bluuebunny/crossref_metadata_2025 huggingface dataset:
Doping-dependent superconducting properties of two-dimensional metals with different types of interparticle coupling (Review)
Authors: Loktev V. M. , Turkowski V. M.
Published: March 2004

The superconducting properties of a two-dimensional metallic system with arbitrary carrier density and both local and various types of attractive indirect boson-exchange interaction in the cases of s- and d-wave pairing are analyzed and reviewed at T=0. In particular, the possibility of a crossover from the Bose–Einstein condensation regime to Bardeen–Cooper–Schrieffer-like superconductivity with growing carrier density and changing coupling in the case of different pairing channels is discussed. Gaussian fluctuations of the order parameter are taken into account, and the carrier density dependence of the gap magnitude is studied. The role of the form of the interparticle attractive interaction in the physical behavior of the system is also considered.
On the possibility of simultaneous spiral and superfluid ordering in a Fermi liquid
Authors: Peletminskii S. V. , Yatsenko A. A. , Shul’ga S. N.
Published: March 2004

A study is made of one of the possible forms of ordering of Fermi systems—superfluid spiral ordering, wherein not only the phase invariance of the state is broken but so are the translational invariance and the invariance with respect to spin rotations. A general method of studying superfluid spiral ordering is formulated on the basis of the Fermi-liquid approach to the consideration of superfluid states. For a one-component Fermi system we obtain the self-consistency equations for four order parameters and the temperature of the simultaneous phase transition to the superfluid and spiral states. The system of equations is investigated in the case of two nonzero order parameters. The transition temperature and the energy gap in the spectrum of elementary fermionic excitations are obtained as functions of the parameter of the spiral. The region of values of the spiral parameter in which the spiral superfluid ordering can exist is determined. The correlation function of the spins in the presence of spiral ordering is investigated.
Depairing critical currents and self-magnetic field effects in submicron YBa2Cu3O7−δ microbridges and bicrystal junctions
Authors: Ivanov Z. G. , Fogel N. Ya. , Yuzephovich O. I. , Stepantsov E. A. , Tzalenchuk A. Ya.
Published: March 2004

We report on depairing critical currents in submicron YBa2Cu3O7−δ microbridges. A small-angle bicrystal grain boundary junction is used as a tool to study the entrance of vortices induced by a transport current and their influence on the I–V curves. The interplay between the depairing and the vortex motion determines a crossover in the temperature dependence of the critical current. The high entrance field of vortices in very narrow superconducting channels creates the possibility of carrying a critical current close to the depairing limit determined by the S–S′–S nature of the small-angle grain boundary junction.
Order parameter phase locking as a cause of a zero bias peak in the differential tunneling conductance of bilayers with electron–hole pairing
Authors: Bezuglyj A. I. , Shevchenko S. I.
Published: March 2004

In n–p bilayer systems an exotic phase-coherent state emerges due to Coulomb pairing of n-layer electrons with p-layer holes. Unlike Josephson junctions, the order parameter phase may be locked by matrix elements of interlayer tunneling in n–p bilayers. Here we show how the phase locking phenomenon specifies the response of the electron–hole condensate to interlayer voltages. In the absence of an applied magnetic field, the phase is steady-state (locked) at low interlayer voltages, VVc. The change in the system dynamics at V=Vc gives rise to a peak in the differential tunneling conductance. The peak width Vc is proportional to the absolute value of the tunneling matrix element |T12|, but its height does not depend on |T12|; thus the peak is sharp for small |T12|. An in-plane magnetic field reduces the peak height considerably. The present results are in qualitative agreement with the zero-bias peak behavior that has recently been observed in bilayer quantum Hall pseudoferromagnets with spontaneous interlayer phase coherence.
Josephson and spontaneous currents at the interface between two d-wave superconductors with transport current in the banks
Authors: Kolesnichenko Yu. A. , Omelyanchouk A. N. , Shevchenko S. N.
Published: March 2004

A stationary Josephson effect in the ballistic contact of two d-wave superconductors with different orientation of the axes and with transport current in the banks is considered theoretically. The influence of the transport current on the current–phase relation of the Josephson and tangential currents at the interface is studied. It is demonstrated that the spontaneous surface current at the interface depends on the transport current in the banks due to the interference of the angle-dependent condensate wave functions of the two superconductors.
Influence of mechanical stress and temperature on the photoluminescence in the low-temperature phase of C60 fullerite
Authors: Avdeenko A. , Gorobchenko V. , Zinoviev P. , Silaeva N. , Zoryanskiı̆ V. , Gorbenko N. , Pugachev A. , Churakova N.
Published: March 2004

