bluuebunny/crossref_metadata_2025 huggingface dataset:
Casimir energy of a ball and cylinder in the zeta function technique
Authors: Lambiase G. , Nesterenko V. V. , Bordag M.
Published: July 2002

A simple method is proposed to construct the spectral zeta functions required for calculating the electromagnetic vacuum energy with boundary conditions given on a sphere or on an infinite cylinder. When calculating the Casimir energy in this approach no exact divergencies appear and no renormalization is needed. The starting point of the consideration is the representation of the zeta functions in terms of contour integral, further the uniform asymptotic expansion of the Bessel function is essentially used. After the analytic continuation, needed for calculating the Casimir energy, the zeta functions are presented as infinite series containing the Riemann zeta function with rapidly falling down terms. The spectral zeta functions are constructed exactly for a material ball and infinite cylinder placed in a uniform endless medium under the condition that the velocity of light does not change when crossing the interface. As a special case, perfectly conducting spherical and cylindrical shells are also considered in the same line. In this approach one succeeds, specifically, in justifying, in mathematically rigorous way, the appearance of the contribution to the Casimir energy for cylinder which is proportional to ln(2π).
The character of the exceptional series of representations of SU(1,1)
Authors: Basu Debabrata , Bal Subrata , Shajesh K. V.
Published: July 2002

The character of the exceptional series of representations of SU(1,1) is determined by using Bargmann’s realization of the representation in the Hilbert space Hσ of functions defined on the unit circle. The construction of the integral kernel of the group ring turns out to be especially involved because of the nonlocal metric appearing in the scalar product with respect to which the representations are unitary. Since the nonlocal metric disappears in the “momentum space,” i.e., in the space of the Fourier coefficients the integral kernel is constructed in the momentum space, which is transformed back to yield the integral kernel of the group ring in Hσ. The rest of the procedure is parallel to that for the principal series treated in a previous paper. The main advantage of this method is that the entire analysis can be carried out within the canonical framework of Bargmann.
Master function approach to quantum solvable models on SL(2,c) and SL(2,c)/GL(1,c) manifolds
Authors: Fakhri H. , Jafarizadeh M. A.
Published: July 2002

By introducing a new parameter as a second associated index for special functions, we construct the three-dimensional differential generators of gl(2,c) Lie algebra together with the corresponding contracted form h4. Non-Casimir quadratic as well as the Casimir of gl(2,c) (and h4) generators can be considered as quantum solvable models on group manifold SL(2,c). Then, by appropriate parametrization of group manifold SL(2,c) and eliminating one of the coordinates, we obtain quantum solvable Hamiltonians on homogeneous manifold SL(2,c)/GL(1,c) with the metric described by master function. We show that two-dimensional Hamiltonian on SL(2,c)/GL(1,c) derived from the reduction of Casimir operator so(4,c) Lie algebra as a three-dimensional Hamiltonian on group manifold SL(2,c), possesses the degeneracy SL(2,c) group and, also, the shape invariance property, where both have para-supersymmetry representations of arbitrary order.
Casimir invariants from quasi-Hopf (super)algebras
Authors: Gould Mark D. , Zhang Yao-Zhong , Isaac Phillip S.
Published: July 2002

We show how to construct, starting from a quasi-Hopf (super)algebra, central elements or Casimir invariants. We show that these central elements are invariant under quasi-Hopf twistings. As a consequence, the elliptic quantum (super)groups, which arise from twisting the normal quantum (super)groups, have the same Casimir invariants as the corresponding quantum (super)groups.
Swihart waves and surface plasmons in a parallel-plate superconducting transmission line
Authors: Melkov G. A. , Egorov Yu. V.
Published: July 2002

The electromagnetic waves propagating inside a parallel-plate transmission line are investigated. In the case of a finite penetration depth of the electromagnetic field into the metal, a longitudinal electric E wave propagates in the the line instead of a transverse electromagnetic wave. At small thicknesses of the dielectric this wave goes over to a Swihart wave, and at large thicknesses of the dielectric it is converted into a surface wave (plasmon). It is shown that there exists an optimum thickness of the superconducting film coating the parallel-plate transmission line, for which the electromagnetic wave experiences the maximum slowing down. Using waveguides for surface waves, one can construct surface-wave microwave resonators. These resonators have a highly uniform microwave current distribution and, have a high concentration of microwave current in the superconducting film, and they are simple to fabricate.
The axisymmetric long-wave instability of a concentric two-phase pipe flow
Authors: Smith Marc K.
Published: July 2002

The long-wave instability in a confined flow system is studied by considering a vertical pipe containing two immiscible fluids arranged in a concentric geometry. Each fluid has a different density, but otherwise their properties are identical. Gravity and an imposed pressure gradient drive a flow in this system, which is susceptible to an axisymmetric long-wavelength instability for any density ratio. When the density ratio is not too different from 1 we find that stable flows are usually downward flows when the lighter fluid is in the center and are usually upward flows when the heavier fluid is in the center. However, there are some parameter ranges in which the opposite is true. We explain this behavior in terms of a physical mechanism for the long-wave instability.
Nonlocality in a forced two-dimensional turbulence
Authors: Ohkitani Koji
Published: July 2002

