events detected by various conditional sampling methods on a one-to-one basis and to investigate the degree of correspondence between them. The conditional-sampling techniques used include some existing ones, such as the uv-quadrant, the VITA, the u-level, and the pattern recognition methods, but also some suggested ones which are based on modifications of existing methods or ideas. The results are presented in two forms. First, the conditional averages of the streamwise and normal velocity fluctuations, and those of the Reynolds stress, are grouped into four classes based on the similarity of the pattern and then compared. Next, the correspondence between events detected by various methods are presented on a scale of zero to one, the latter indicating complete correspondence. The conditional-averaged patterns show very differing results for different methods. Also, very poor correspondences have been obtained between some pairs of methods. It is concluded that these methods may detect events of a different nature or different phases of the same event, and thus cause such discrepancies. The results are also discussed by relating them to the physics of the flow and coherent motions known as ejection and sweep.
Research note on the steady Poiseuille flow through pipes with multiple connected cross sections
Authors: Ranger K. B.
Published: July 2002

This note is concerned with steady Poiseuille flow through a pipe with a multiple connected cross section. The volumetric flux rate through a pipe with two regions of annular flow is contrasted with the flux through a one region of annular flow, in which the fluid cross-sectional area is the same in both cases. It is found that it is possible to generate both increased and decreased fluid dynamic efficiency in terms of volumetric flux rate, according to the relative ratio of the radii in the two regions of annular flow.
Interaction of evaporating and condensing particles in the free-molecular regime
Authors: Kogan M. N. , Bobrov I. N. , Cercignani C. , Frezzotti A.
Published: July 2002

In a previous paper it was shown that repulsive/attractive forces arise between evaporating/ condensing particles in the free-molecular regime. Here we obtain explicit expressions for these forces in the case of spherical particles with equal temperatures. The temperature of the surrounding vapor is, generally speaking, different from that of the particles. Numerical results are obtained for different values of the ratios between particle and vapor temperatures and pressures, of the particles radii and of the evaporation coefficients. In the case when the evaporation coefficient equals unity, an exact expression is obtained for the force between particles of different radii. A simple model describing coagulation processes and taking the above-mentioned forces into account is proposed. It is shown that for large values of the vapor supersaturation, the influence of these forces on the coagulation rate may be very pronounced.
Mixedness in the formation of a vortex ring
Authors: Verzicco R. , Orlandi P.
Published: July 2002

The mixing process in the formation of an axisymmetric vortex ring is analyzed by direct numerical simulation. After the initial phase, when the impulse is imparted to the fluid, the mixing increases linearly in time with a slope that is directly proportional to the vortex circulation (Γ) and to reactants diffusivity to the power −1/3 (Pe−0.33). In addition, for reacting flows with equivalence ratio (s) different from 1, it has been found that as s decreases the mixing first decreases and then increases. An explanation for this behavior is given.
Some further extensions of the Cercignani–Lampis gas–surface interaction model
Authors: Lord R. G.
Published: July 2002

A recent paper has described extensions of the Cercignani–Lampis scattering kernel to cover (i) diffuse scattering with partial accommodation of translational kinetic energy and (ii) accommodation of vibrational energy of a diatomic molecule modelled as a rigid rotor/harmonic oscillator. The models are here further extended to cover the cases of partially diffuse scattering and of the anharmonic oscillator model of molecular vibration. The new models, like the old, satisfy detailed balance or reciprocity, thereby ensuring the preservation of an equilibrium distribution, and can be conveniently implemented in direct simulation Monte Carlo calculations. The results of some calculations are presented.
A numerical coupled model for studying air–sea–wave interaction
Authors: Ly Le Ngoc
Published: July 2002