The results of a study of the low-temperature (5–90 K) photoluminescence of thin films of C60 obtained by vacuum deposition on heated mica substrates are reported. The structure of the films is analyzed by the method of high-energy electron diffraction. The features of the luminescence of structural traps (X traps), which arise on account of mechanical stresses created by bending of C60 films of different structure on mica substrates, are investigated for the first time. The temperature behavior of the photoluminescence bands due to defects of this kind is investigated. The processes of trapping and transport of electronic excitations in the low-temperature phase of C60 are discussed.
Creep of beta-tin single crystals at subkelvin temperatures
Authors: Natsik V. D. , Soldatov V. P. , Ivanchenko L. G. , Kirichenko G. I.
Published: March 2004

The creep of β-Sn single crystals oriented for slip in the (100)〈010〉 system is investigated in the temperature range 0.45–4.2 K. A transient creep, decaying in time by a logarithmic law, is registered both above and below 1 K. The temperature dependence of the coefficient of logarithmic creep is studied in detail, and the existence of two qualitatively different regions of its behavior is established: in the interval 4.2–1.2 K the coefficient increases linearly with decreasing temperature, while below 1 K the creep acquires an athermal character and the coefficient remains constant. It is shown that the regularities observed in the experiment are in accord with the idea that the kinetics of creep in pure β-Sn is governed by the motion of dislocations in the Peierls potential relief by a mechanism of nucleation of kink pairs on the dislocation lines. This process entails the overcoming of a small effective potential barrier of the order of 0.001 eV: in the temperature region T<1 K the nucleation of kink pairs occurs by a quantum tunneling effect, and the creep is of a purely quantum character; at higher temperatures the leading role is played by thermal fluctuations, and the deformation kinetics corresponds to the classical ideas of thermally activated creep. Empirical estimates are obtained for the density of mobile dislocations and the work hardening coefficient.
An inverse problem in coupled mode theory
Authors: Sacks Paul
Published: March 2004

We study an inverse problem for the Zakharov–Shabat system which is motivated by an application to the design of co-directional couplers with prescribed response properties.
Geodesic flow on (super-) Bott–Virasoro group and Harry Dym family
Authors: Guha Partha
Published: March 2004

We show various Harry Dym type equations and Super Harry Dym equations, introduced by Brunelli, Das, and Popowicz [2003 Supersymmetric extensions of the Harry Dym hierarchy, J. Math. Phys. 44, 4756–4767 (2003)], follow from the geodesic flows on the Bott–Virasoro group and its supersymmetric generalization, superconformal group. In fact, their bi-Hamiltonian structures can be derived from the Lie Poisson structures on the (super-) Bott–Virasoro orbit. We also show that that m2KdV or Calogero–Degasperis equation is also connected to the Bott–Virasoro group.
Equilibrium states for the Bose gas
Authors: Vandevenne Lieselot , Verbeure André , Zagrebnov Valentin A.
Published: March 2004

The generating functional of the cyclic representation of the canonical commutation relations (CCR) representation for the thermodynamic limit of the grand canonical ensemble of the free Bose gas with attractive boundary conditions is rigorously computed. We use it to study the condensate localization as a function of the homothety point for the thermodynamic limit using a sequence of growing convex containers. The Kac function is explicitly obtained proving nonequivalence of ensembles in the condensate region in spite of the condensate density being zero locally.
Variational derivation of relativistic fermion–antifermion wave equations in QED
Authors: Terekidi Andrei G. , Darewych Jurij W.
Published: March 2004

We present a variational method for deriving relativistic two-fermion wave equations in a Hamiltonian formulation of QED. A reformulation of QED is performed, in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. The reformulation permits one to use a simple Fock-space variational trial state to derive relativistic fermion–antifermion wave equations from the corresponding quantum field theory. We verify that the energy eigenvalues obtained from the wave equation agree with known results for positronium.
On the absolutely continuous and negative discrete spectra of Schrödinger operators on the line with locally integrable globally square summable potentials
Authors: Rybkin Alexei
Published: March 2004

For one-dimensional Schrödinger operators with potentials q subject to ∑n=−∞∞(∫nn+1|q(x)|dx)2<∞, we prove that the absolutely continuous spectrum is [0,∞), extending the 1999 result due to Dieft–Killip. As a by-product we show that under the same condition the sequence of the negative eigenvalues is 3/2-summable improving the relevant result by Lieb–Thirring.
Comment on “Two-dimensional, highly directive currents on large circular loops” [J. Math. Phys. 41, 6130 (2000)]
Authors: Stoyanov B. J.
Published: March 2004