Nonlocality of the enstrophy cascade is revealed numerically by showing that the palinstrophy production is dominated by extremely elongated wave-number triads. More than 85% of the palinstrophy production comes from such triads whose ratio of the smallest wave number to the middle is less than that of the dissipation length to the diameter of the coherent vortices. Such high nonlocality casts some doubt on the universality of the scaling law of energy spectrum.
On the motion of small particles in a homogeneous turbulent shear flow
Authors: Yeh Fungee , Lei U.
Published: July 2002

The motion of small spherical solid particles is simulated numerically in a homogeneous turbulent gas shear flow generated by the large eddy simulation for two different mean shear rates (Γ), 12.9 sec−1 and 44 sec−1, which correspond to two different flow regimes. The results include a detailed study of the effect of the particle’s inertia and the particle’s free-fall velocity in still fluid (vd) on the particle dispersion and settling velocities. Let 〈YiYj〉 be the displacement tensor of the particles, where subscripts 1, 2, and 3 refer to the streamwise, the upward, and the spanwise directions, respectively. For the case with Γ=12.9 sec−1, the turbulence intensity of the flow decreases as time (t) increases and approaches an essentially constant value. It was found that 〈Y21〉∝t3, 〈Y22〉∝t, and 〈Y23〉∝t essentially when Γt=3–5, which agrees with the asymptotic behavior of the previous theoretical result for the fluid point dispersion in a stationary sheared turbulence. For the case with Γ=44 sec−1, the turbulence intensity of the flow increases with time monotonically. It was found that 〈Y21〉∝t4, 〈Y1Y2〉∝t3, 〈Y22〉∝t2, and 〈Y23〉∝t2 for large values of Γt. For both cases with different Γ’s, a particle falling in the direction perpendicular to the mean flow is found to approach an asymptotic state and the relative velocity between the particle and the fluid reaches a constant value. A particle leads the fluid in the streamwise direction but falls less rapidly in sheared turbulence than that in still fluid. It is also found that the magnitudes of the relative velocity components between the particle and the fluid in a turbulent shear flow are less than those in a corresponding laminar Couette flow.
Vortex rings of one fluid in another in free fall
Authors: Baumann Nicholas , Joseph Daniel D. , Mohr Paul , Renardy Yuriko
Published: July 2002

Experiments in which vortex rings of one immiscible liquid are created in another from drops falling from rest under gravity are presented and interpreted. These rings are associated with circulations generated by viscosity and, unlike classical vortex rings which occur in miscible liquids at high Reynolds numbers, they can exist even at very low Reynolds numbers. Since the rings do not diffuse, they are well-defined. Nonetheless, there are many similarities in the dynamics of formation and flow of miscible and immiscible rings. Parameters are identified which appear to correlate the authors’ observations and photographs of some of the more interesting events are shown.
Large- and small-scale stirring of vorticity and a passive scalar in a 3-D temporal mixing layer
Authors: Comte Pierre , Lesieur Marcel , Lamballais Eric
Published: July 2002

With the aid of a three-dimensional direct-numerical simulation (using pseudospectral methods) at high resolution (1283 grid points in a cubic box containing four fundamental longitudinal wavelengths), the origin and topology of the longitudinal vortex filaments which appear in the temporally growing mixing layer are investigated. The basic velocity field is a hyperbolic-tangent profile U tanh 2y/δi, with a Reynolds number Uδi/ν=100. The basic flow is forced initially by two small Gaussian random perturbations: a three-dimensional one, of kinetic energy ε3D U2, and a two-dimensional one, of kinetic energy ε2D U2. For ε2D=10−4 and ε3D=10−5, quasi-two-dimensional large coherent Kelvin–Helmholtz rolls form and merge. Because of unstable oblique modes, they oscillate slightly as in the translative instability proposed by Pierrehumbert and Widnall [J. Fluid Mech. 114, 59 (1982)], but not exactly in phase. Between these big rollers, weak vortex lines are stretched. For ε2D=0 and ε3D=10−4 the oblique modes observed in the previous case yield local roll-ups and pairings occurring in certains regions of the span only, giving rise to a large-scale vortex lattice similar to that observed by Nygaard and Glezer in forced experiments [Phys. Fluids A 2, 461 (1990)]. This is numerical evidence of Pierrehumbert and Widnall’s helical-pairing instability. Furthermore, a thin and intense streamwise hairpin vortex appears, stretched in between the large vortices of the lattice. A low Reynolds number counterpart of the mixing transition occurs during the second pairing, characterized by short k−5/3 subranges in the spectra, intense vorticity extrema, and intermittent distributions of local helicity.
On interactions between two finite-core hetons
Authors: Valcke S. , Verron J.
Published: July 2002

Interactions between two finite-core hetons are investigated numerically in a two-layer quasigeostrophic model. A heton is a pair of opposite-sign vortices in adjoining layers. The point vortex analysis by Hogg and Stommel [Proc. R. Soc. London Ser. A 397, 1 (1985)] is generalized and the influence of finite cores is specified. Three types of interaction depending on the stratification and initial separation between the hetons are identified. In particular it is found that, for a relatively weak stratification, a heton-specific interaction can prevent the normal merging of same-layer vortices.
A small-scale turbulence model
Authors: Lundgren T. S.
Published: July 2002