A numerical coupled model of air–sea–wave interaction is developed to study the influence of ocean wind waves on dynamical, turbulent structures of the air–sea system and their impact on coupled modeling. The model equations for both atmospheric and oceanic boundary layers include equations for: (1) momentum, (2) a k-ε turbulence scheme, and (3) stratification in the atmospheric and oceanic boundary layers. The model equations are written in the same form for both the atmosphere and ocean. In this model, wind waves are considered as another source of turbulent energy in the upper layer of the ocean besides turbulent energy from shear production. The dissipation ε at the ocean surface is written as a linear combination of terms representing dissipation from mean flow and breaking waves. The ε from breaking waves is estimated by using similarity theory and observed data. It is written in terms of wave parameters such as wave phase speed, height, and length, which are then expressed in terms of friction velocity. Numerical experiments are designed for various geostrophic winds, wave heights, and wave ages, to study the influence of waves on the air–sea system. The numerical simulations show that the vertical profiles of ε in the atmospheric and oceanic boundary layers (AOBL) are similar. The magnitudes of ε in the oceanic surface zone are much larger than those in the atmospheric surface zone and in the interior of the oceanic boundary layer (OBL). The model predicts ε distributions with a surface zone of large dissipation which was not expected from similarity scaling based on observed wind stress and surface buoyancy. The simulations also show that waves have a strong influence on eddy viscosity coefficients (EVC) and momentum fluxes, and have a dominated effect on the component of fluxes in the direction of the wind. The depth of large changes in flux magnitudes and EVC in the ocean can reach to 10–20 m. The simulations of surface drift currents confirm that the currents are overestimated if the surface waves are not considered.
Dynamical model for turbulence. III. Numerical results
Authors: Canuto V. M. , Dubovikov M. S. , Cheng Y. , Dienstfrey A.
Published: July 2002

We present the numerical solutions of the equations for turbulence developed in papers I and II. (1) The model predicts the Kolmogorov law and Ko=5/3, in accord with recent data; (2) in the inertial-conductive regime, the model predicts the Corrsin spectrum for the temperature variance and the Batchelor constant Ba=σt Ko, where σt=0.72 is the turbulent Prandtl number; (3) the predicted energy spectrum in the dissipation region is in agreement with recent laboratory measurements; (4) in the inertial-convective region, the temperature variance spectrum is closer to the spectrum (−11/3) obtained by LES when the velocity field is rapidly stirred at all scales than(−17/3), which holds when the velocity field is frozen in time and has a Gaussian statistics; (5) for freely decaying turbulence, the power law spectra for energy and temperature variance, as well as the velocity and temperature integral scales, agree with the most recent LES data; (6) after a few evolutionary times, the skewness S reaches S=0.5, in accord with a variety of data; (7) for shear-driven flows, the Reynolds stress spectrum E12(k) has an inertial regime with a power −7/3, in accord with recent data; (8) for two shear-driven flows, plane strain and axisymmetric contraction, turbulent kinetic energy, Reynolds stress tensor, and dissipation rate εij versus time compare very well with DNS data; (9) the slow and rapid parts of the pressure–strain correlation tensor compare with DNS data better than with the three most widely used phenomenological models. The rapid parts are also in excellent agreement with the DNS data; (10) for homogeneous shear, turbulent kinetic energy and Reynolds stress tensor versus time match quite closely LES data. We recall that the model does not contain any free parameters.
On the nature of vortex interactions and models in unforced nearly-inviscid two-dimensional turbulence
Authors: Dritschel David G. , Zabusky Norman J.
Published: July 2002

A powerful feature-tracking tool is applied to several high-resolution, very long-duration, regularized contour dynamics (contour surgery) simulations of unforced nearly-inviscid two-dimensional turbulence (2DT) on the surface of a sphere. Particularly low density gases of vortices (i.e. on average, very widely separated vortices) are examined to ascertain the nature of their interactions. The simplest (minimal) model system is studied, namely a set of vortex patches of just two vorticity values, ±ω0, whose total circulation is zero. The areas of the patches are selected initially from a pre-assigned, stable (nearly time invariant) power-law distribution. When the vorticity occupation fraction f≳0.01, often more than three vortices are found relatively close together at the onset of a strong interaction. But, when f≲0.01, all such interactions involve only three nearby vortex patches, not all having the same sign of vorticity. This is related to the well-known collapse of three singular (point) vortices. Thus, under these conditions, isolated two-vortex interactions, which have figured in recent ad hoc theories and models for decaying 2DT, cannot occur. Taking into account these results, we propose an asymptotically-motivated and computationally-efficient ‘‘reduced’’ model.
Spin-up in a circular tank with a radial barrier
Authors: van de Konijnenberg J. A. , Wessels T. L. , van Heijst G. J. F.
Published: July 2002

The time-dependent motion of fluid in a circular tank with a radial barrier as a result of an increase in angular velocity of the tank is investigated. The length of the barrier is considered as the main experimental parameter. The flow field immediately after the increase in angular velocity is calculated analytically. Experiments have been performed with a tank placed on a rotating table. Quantitative results for the time-dependent flow were obtained by the tracking of small particles floating at the free surface of the fluid. The flow appears to be characterized by separation from the end of the barrier and the subsequent formation of a stable vortex pattern. The trajectory of the vortex that is shed from the end of the barrier is determined with dye visualization, and compared with analytical results from a point-vortex model.
Wetting of heterogeneous surfaces: Influence of defect interactions
Authors: Paterson A. , Fermigier M.
Published: July 2002