Margetis and Fikioris, apparently unaware of the earlier results available in the literature, used an elaborate Mellin transform technique to obtain an asymptotic approximation for a particular case of a Bessel function integral. Here, the earlier, more general results are pointed out.
Classification of static plane symmetric space–times according to their matter collineations
Authors: Sharif M.
Published: March 2004

In this paper we classify static plane symmetric space–times according to their matter collineations. These have been studied for both cases when the energy–momentum tensor is nondegenerate and also when it is degenerate. It turns out that the nondegenerate case yields either four, five, six, seven, or ten independent matter collineations in which four are isometries and the rest are proper. There exists three interesting cases where the energy–momentum tensor is degenerate but the group of matter collineations is finite-dimensional. The matter collineations in these cases are either four, six, or ten.
Noncommutative geometry of super-Jordanian OSph(2/1) covariant quantum space
Authors: Aizawa N. , Chakrabarti R.
Published: March 2004

Extending a recently proposed procedure of construction of various elements of differential geometry on noncommutative algebras, we obtain these structures on noncommutative superalgebras. As an example, a quantum superspace covariant under the action of super-Jordanian OSph(2/1) is studied. It is shown that there exist a two-parameter family of torsionless connections, and the curvature computed from this family of connections is bilinear. It is also shown that the connections are not compatible with the metric.
Existence and uniqueness of global solution of the Hasegawa–Mima equation
Authors: Guo Boling , Han Yongqian
Published: March 2004

The Hasegawa–Mima equation is the simplest nonlinear model to investigate drift waves and drift-wave turbulence. In this article, we establish the existence and uniqueness of a global weak solution for the Cauchy problem of the two-dimensional Hasegawa–Mima equation. Moreover, if the background particle density is homogeneous in the x-direction, there is a unique global regular solution.
Eigenvalue distribution of large weighted random graphs
Authors: Khorunzhy O. , Shcherbina M. , Vengerovsky V.
Published: March 2004

We study eigenvalue distribution of the adjacency matrix A(N,p) of weighted random graphs Γ=ΓN,p. We assume that the graphs have N vertices and the average number of edges attached to one vertex is p. To each edge of the graph eij we assign a weight given by a random variable aij with zero mathematical expectation and all moments finite. In the first part of the paper, we consider the moments of normalized eigenvalue counting function σN,p of A(N,p). Assuming all moments of a finite, we obtain recurrent relations that determine the moments of the limiting measure σp=limN→∞σN,p. The method developed is applied to the Laplace operator ΔΓ closely related with A(N,p). Using the recurrent relations, we analyze the form of σp for the both of random matrix families. In the second part of the paper we consider the resolvents G(A,Δ)(z) of A(N,p) and ΔΓ of ΓN,p and study the functions fN(A,Δ)(z,u)=(1/N)∑k=1N exp{−uGkk(A,Δ)(z)} in the limit N→∞. We derive closed equations that uniquely determine the limiting functions f(A,Δ)(z,u). These equations allow us to prove the existence of the limiting σp for adjacency matrix and the Laplace operator under a rather weak condition that only the fourth moment of aij is finite. Besides, equations for f(A,Δ)(z,u) give us the asymptotic expansions for the Stieltjes transform of the limiting σp with respect to z−k and pk.
Ideally embedded space–times
Authors: Haesen Stefan , Verstraelen Leopold
Published: March 2004

Due to the growing interest in embeddings of space–time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson–Walker space–time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.
The magnetic Weyl calculus
Authors: Măntoiu Marius , Purice Radu
Published: March 2004

In the presence of a variable magnetic field, the Weyl pseudodifferential calculus must be modified. The usual modification, based on “the minimal coupling principle” at the level of the classical symbols, does not lead to gauge invariant formulas if the magnetic field is not constant. We present a gauge covariant quantization, relying on the magnetic canonical commutation relations. The underlying symbolic calculus is a deformation, defined in terms of the magnetic flux through triangles, of the classical Moyal product.
Bound states in coupled guides. I. Two dimensions
Authors: Linton C. M. , Ratcliffe K.
Published: March 2004

Bound states that can occur in coupled quantum wires are investigated. We consider a two-dimensional configuration in which two parallel waveguides (of different widths) are coupled laterally through a finite length window and construct modes which exist local to the window connecting the two guides. We study both modes above and below the first cutoff for energy propagation down the coupled guide. The main tool used in the analysis is the so-called residue calculus technique, in which complex variable theory is used to solve a system of equations which is derived from a mode-matching approach. For bound states below the first cutoff a single existence condition is derived, but for modes above this cutoff (but below the second cutoff), two conditions must be satisfied simultaneously. A number of results have been presented which show how the bound-state energies vary with the other parameters in the problem.
Onset of Manifest Convection in a Layer of Fluid with a Time-Dependent Surface Temperature
Authors: Foster Theodore D.
Published: March 2004