A previously derived analytical model for the small-scale structure of turbulence is reformulated in such a way that the energy spectrum may be computed. The model is an ensemble of two-dimensional (2-D) vortices with internal spiral structure, each stretched by an axially symmetric strain flow. Stretching and differential rotation produce an energy cascade to smaller scales in which the stretching represents the effect of instabilities and the spiral structure is the source of dissipation at the end of the cascade. The energy spectrum of the resulting flow may be expressed as a time integration involving only the enstrophy spectrum of the time evolving 2-D cross-section flow, which may be obtained numerically. Examples are given in which a k−5/3 spectrum is obtained by this method. The k−5/3 inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the 2-D enstrophy spectrum. The results are found to be insensitive to time dependence of the strain rate, including even intermittent on-or-off strains.
Absolute and convective instability of a viscous liquid jet surrounded by a viscous gas in a vertical pipe
Authors: Lin S. P. , Lian Z. W.
Published: July 2002

The absolute and convective instability of a viscous liquid jet emanating into a viscous gas in a vertical pipe is analyzed in a parameter space spanned by the Reynolds number, the Froude number, the Weber number, the viscosity ratio, the density ratio, and the diameter ratio. The numerical results of the analysis are used to demonstrate that reduction in gravity tends to enhance the Rayleigh mode of convective instability which leads to the breakup of a liquid jet into drops of diameters comparable with the jet diameter. On the contrary, the Taylor mode of convective instability that leads to atomization is retarded at reduced gravity. The Rayleigh mode becomes absolutely unstable when the Reynolds number exceeds a critical value for a given set of the rest of the relevant parameters. The domain of absolute instability is significantly enlarged when the effect of gas viscosity is not neglected.
Capillary instability of thin liquid film on a cylinder
Authors: Yarin Alexander L. , Oron Alexander , Rosenau Philip
Published: July 2002

The capillary instability of a thin liquid layer on a cylinder is studied. Using an integral approach and lubrication approximation, transport equations governing the spatiotemporal evolution of a film thickness and the temperature along the film are obtained. Evolution of the system under both isothermal and nonisothermal conditions is studied numerically. It is shown that nonlinear interaction of the linearly unstable modes begets an additional mode with a wavelength equal to that of the fastest growing wave. This, in turn, causes the formation of satellite drops along with the main ones. Application of these results in a possible continuous technology of high-temperature superconductor wire fabrication is discussed.
Chaotic flow in rotating lid cavities
Authors: Hadid Ali H.
Published: July 2002

Numerical computations are performed to investigate the structure and evolution of flow in a two-dimensional axisymmetric rotating lid cavity. Frequency decompositions, phase diagrams, and flow visualization are used to monitor the changing kinematics of the flow as the speed of the rotating side wall is increased. For the flow regimes investigated, the approach to steady state is characterized by oscillatory instabilities, quasiperiodic flow, and chaotic flow leading to turbulence. A detailed study of the physical mechanisms involved in the computed flow field indicates the existence of at least two independent frequencies at a rotational Reynolds number Re in the range of 8×105 to 9×105. At Re≳106, a multiple of independent frequencies appear in the spectrum that indicate a transition to turbulence. This seems to be consistent with the experiments of Daily and Nece [ASME J. Basic Eng. 82, 217 (1960)] for the Reynolds number at which transition to weak turbulence is observed and with the theoretical scenario of Ruelle and Takens [Commun. Math. Phys. 20, 167 (1967)] for the transition to turbulence.
On evolution equations for thin films flowing down solid surfaces
Authors: Frenkel Alexander L.
Published: July 2002

A wavy free-surface flow of a viscous film down a cylinder is considered. It is shown that if the cylinder radius is large, as compared to the film thickness, the long-wave perturbation approach yields a rather simple evolution equation. This nonlinear equation is similar to the well-known Benney equation of planar films, and becomes exactly the latter in the limit of infinite radius. Thus it is the annular-case analog—which was missing in the literature—of the Benney equation. It is argued that under conditions implicitly implied in their derivation, the Benney-type equations are not uniformly valid for large times. However, both the new and Benney equations are important heuristically—as sources of other, simpler, equations which, in certain domains of system parameters, are valid for all time. Also, the new equation of annular films is important as a qualitative model incorporating all significant physical factors.
Collisional transport treatment of surface plasma structures
Authors: Montierth L. M. , Morse R. L. , Neuman W. A.
Published: July 2002