We investigate the motion of a fluid interface through a thin cell, used as a model for porous media with heterogeneous wettability properties. We analyze how the distribution of wettability defects modifies the shape of the advancing interface. Solid substrates are prepared with a photolithography technique to create wettability defects. Several distributions of defects are generated, with different surface densities and different position ordering. The amplitude of fluctuation of the fluid interface is measured for the different defect distributions and with or without gravity stabilization of the interface. When the interface is stabilized by gravity, the capillary length sets the distance below which defects strongly cooperate to pin the interface and trap air bubbles. Trapping of the advancing interface by the defects is dependent on the spatial distribution of defects. The interface fluctuation is much larger for strongly disordered distributions and is related to a correlation length of the defect pattern.
Large-eddy simulation of free-surface decaying turbulence with dynamic subgrid-scale models
Authors: Salvetti M. V. , Zang Y. , Street R. L. , Banerjee S.
Published: July 2002

This paper describes large-eddy simulations of decaying turbulence in an open channel, using different dynamic subgrade-scale models, viz. the dynamic model of Germano et al. [Phys. Fluids A 3, 1790 (1991)] (DSM), the dynamic mixed model in Zang et al. [Phys. Fluids A 5, 3186 (1993)] (DMM), and the dynamic two-parameter model of Salvetti and Banerjee [Phys. Fluids 7, 2831 (1995)] (DTM). These models are incorporated in a finite-volume solver of the Navier–Stokes equations. A direct numerical simulation of this flow conducted by Pan and Banerjee [Phys. Fluids 7, 1649 (1995)] showed that near the free surface turbulence has a quasi-two-dimensional behavior. Moreover, the quasi-two-dimensional region increases in thickness with the decay time, although the structure remains three-dimensional in the central regions of the flow. The results of the large-eddy simulations show that both the DMM and the DTM are able to reproduce the features of the decay process observed in the direct simulation and to handle the anisotropic nature of the flow. Nevertheless, the addition of the second model coefficient in the DTM improves the agreement with the direct simulation. When the DSM is used, significant discrepancies are observed between the large-eddy and the direct simulations during the decay process at the free surface.
The linear evolution of centrifugal instabilities in curved, compressible mixing layers
Authors: Owen D. J. , Seddougui S. O. , Otto S. R.
Published: July 2002

The linear development of Görtler vortices in a curved compressible mixing layer is studied. It has been shown both experimentally and theoretically that the curved mixing layer can support a centrifugal mode, which is believed to be similar to the Görtler vortex mode. This study follows the corresponding incompressible study of Otto, Jackson, and Hu, and attempts to demonstrate the effects compressibility has on the growth of such modes [J. Fluid Mech. 315, 85 (1996)]. The ultimate downstream fate of the modes is studied in the high Taylor/Görtler number regime. The problem of the third boundary condition inherent to the mixing layer model is addressed using the set of boundary conditions for both subsonic and supersonic flows derived by Ting [J. Math. Phys. 28, 153 (1959)]. A class of modes is discussed that have no counterpart in the uniform temperature incompressible case.
The generation of internal waves by a towed sphere and its wake in a thermocline
Authors: Robey Harry F.
Published: July 2002

This report describes a combined experimental and numerical study of internal gravity waves generated by a sphere which is towed horizontally in a density stratified fresh water tank which exhibits a strong thermocline at mid-depth. The Reynolds number range covered extends from 2000<Re=UD/ν<100 000, and the Froude number range was 0.44<Fr=U/NmaxD<22. Both the kinematics as well as the dynamics of the internal waves are studied. The internal wave field is shown to be generated by two very distinct types of sources, one stationary with respect to the body and one which is nonstationary. The stationary part of the internal wave field is shown to be generated by an “effective” body comprised of the sphere plus a stationary separation bubble which follows it. The nonstationary part of the internal wave field is shown to be generated by the nonstationary oscillations associated with the large-scale eddies of the turbulent wake. While such nonstationary internal waves have been observed in previous investigations, their physical origin has not been clearly identified. This paper presents a simple physical model for their generation.