Experiments have been performed in deep layers of fluid in which the bottom surface temperature was increased at a constant rate. It was found that when the thermal boundary layer was only a small fraction of the total depth of the fluid layer, the onset of manifest convection was independent of the layer depth. The predictions of linear time-dependent theory that the time of onset of manifest convection should vary with the - 25 power of the rate of bottom surface temperature increase and that the horizontal spacing of the convection cells should vary with the - 15 power of the rate of bottom surface temperature increase were verified within reasonable limits.
Similarity Model of an Explosion in a Rarefied Atmosphere
Authors: Holway Lowell H.
Published: March 2004

A similarity solution recently given by Stuart for spherically symmetric flow following an explosion in a rarefied atmosphere is extended by requiring it to satisfy the hydrodynamic energy conservation equation. This additional constraint allows one to determine the functional form of the pressure and density and avoids the necessity of making the virial theorem approximation. The differential equation for the radius of the disturbance is different from the earlier theory, especially at late times when it shows that the kinetic energy eventually is completely transformed into internal energy, but the disturbance velocities are identical in the limit as R → 0.
Experiments on Hartmann Channel Flow in Plasmas
Authors: Sonju Otto K. , Kruger Charles H.
Published: March 2004

An experimental study of subsonic Hartmann channel flow of a plasma is described. A partially ionized gas, consisting of high-temperature atmospheric-pressure potassium-seeded combustion products, was passed through an insulated rectangular channel in the presence of a transverse magnetic field. The influence of the electrical-conductivity profile within the plasma was studied by systematically varying the wall temperature with respect to the mean plasma temperature. The effect of the magnetic field was found to be sensitive to this temperature difference. Only situations where the wall temperature is less than the mean plasma temperature have been investigated. With wall temperatures several hundred degrees below the mean plasma temperature, an increase in wall-shear stress of about 30% is observed, as compared with a factor-of-2 increase found in the corresponding uniform conductivity, liquid metal experiments. The experimental data for laminar flow agree well with the results of an approximate analysis. Turbulence-damping effects, Hall-parameter effects and fluid-property-variation effects are discussed. The turbulence-damping effect is smaller in the present experiments than in the mercury-flow experiments. No pressure gradients were observed in the u × B direction. A complete correlation of the data is proposed.
Application of Kubo's Modified Theory of Brownian Motion to a Plasma
Authors: Walsh John E.
Published: March 2004

Kubo's modified theory of Brownian motion is used to calculate the friction experienced by a plasma electron. It is found that the spectral decomposition of the average Coulomb interaction is similar in functional form to the Landau damping decrement. It is also shown that when this friction is summed over the large wavenumber region of the spectrum the usual collision frequencies result.
Finite Larmor Radius Effects in Plasmadynamics—Magnetosonic Disturbance
Authors: Kinsinger R. E. , Auer P. L.
Published: March 2004

A disturbance of finite amplitude propagating across an initially uniform axial magnetic field within an initially uniform plasma of infinite extent is considered. The Vlasov equation is solved explicitly to second order in the adiabatic smallness parameter ε = (ωT)−1 = (R/L), with symbols defined in the text. It is shown also that the hierarchy of moment equations resulting from the Vlasov equation may be ordered to yield directly an expansion in powers of ε. The two methods yield equivalent results to second order. The fluid dynamic equations for each plasma species along with Maxwell's equations form a complete set which can be terminated consistently in second order. As an illustration, the dispersion of linearized magnetosonic waves to second order in ε is obtained.
Dispersion of Ion-Acoustic Waves
Authors: Joyce Glenn , Lonngren Karl , Alexeff I. , Jones W. D.
Published: March 2004

The dispersion of ion-acoustic waves in quiescent rare-gas discharge plasmas has been investigated experimentally and theoretically. Experimentally, various grid systems were used to generate the waves which were studied using a time-of-flight technique. The experimental results show that two separate propagating phenomena appear. The slower propagating disturbance is the ion-acoustic wave, obeying the theoretically predicted dispersion behavior. The faster propagating disturbance, though superficially resembling a wave, is composed of bursts of ions produced by the driving potentials placed on the grids and would appear to be related to the “free streaming” term found by Landau. Previous theoretical models of ion-wave propagation have untilized either purely initial-value or steady-state, boundary-value calculations. A model is presented which more nearly simulates the experimental time-of-flight studies of finite packets of ion waves generated by finite sine-wave bursts.
Spatial Growth of Waves in a Beam-Plasma System
Authors: Malmberg J. H. , Wharton C. B.
Published: March 2004