Calculations are shown of the structure of plasmas in equilibrium with solid surfaces that reemit incident plasma ions as relatively cold neutral gas. A numerical transport model that includes a Fokker–Planck treatment of ion–ion collisions obtains the distribution function for ions in a phase space of one spatial coordinate and two velocities. This is done self-consistently with an electrostatic potential, a Maxwell–Boltzmann description of electrons, and electron impact ionization of the reemited neutrals. Solutions are obtained from a higher temperature kinetic regime where Coulomb collisions are nearly negligible to a lower temperature regime where plasma behavior is approximately fluidlike. A result of these calculations is the resolution of an ambiguity posed by previous kinetic regime calculations that omitted ion–ion collisions and obtained a family of solutions for each set of physical parameters [Phys. Rev. Lett. 49, 650 (1982); Phys. Fluids B 1, 448 (1989)]. The physically correct solution for semi-infinite surface plasmas is shown to be the member of each family that maximizes the ion thermal conduction to the surface and the magnitude of a maximum in the electrostatic potential that is found in these and the previous calculations. Further results are in agreement at lower temperatures with solutions obtained from a fluid model and the identification of the correct boundary condition on normal flow velocity to be used in fluid models.
Nonlinear analysis of Coulomb relaxation of anisotropic distributions
Authors: Schamel H. , Hamnén H. , Düchs D. F. , Stringer T. E. , O’Brien M. R.
Published: July 2002

The bi-Maxwellian model is employed to study the time evolution of anisotropic distributions resulting from Coulomb collisions. The rate of change of temperatures caused by like-particle collisions is described by a single ordinary differential equation for Ε, where Ε=T⊥/T∥. It exhibits a logarithmic singularity in the limit Ε→0, expressing the velocity space geometry and nonlinearity in the collision operator. The temporal relaxation is compared with a numerical solution of the nonlinear Fokker–Planck equation and is found to be insensitive to changes in the collision operator in the case of Ε>1. For Ε<1, however, the relaxation toward thermal equilibrium turns out to be dependent on the chosen model. The influence of unlike-particle collisions is also investigated.
A possible mechanism of current termination in a reversed field pinch
Authors: Nagata A. , Masamune S. , Arimoto H. , Yamada S. , Sato K. I. , Tamaru T.
Published: July 2002

A rapid growth of magnetic fluctuations resulting from the m=1 and m=2 modes and succeeding stop of rotation of these modes have been found as the precursor phenomena of current termination in the STP-3(M) [Trans. Inst. Elec. Eng. Jpn. 107-B, 469 (1987)] reversed field pinch. By deepening the field reversal at the wall, these precursors disappear and the current duration becomes much longer. It is found that sudden current termination is caused by a rapid growth of resistive tearing modes mainly because of nonlinear coupling of the m=1 mode.
Fully toroidal fluid model for low-frequency localized modes in magnetized plasmas
Authors: Nilsson J. , Liljeström M. , Weiland J.
Published: July 2002

A fully toroidal fluid model for the low-frequency ion density response has been compared with the gyrokinetic response in the electrostatic limit. In general a good agreement is obtained, particularly for unstable modes and modes propagating in the electron drift direction. In particular, good agreement for the stability threshold of ηi modes in the most interesting parameter regimes is obtained. The magnetic drift resonances are found to be destabilizing close to marginal stability.
Magnetic field amplification and saturation in two-dimensional magnetohydrodynamic turbulence
Authors: Biskamp D. , Welter H.
Published: July 2002

Two-dimensional (2-D) magnetohydrodynamic turbulence is investigated for weak initial magnetic fields using numerical simulation. It is found that the magnetic field is amplified owing to the formation of flux sheets with saturation due either to resistive diffusion (kinematic regime) or to nonlinear effects (dynamic regime). In the kinematic regime, which corresponds to the problem of passive scalar convection by 2-D Navier–Stokes turbulence, the saturation value of the magnetic energy is observed to scale as EMmax∝η−0.8 in approximate agreement with a simple theoretical estimate, EMmax/EM(0)≂Rm, where Rm is the magnetic Reynolds number. Because of the strongly disparate kinetic and magnetic energy spectra in the kinematic regime, roughly EVk∼k−3, EMk∼k, dynamic interaction on small scales already occurs at very small global energy ratios EM/EV, giving rise to strongly enhanced kinetic energy dissipation. In the fully dynamic regime (reached for EM/EV‖t=0>R−1m) global magnetic and kinetic energies become tightly coupled, with EM/EV being approximately constant in time and the energy dissipation rates being independent of the collisional diffusion coefficients. Finally, the effect of the magnetic Prandtl number Pr=μ/η is discussed.
Electromagnetic effects in fluctuations of nonequilibrium plasmas and applications to alpha diagnostics
Authors: Chiu S. C.
Published: July 2002

A generalized fluctuation–dissipation theorem is obtained for current and density correlation spectrum of a nonequilibrium plasma. Although normally significant density fluctuations occur in only electrostatic modes, the fast mode in the lower-hybrid range of frequencies gives an exceptional example in which the mode is nontrivially electromagnetic, and yet the density fluctuations are comparable to the slow mode, which is well approximated by electrostatic approximation. This fact has quite important implications on the scattering of electromagnetic waves by nonequilibrium plasmas such as fusion plasmas with energetic α particles. It makes microwave scattering a more plausible scheme for α diagnostics.
The role of ion momentum in stimulated Raman scattering
Authors: McKinstrie C. J. , Yu M.
Published: July 2002

A systematic study is made of momentum conservation in stimulated Raman scattering. The time-averaged light-wave momentum is carried by the electromagnetic field, as is well known. However, in cold electron–ion plasma, none of the time-averaged Langmuir-wave momentum is carried by the electric field or by the electrons; an ion drift is established which carries the Langmuir-wave momentum. This drift Doppler shifts the Langmuir-wave frequency by a small amount, but does not hinder the development of stimulated Raman scattering.
Anomalous transports associated with the helicity transport in a plasma
Authors: Yoshida Z. , Hasegawa A.
Published: July 2002

Heat and particle transports which are associated with the helicity transport are obtained in a current-carrying plasma. The helicity flux represents the transport of parallel current density and is produced by an electric field with a circularly polarized component. Fluctuations with circularly polarized components induce finite average in cross-field nonlinear parallel current, which leads to generation of frictional electron heat flux as well as ion nonlinear polarization current that produces particle flux. The circular polarization of the perturbed electric field thus relates the helicity flux, electron heat flux, and the particle flux in such a manner that the heat and the particle transports in the direction opposite to the helicity flux. This result applies whether the helicity is injected externally by oscillating fields or it is generated internally in the plasma.
Formation of presheath and current-free double layer in a two-electron-temperature plasma
Authors: Sato Kunihiro , Miyawaki Fujio
Published: July 2002

Development of the steady-state potential in a two-electron-temperature plasma in contact with the wall is investigated analytically. It is shown that if the hot- to cold-electron temperature ratio is of the order of 10, the potential drop in the presheath is allowed to have either a small value characterized by the cold electrons or a large value by the hot electrons, and discontinuously changes at a critical value for the hot- to total-electron density ratio. It is also found that the monotonically decreasing potential structure, which consists of the first presheath, a current-free double layer, the second presheath, and the sheath, can be steadily formed in a lower range of the hot- to total-electron density ratio around the critical value. The current-free double layer is set up due to existence of the two electron species and cold ions generated by ionization so as to connect two presheath potentials at different levels.
Kinetic theory of self-similar expansion of a dusty plasma
Authors: Luo H. , Yu M. Y.
Published: July 2002

The one-dimensional quasineutral self-similar expansion of a dusty plasma is investigated using kinetic theory. The light electrons and ions are assumed to be in local thermodynamic equilibria and the heavy multiply charged dust particles collisionless. It is found that, within a few τ’s, where τ is the self-similar variable, the velocity distribution of the dust particles becomes highly asymmetrical and narrow, and the dust density vanishes.
Linear and electronic transport in strongly coupled binary ionic mixtures. Applications to the hydrogen–helium system
Authors: Léger D. , Deutsch C.
Published: July 2002

This paper is devoted to a systematic investigation of linear transport properties in strongly coupled binary ionic mixtures of pointlike ions interacting solely through Coulomb interactions. The basic formalism rests upon suitable extensions of the Boltzmann–Ziman equation. Validity conditions for the Lorentzian approximation are thoroughly discussed. High temperature and inelastic contributions to electron transport are emphasized. The formalism is, hereafter, specialized to a thorough investigation of electric, thermal, and mechanical transport coefficients. Basic transport quantities are expressed under a reduced form that allows an easy analytical treatment of temperature and inelastic corrections, parametrized with α=T/TF and ■=βℏω, respectively. The former are derived from exact solutions of transport equation through various jellium dielectric functions. Calculation of inelastic contributions is performed through the variational method. Electron transport at T=0 is then thoroughly investigated, including electric and thermal conductivities as well as thermopower and shear viscosity. These results are furthermore extended to an exact calculation of the electric conductivity up to order α2 including properly inelastic contributions, derived in terms of successive moments of the ion–ion structure factors.

Results are presented under an analytic and compact form, convenient for a numerical implementation to strongly coupled H+–He2+ mixtures of astrophysical interest. Calculations are performed within binary ionic mixture (BIM) and polarized BIM (PBIM) frameworks, respectively. Ion–ion structure factors are computed through the hypernetted-chain (HNC) scheme, by neglecting bridge diagrams. Most of these results pertain to homogeneous phases. First, the focus is on BIM and a systematic investigation of the Γ-rs and c2 dependence of the transport quantities is performed. Also, attention is paid to the influence of the jellium dielectric function. The T=0 elastic limit is considered first. Next, inelastic and finite temperature corrections are addressed, and BIM to PBIM results are compared. Finally, the electric resistivity behavior is investigated in the vicinity of critical demixing. Discrepancy between BIM and PBIM are thus stressed.
Synchrotron radiation and absorption at 3ωce with X-mode–O-mode coupling
Authors: Hu J. L. , Swanson D. G.
Published: July 2002

The mode conversion-tunneling equation with weakly relativistic absorption at 3ωce has been solved by using the Green function method. The numerical results show that the reflection and conversion coefficients are dramatically reduced when relativistic absorption is included, while the transmission coefficients and the conversion coefficient from the X-mode on the high field side to the O-mode on the low field side are independent of absorption. The reduction of these coefficients leads to the reduction of the asymmetry in the absorption between different wave branches. The numerical results also show that the relativistic effect is important even for a relatively low temperature plasma. An important relationship between solutions is expressed by the reciprocity relations which have been proved for any harmonic number. These analyses modify the interpretation of electron cyclotron emission (ECE).
Lagrangian description of ion dynamical effects in plasma diodes
Authors: Schamel H. , Bujarbarua S.
Published: July 2002