An experiment on spatially growing electron plasma waves in a beam-plasma system is described. The properties of the electron beam and the plasma separately are known from accurate, independent measurements. Using a “test wave” technique, the dispersion of the waves in the presence and absence of the beam and their linear growth rate as a function of frequency were measured. The growth of a spectrum of waves from broad-band noise and the termination of the growth due to nonlinear effects were observed.
Low-Frequency Waves and Instabilities on the Positive Column in a Magnetic Field. III. Experiments on the m = 1 Azimuthal Mode
Authors: Duncan A. J. , Forrest J. R. , Crawford F. W. , Self S. A.
Published: March 2004

In papers I and II of this series [Phys. Fluids 12, 303 and 316 (1969)], a theory describing low-frequency wave propagation along a weakly ionized positive column in a magnetic field, Bz, was developed and studied numerically. Paper III describes experimental verification of the analysis, based on observation of electron waves propagating along a low-pressure mercury-vapor discharge. The theory predicts that for propagation in the direction of the axial electron drift, an azimuthal mode number m ≥ 1, and rotation in the sense of the electron diamagnetic drift, these helical waves should show a transition with increasing Bz from damping to spatial growth. Measurements of the wave dispersion characteristics as a function of Bz are presented for the first two radial modes of m = 1. They show reasonable quantitative agreement with theory. The behavior of the spectrum of self-excited waves, and the dependence of the steady axial electric field on Bz, are interpreted in terms of the linear perturbation theory. It is suggested that, for a low-pressure discharge, instability sets in first for high-order modes, localized near the outer radius, and spreads to low-order modes as Bz is increased.
Drift Mirror Instability in the Magnetosphere
Authors: Hasegawa Akira
Published: March 2004

A new theory of the mirror instability is developed which includes the effects of ∇B and ∇n, finite Larmor radius, and a coexisting cold plasma. It is shown that the instability becomes overstable with a frequency equal to the drift wave frequency, which may be determined by the wave-number that gives the maximum growth rate. The theory is applied to explain the sudden kink in the increase (decrease) of proton flux (magnetic field) and the subsequent oscillations observed during a storm time on 18 April 1965 by detectors on the Explorer 26 satellite.
Electromagnetic Wave Scattering from a Magnetically Confined High-Temperature Plasma
Authors: Nee S. F. , Pechacek R. E. , Trivelpiece A. W.
Published: March 2004

Electromagnetic wave scattering from a charged particle confined to a circular orbit is studied for cases where relativistic corrections must be included in the analysis to obtain a valid description for the spatial and spectral distribution of scattered radiation. The results are compared with the scattering calculated on the basis of a two-dimensional isotropic distribution of straight-line orbits. It is shown that the two calculations produce the same spectrum of scattered radiation provided the fact that the scattering region is finite in the direction of the observer is included in the analysis.
Scalar Radiative Transport Model for Microwave Scattering from a Turbulent Plasma
Authors: Feinstein David L. , Granatstein Victor L.
Published: March 2004

The scalar radiative transport equation is solved in an interative manner for the backscattered reflected intensity. A model for the direct and cross-polarized cross section is derived in terms of the first two terms of the iterated series. Model calculations agree to good approximation with an experiment where microwaves are scattered from a turbulent plasma column. At very low plasma density fluctuations (less than 0.01 of the critical plasma density) a single scatter regime exists where the direct cross section is proportional to the square of the plasma density fluctuations and the cross-polarized cross section is much less than the direct cross section. As the fluctuations increase, this single scatter regime is followed by a regime where multiple scattering makes a significant contribution to the backscattered signal; here, the magnitude of the cross-polarized cross section is approximately 0.1 of the magnitude of the direct cross section. Finally, when the plasma density fluctuations are about 0.1 of the critical plasma density, the wave is strongly attenuated by scattering and the cross sections saturate as a function of the plasma density fluctuations. The model also predicts the observed variation of the cross section with angle of incidence. Suggestions for future work are made.
Study of the Influence of a Grid on the Plasma in a Single-Ended Q-Machine
Authors: Andersen S. A. , Jensen V. O. , Nielsen P.
Published: March 2004

The mechanism of the interaction between a biased grid and the plasma in a “single-ended” Q-machine was studied experimentally. It was found that the grid reflects some of the ions in the plasma flow. The number and velocity distribution of the reflected ions depend on the bias of the grid, on the plasma density, and on the distance between the grid wires. The reflected ions move as freely streaming particles except at high densities, where binary collisions are of importance. A small sinusoidal voltage applied to the biased grid excites an upstream wave with dispersion properties that can be explained as phase mixing of freely streaming particles reflected by the grid.
Measurements of Large Disturbances in Laminar Pipe Flow Using a Laser-Doppler Flowmeter
Authors: Hanson Wayne A. , Jankowski Daniel F. , Berman Neil S.
Published: March 2004

Large axisymmetric disturbances were generated in a pipe using a sleeve oscillating at the wall. Downstream decay of the fluctuating velocities measured by a laser-Doppler velocimeter show slower rates of decay than for small disturbances.
Significance of the Soret Effect in the Rayleigh-Jeffreys' Problem
Authors: Hurle D. T. J. , Jakeman E.
Published: March 2004

Overstable solutions of the thermosolutal Rayleigh-Jeffreys' problem can occur for concentration gradients in liquids which are so small that they could be generated by the Soret effect, even in nominally pure liquids.
Radiative Transfer in a Moving Fluid
Authors: Pomraning G. C.
Published: March 2004

It is shown that an equation of transfer due to Fraser can be simplified. This equation describes photon transport, including the effects of scattering from a Maxwellian gas of electrons, in a moving fluid.
Magnetic Guarding of Supports
Authors: Lehnert B.
Published: March 2004

It is shown that so far there is no experimental proof that magnetic guarding is ineffective, contrary to conclusions drawn from a strongly restricted plane model.
Series Developments and Finite-Difference Calculations in the Laminar Boundary Layer
Authors: Frössling Nils
Published: March 2004

Work concerning the calculation of laminar boundary layers has been carried out utilizing high-speed computers. The velocity and the temperature in the boundary layers have been calculated with generalized Blasius series and with finite-difference methods. The series are applicable for the very general outer velocity distribution U = xm(u0 + u1xn + u2x2n + . . .), where m, n, and ui are arbitrary constants. Universal functions for the velocity and the temperature are derived and calculated once and for all.
Viscous Mixing of Incompressible Fluids in the Boundary-Layer Approximation
Authors: Koryavov P. P. , Pavlovsky Yu. N.
Published: March 2004

Group analysis is applied to the equations of the incompressible viscous fluid flow in a narrow mixing region. It is shown that the solution of the problem depends on one parameter when the pressure is constant in the mixing region and on two parameters when the pressure changes along the flow. For some values of these parameters classical solutions, such as jet flow and wake flow are obtained; for others, nonclassical solutions also having a definite physical meaning are obtained, such as the expanding jet flow, mixing of two flows with parabolic profiles, the flow in the plane channel with curved walls, and with injection through the walls, and some others.
Computing Problems in Nonlinear Hydrodynamic Stability
Authors: DiPrima R. C. , Rogers E. H.
Published: March 2004

Questions arising in nonlinear hydrodynamic stability such as the calculation of an equilibrium flow field when the basic flow is unstable, wavenumber selection, and successive instabilities are considered for the classical problem of flow between concentric rotating cylinders. Recent numerical and analytical work dealing with calculation of the Taylor vortex of a given axial wavelength, the selection of the axial wavelength, the subsequent breakdown of the Taylor-vortex flow to wavy-vortex flow, and the calculation of the wavy-vortex flow is reviewed. Some of the open questions, possible methods of solving them, and the order of magnitude of the required calculations are discussed.
Numerical Study of the Collapse of a Perturbation in an Infinite Density Stratified Fluid
Authors: Wessel W. Roy
Published: March 2004

The problem of finding the time-dependent flow resulting from perturbing a small quantity of fluid in an infinite two-dimensional fluid having a vertical density stratification is discussed. Since nonturbulent flow in an incompressible fluid is well described by the Navier-Stokes equations in the Boussinesq approximation, these partial differential equations were approximated by an appropriate set of finite difference equations which were then solved numerically on a computer for a number of physically interesting cases. The equations to be solved and the algorithm to solve them are described and a comparison is made between the computational results and some experimental results. A collapsing perturbation is an efficient generator of internal waves, and these are clearly depicted in film images produced directly by the computer. Physical experiments with collapsing mixed regions in a fluid with linear density stratification have revealed distinctive patterns of internal wave propagation and flow of the mixed fluid; patterns that are accurately duplicated in corresponding numerical computations that are discussed.
Numerical Model for Wind-Driven Circulation of the Oceans of the World
Authors: Sag T. W.
Published: March 2004