A novel integral formulation of the plasma diode dynamics on the slow ion time scale is derived under the assumptions of a negligible ion pressure and a slow electron response described by an equation of state. Equilibrium solutions are constructed for several particle injection conditions at the cathode and for arbitrary anode potentials. In addition, structural stability arguments are presented and applied to the class of equilibria related to equal particle injection conditions.
Ion-cyclotron resonance heating by means of the fast wave in a longitudinally inhomogeneous magnetic field
Authors: Lashmore-Davies C. N. , Fuchs V. , Cairns R. A.
Published: July 2002

The coupling between the fast wave and the slow ion-cyclotron wave in a plasma in which the equilibrium magnetic field is longitudinally inhomogeneous is reconsidered, using a model studied by White, Yoshikawa, and Oberman [Phys. Fluids 25, 384 (1982)]. Such a coupling can only occur when a second ion species is present and for finite k⊥. This configuration is of relevance to mirrors and also tokamaks. An approximate dispersion relation is obtained from the usual cold plasma model by replacing all slowly varying quantities by their value at the coupling point. The resulting equation preserves the cutoff properties of the original equation. The approximate dispersion relation is then used to analyze the mode conversion of the fast wave to the slow wave at the minority resonance. For N⊥≡cAk⊥/ω ≪1 the transmission coefficient is close to unity but for N⊥ ≲1 the transmission becomes very weak and for incidence from the stronger field region, the absorption becomes strong. When the wave is incident from the weaker field region the maximum absorption as a function of the minority fraction and N⊥ is 25%. Our results are obtained using second-order coupling theories, the advantages of which clearly emerge from this example.
Effects of ‘‘Kalliroscope’’ flow visualization particles on rotating Couette–Taylor flow
Authors: Dominguez-Lerma M. A. , Ahlers Guenter , Cannell David S.
Published: July 2002

Experimental results are presented which show that Taylor vortex flow in a vertically mounted rotating Couette system, visualized with a ‘‘Kalliroscope’’ suspension evolves to a spatially nonperiodic flow which is also nonperiodically time dependent. These effects are most noticeable in systems of large aspect ratio and depend on the concentration of the suspension. Experimental evidence is presented that suggests that these phenomena are caused by the evolution of a periodic variation of the Kalliroscope particle concentration along the cylinder axis and parallel to the gravitational field.
Squire’s theorem for two stratified fluids
Authors: Hesla Todd I. , Pranckh Ferdinand R. , Preziosi Luigi
Published: July 2002

It is demonstrated that only two-dimensional perturbations need be considered in determining the marginal stability boundary in the parameter space for the incompressible, parallel flow of two stratified, homogeneous, immiscible fluids, with constant interfacial tension, bounded by two (possibly moving) parallel plates.
Simulation study of two-ion hybrid resonance heating
Authors: Riyopoulos S. , Tajima T.
Published: July 2002

A one-dimensional low-noise, low-frequency electromagnetic particle simulation code that is appropriate for investigation of ion-cyclotron resonance heating (ICRH) is developed. Retaining the hyperbolicity of the electromagnetic waves and exploiting nearly one-dimensional characteristics (perpendicular to the external magnetic field) of the ICRH, the guiding center electron approximation for the transverse electronic current calculation is used. Mode conversion of the incoming magnetosonic wave into the electrostatic ion–ion hybrid mode is observed accompanied by strong ion heating. The dependence of this heating on the different plasma parameters is examined through a series of simulations, focusing mainly on wave incidence from the high field side. Because k∥=0 in the runs, the conventional Landau damping cannot explain the ion heating. Nonlinear mechanisms for energy transfer are discussed. The numerical results demonstrate the importance of the nonlinear wave–particle interaction for energy absorption during radio-frequency heating in the ion-cyclotron regime.
Ballooning vortex in magnetohydrodynamics
Authors: Shukla P. K. , Rao N. N.
Published: July 2002

Making use of the ideal magnetohydrodynamics, a set of coupled equations is derived which governs the dynamics of nonlinear ballooning modes. Criteria for the existence of a class of ballooning dipole vortices are presented.
Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker–Planck equation
Authors: Epperlein E. M. , Haines M. G.
Published: July 2002

Significant departures from standard transport coefficients [e.g., Sov. Phys. JETP 6, 338 (1958)] have been found for the electron current and heat flux in a fully ionized plasma. These have been discovered by carrying out a direct and accurate numerical solution of the linearized Fokker–Planck equation using a Cartesian tensor expansion of the distribution function. The results, which were carried out for plasmas of various atomic numbers, show the presence of major inaccuracies (errors of up to 65%) in Braginskii coefficients β■, κ⊥, and κ■ (as conventionally defined) for Hall parameters ωτ in the range 0.3≲ωτ≲30. Surprisingly, α■ and β⊥ are found to depend on τ/(ωτ)2/3 and 1/(ωτ)5/3, and not on τ/(ωτ) and 1/(ωτ)2, respectively, as ωτ→∞. An analytic expansion for large ωτ verifies this result, showing that the relatively cold unmagnetized electrons in the distribution function play a dominant role in the cross-field transport. The numerical results are fitted to within 15% to a polynomial in ωτ for various values of Z.
Direct mode–mode coupling observation in the fluctuations of nonstationary transparent fluid
Authors: Grésillon D. , Mohamed-Benkadda M. S.
Published: July 2002