A two-dimensional linear steady-state model of the ocean circulation of the world which includes the effects of the rotation of the earth, lateral and bottom friction, and a steady-state wind stress is considered. The two-dimensional equations of motion for mass transports are obtained by integration of the equations of motion with respect of depth and linearization. A stream function ψ for the mass transports is then introduced and a fourth-order partial differential equation for ψ is obtained. The boundary conditions ψ = const.and ∂ψ/∂n = 0 are implemented at the land-sea boundaries of the model, which correspond closely to actual boundaries except that small isolated islands are omitted and larger islands such as Australia are joined to the mainland. The numerical solution of the partial differential equation is achieved by approximating it by finite difference equations on the Mercator projection of the earth, and solving these equations by a combination of iterative and direct techniques. The finite difference equations involve values of ψ at certain land grid points near the boundaries, and at each stage of the iteration, values of ψ are assigned to these points in such a way that the boundary conditions are satisfied for the current approximation to ψ The results so far produced qualitatively agree very well with the known patterns of ocean circulation. Western boundary currents such as the Gulf Stream are prominent and smaller circulations such as the eddies off the coast of Antarctica are also present.
Numerical Solution of the Elliptic Equations for Transport of Vorticity, Heat, and Matter in Two-Dimensional Flow
Authors: Runchal A. K. , Spalding D. B. , Wolfshtein M.
Published: March 2004

A finite-difference method is presented for the solution of the elliptic differential equations for the steady transport of momentum, heat, and matter in two-dimensional domains. Special features of the method include an unsymmetrical formulation for the convection terms, which promotes convergence at some cost in accuracy; obedience to the conservation equations for all subdomains; the use of Gauss-Seidel iteration procedure; employment of grids having nonuniform mesh; and a novel treatment of the boundary condition for vorticity. Solutions are presented for the laminar flow and heat transfer inside a square cavity with a moving top, an impinging jet, and a Couette flow with mass transfer. The influence of the Reynolds and Prandtl numbers, and of the impinging jet “free” boundary conditions is studied, and the results of the computations are shown to agree with existing physical knowledge. The influence of mesh size, mesh nonuniformity, and the vorticity wall boundary condition on convergence and accuracy is studied. It is shown that convergence may be secured for a wide range of Reynolds numbers with coarse-meshed grids. The convergence and computation speed appear to be satisfactory for many purposes; the accuracy of the solutions is discussed, and some improvements are suggested.
Time Dependence of Thermal Convection in a Bounded Rotating System
Authors: Quon C.
Published: March 2004

The time dependence of the velocity and the temperature field of an axisymmetric state in a rotating annulus where convection is a dominant mechanism for heat transfer is studied numerically. The development of the various terms in the momentum and heat equations is followed through time until steady state is achieved. Inertial oscillations dominate the interior motion at the initial stage. Sixteen revolutions of the annulus are necessary for the system studied here to attain the quasisteady state. It is found that both heat and momentum diffusion are important in the interior, even though convection dominates the heat flow in the boundary layers.
Computer Studies of Time-Dependent Turbulent Flows
Authors: Hirt C. W.
Published: March 2004

Two aspects of turbulence can be studied with existing computer technology. One of these is the study of the initial stages in the breakdown of a laminar flow into turbulence. The other is the study of the gross effects of turbulence on a mean flow. The laminar instability problem is hampered by difficulties in calculating high Reynolds number flows, because finite difference approximations introduce diffusionlike truncation errors that can obscure the effects of a real viscosity. These errors also influence the computational stability of numerical solutions. If only the mean effects of turbulence on a flow are of interest, the difficulties in calculating high Reynolds number flows can usually be avoided, because the effective turbulent viscosity is often larger than the molecular viscosity and is not as likely to be obscured by finite difference errors. A method of this type is presented, in which the turbulence is characterized by three field variables: a turbulence energy density, a turbulence viscosity, and a turbulence scale of size. These variables satisfy transport equations describing convection, creation, diffusion, and decay processes. Since these equations are highly nonlinear, numerical solutions are necessary to extract their full potential.
Computation of the Energy Spectrum in Homogeneous Two-Dimensional Turbulence
Authors: Batchelor G. K.
Published: March 2004