An experimental method by which a given time and space fluctuating medium can be qualified as equilibrium (laminar), or turbulent, is presented. It employs an optical observation to obtain directly the complex amplitude of the space Fourier transform of mass density distribution in a transparent gas. This observation is provided by coherent Rayleigh scattering and heterodyne detection. Several Fourier modes with different wavenumbers and frequencies are observed simultaneously. Their nonlinear quadratic mode–mode coupling is analyzed by using third-order moment statistics and the full space-time bispectrum. An experiment using this double (optical and numerical) technique on the air density fluctuations in a round free-jet is reported. Significant nonlinear coupling is observed in the mixing layer and in the fully developed turbulence zone.
Compressible rotational flows generated by the substitution principle
Authors: Azara J. L. Rodriguez , Emanuel George
Published: July 2002

A theory is developed for compressible rotational flow that is based on the substitution principle. The theory encompasses a formula for the transformation of the vorticity under the principle. Solutions are found for four rotational flows. These are the rotational counterparts of a parallel flow, flow behind a planar oblique shock wave, Prandtl–Meyer flow, and Taylor–Maccoll flow. A surprising variation of the vorticity is found for the planar oblique shock wave and the Prandtl–Meyer flow. Irrotational flow behind a curved shock wave, where the upstream flow is rotational, is examined and shown not to be possible.
Influence of streamwise vortices on Tollmien–Schlichting waves
Authors: Nayfeh Ali H. , Al-Maaitah Ayman
Published: July 2002

An analysis is presented of the influence of steady quasiperiodic streamwise vortices on Tollmien–Schlichting (TS) waves. The vortices act as parametric exciters for the TS waves. The present analysis is for the subharmonic resonance in which the spanwise wavenumber of the vortices is twice that of the TS wave. Floquet theory is used to derive an eigenvalue problem for the complex streamwise wavenumber, which is then solved using a shooting technique. The results show that there are two components of the solution, one is stabilized and the other is destabilized by the vortices. For the same flow characteristics, calculations were obtained from the theory which Nayfeh [J. Fluid Mech. 107, 441 (1981)] developed using the method of multiple scales. The results obtained from both approaches are in excellent agreement.
The Stokes drag due to the sliding of a smooth plate over a finned plate
Authors: Wang C. Y.
Published: July 2002

The relative sliding motion of a smooth plate over a periodically finned plate is studied under the Stokes limit. The resulting harmonic or biharmonic equations with mixed boundary conditions are solved by eigenfunction expansions and collocation. The drag is determined as a function of fin height and fin spacing.
Control of an axisymmetric jet using vortex generators
Authors: Zaman K. B. M. Q. , Reeder M. F. , Samimy M.
Published: July 2002

The results of an experimental investigation on the effect of vortex generators, in the form of small tabs at the nozzle exit on the evolution of a jet, are reported in this paper. Primarily tabs of triangular shape are considered, and the effect is studied up to a jet Mach number of 1.8. Each tab is found to produce a dominant pair of counter-rotating streamwise vortices having a sense of rotation opposite to that expected from the wrapping of the boundary layer. This results in an inward indentation of the mixing layer into the core of the jet. A triangular-shaped tab with its apex leaning downstream, referred to as a delta tab, is found to be the most effective in producing such vortices, with a consequential large influence on the overall jet evolution. Two delta tabs, spaced 180° apart, completely bifurcate the jet. Four delta tabs stretch the mixing layer into four ‘‘fingers,’’ resulting in a significant increase in the jet mixing downstream. For six delta tabs the mixing layer distortion settles back to a three finger configuration through an interaction of the streamwise vortices. The tabs are found to be equally effective in jets with turbulent or laminar initial boundary layers. Two sources of streamwise vorticity are postulated for the flow under consideration. One is the upstream ‘‘pressure hill,’’ generated by the tab, which constitutes the main contributor of vorticity to the dominant pair. Another is due to vortex filaments shed from the sides of the tab and reoriented downstream by the mean shear of the mixing layer. Depending on the orientation of the tab, the latter source can produce a vortex pair having a sense of rotation opposite to that of the dominant pair. In the case of the delta tab, vorticity from the two sources add, explaining the strong effect in that configuration.
Compressibility effects on the passive scalar flux within homogeneous turbulence
Authors: Blaisdell G. A. , Mansour N. N. , Reynolds W. C.
Published: July 2002

Compressibility effects on turbulent transport of a passive scalar are studied within homogeneous turbulence using a kinematic decomposition of the velocity field into solenoidal and dilatational parts. It is found that the dilatational velocity does not produce a passive scalar flux, and that all of the passive scalar flux is due to the solenoidal velocity.
Numerical investigation of 2D convection with extremely large viscosity variations
Authors: Moresi L.-N. , Solomatov V. S.
Published: July 2002

Previous experimental studies of convection in fluids with temperature-dependent viscosity reached viscosity contrasts of the order of 105. Although this value seems large, it still might not be large enough for understanding convection in the interiors of Earth and other planets whose viscosity is a much stronger function of temperature. The reason is that, according to theory, above 104–105 viscosity contrasts, convection must undergo a major transition—to stagnant lid convection. This is an asymptotic regime in which a stagnant lid is formed on the top of the layer and convection is driven by the intrinsic, rheological, temperature scale, rather than by the entire temperature drop in the layer. A finite element multigrid scheme appropriate for large viscosity variations is employed and convection with up to 1014 viscosity contrasts has been systematically investigated in a 2D square cell with free-slip boundaries. We reached the asymptotic regime in the limit of large viscosity contrasts and obtained scaling relations which are found to be in good agreement with theoretical predictions.
Instabilities of the Type I Long’s vortex at large flow force
Authors: Ardalan K. , Draper Kevin , Foster M. R.
Published: July 2002

The temporal inertial instabilities of the Type I Long’s vortex for large values of the flow force, M, are explored. It is found that growth rates and wave speeds obtained numerically for the exact vortex profiles agree very well with those obtained for large-M profiles found by asymptotic means. Agreement is excellent, so the large-M structure and inertial instability modes of the Type I Long’s vortex are now well established. It is determined that the modes computed here are ring modes. Both exact and asymptotic solutions display a spurious instability mode, which vanishes for increased resolution.
Anomalous behavior during leveling of thin coating layers with surfactant
Authors: Schwartz L. W. , Cairncross R. A. , Weidner D. E.
Published: July 2002

Our recently-published linear analysis [Schwartz et al., Langmuir 11, 3690 (1995)] demonstrated that an initially rippled thin layer of Newtonian liquid with uniformly distributed surfactant may level in unexpected ways. While the presence of surfactant will, in general, slow the rate of leveling compared to that of a perfectly clean system, there was shown to exist a realistic parameter range where increasing, rather than reducing, the amount of surfactant present will hasten leveling. Here, for the two-dimensional problem, we investigate the importance of nonlinearity though numerical solution of (i) the unsteady lubrication form of the evolution equations with surfactant, and (ii) finite-element solution of the exact governing equations for slow viscous flow. Confirmation of the linear results is demonstrated and quantitative discrepancy only appears for large-amplitude and short-wavelength ripples. Surface tension gradient driven flow explains the anomalies; for moderate surfactants, the surface quickly ‘hardens,’ leading to a decay rate of one-quarter of the clean-surface rate, while for weak surfactants, leveling proceeds to a plateau level which decays much slower than the hard-surface result.
Three-dimensional features of particle dispersion in a nominally plane mixing layer
Authors: Marcu B. , Meiburg E.
Published: July 2002

Navier–Stokes simulations of a temporally growing mixing layer are employed to investigate three-dimensional mechanisms for the dispersion and accumulation of small, heavy, spherical particles. It is found that in particular the presence of the streamwise braid vortices gives rise to additional dynamical effects that modify the concentration, dispersion, and suspension patterns observed in two-dimensional situations. Intense stretching and folding by the evolving three-dimensional vorticity field, when combined with inertial effects such as ejection by the concentrated streamwise vortices, strongly distorts the geometry of both clear fluid and particle laden regions. Different time scales can be associated with the spanwise and streamwise vortices, so that these distinct vortical systems can selectively affect different classes of particles.
The effect of small pipe divergence on near critical swirling flows
Authors: Rusak Z. , Judd K. P. , Wang S.
Published: July 2002

The effect of small pipe divergence on an inviscid, incompressible, near critical axisymmetric swirling flow is investigated. The singular behavior of a regular expansion solution, in terms of the pipe divergence parameter, around the critical swirl of a flow in a straight pipe is demonstrated. This singularity infers that large-amplitude disturbances may be induced by the small pipe divergence when incoming flows have a swirl level near the critical swirl. In order to gain insight to the behavior of flows in this swirl range, a small-disturbance analysis is developed. It is found that a small but finite pipe divergence breaks the transcritical bifurcation of solutions of a flow in a straight pipe into two equilibrium solution branches. These branches fold at limit swirl levels near the critical swirl resulting in a finite gap of swirl that separates the two branches. This suggests that no near-columnar axisymmetric state can exist within this range of incoming swirl around the critical level; the flow must develop large disturbances in this swirl range. Beyond this range, two steady states may exist under the same inlet/outlet conditions. However, when the pipe divergence is increased, this special behavior uniformly changes into a branch of solutions with no fold. A weakly nonlinear approach to study the effect of slight pipe divergence on standing waves in a long pipe is also derived. The behavior of the asymptotic solutions match the bifurcation diagrams from previous theoretical and numerical studies and extends their results. The relevance of the results to axisymmetric vortex breakdown in a diverging pipe is discussed.