Two-dimensional and three-dimensional turbulence have different properties, but both contain the two basic ingredients of randomness and convective nonlinearity, and some of the statistical hypotheses which have been proposed for three-dimensional turbulence should be applicable to two-dimensional motion. This justifies a numerical integration of the unaveraged equations of motion in two dimensions with random initial conditions as a means of testing the soundness of ideas such as those leading to the Kolmogoroff equilibrium theory. In spatially homogeneous two-dimensional turbulence, the mean-square vorticity is unaffected by convection and can only decrease under the action of viscosity. Consequently the rate of dissipation of energy tends to zero with the viscosity (v). On the other hand, the mean-square vorticity gradient is increased by convective mixing, and it seems likely that the rate of decrease of mean-square vorticity tends to a nonzero limit κ as ν → 0. This suggests the existence of a “cascade” of mean-square vorticity at large Reynolds number, and an “equilibrium range” in the vorticity spectrum determined by the parameters κ and ν alone to which familiar dimensional arguments can be applied. Also, the energy and vorticity-containing components presumably settle down to an approximate similarity state determined by the total energy alone. A numerical integration of the equation of motion to test such similarity relations was attempted at Cambridge some years ago by R. W. Bray. The velocity distribution was represented by spectral lines at vector wavenumbers of the form (p,q), where p and q are integers and (p2 + q2)1/2 < 10, and the integration was carried out to times at which an appreciable amount of vorticity had been transferred to the larger wavenumbers. The results obtained with the rather small computing machine available at the time were not decisive, but they were consistent with the development of the expected k−1 form of the vorticity spectrum.
Numerical Methods for the Simulation of Turbulence
Authors: Orszag Steven A.
Published: March 2004

Two schemes for the numerical solution of the Navier-Stokes equations at moderate Reynolds number are discussed. The essential ingredient of the present methods is the use of the fast Fourier transform. In one scheme, discrete Fourier transformation is used to compute the convolution sums appearing in the formally Fourier-transformed Navier-Stokes equations. This results in an aliasing-free, energetically conservative (when ν = 0) scheme that can be used convincingly as a model on which to test turbulence theories. The second scheme calculates in real space. Fast Fourier transform is used to solve Poisson's equation for the pressure. The latter scheme offers the advantages of speed and flexibility. The schemes are critically compared and a survey of applications is made.
Nonlinear Wave Expansion for Turbulence in the Burgers' Model of a Fluid
Authors: Tatsumi Tomomasa
Published: March 2004

A new scheme of expansion of the turbulent velocity field is proposed and applied to the Burgers' one-dimensional model turbulence. The velocity field of the Burgers' turbulence is expanded into a series of nonlinear waves of sawtooth profile, each of which is an asymptotic solution of the Burgers' equation for extremely large Reynolds numbers R. The effect of the interaction between waves of different wavenumbers k is estimated approximately, and the possible form of the energy distribution of nonlinear waves G(k∥ is determined. The energy spectrum E(k), the velocity correlation, and the energy decay law are calculated numerically adopting a particular distribution of G(k). The spectrum has the asymptotic tail E(k) ∝k−2 for k → ∞ reflecting the discontinuous structure of the turbulent field at infinite R. The energy decays in time inversely proportional to the square of the time. Theoretical results are compared with results due to the numerical experiment of Jeng and others, and the agreement appears to be excellent.
Practical Investigation of Convective Difference Approximations of Reduced Dispersion
Authors: Fromm J. E.
Published: March 2004

A survey of commonly used approximations to the Eulerian form of the equations of ideal fluid flow is given. Comparisons are made through amplitude and phase properties as determined by linear stability analysis. The unacceptable amplitude damping of first-order approximations is reiterated. For second-order approximations the discussion emphasizes numerical dispersion effects and shows that the familiar stable forms do not differ significantly in relative merit. Fourth-order improvements are discussed with reference to further extensions which minimize dispersion. Conservative forms of the approximations are given along with experimentally determined properties regarding their nonlinear behavior in fluid-dynamic calculations. Comments relating to fluid-dynamic instability versus numerical instability are included.
Criterion for Filtering Parasite Solutions in Numerical Computations
Authors: Zeytounian R. Kh.
Published: March 2004

Fluid dynamics problems often involve boundary conditions at infinity. In the case of numerical computation the most serious difficulty arises from the practical impossibility of reaching such conditions. It is then necessary to transform the problem either into a Cauchy problem, or into a boundary-value problem within a limited domain. Generally, this process entails the regrettable consequence of bringing up as parasites in the solution some of the eigenfunctions pertaining to the equation. A method is proposed to filter these parasite solutions; its principle is the introduction of a certain functional controlling the error due to the parasite solutions, in a given domain. The method is illustrated by some numerical results concerning the computation of a flow downstream of an obstacle within a gravitational field.
Steady Two-Dimensional Viscous Flow of an Incompressible Fluid past a Circular Cylinder
Authors: Takami Hideo , Keller Herbert B.
Published: March 2004

Numerical solutions of the steady Navier-Stokes equations are presented for two-dimensional flows past a circular cylinder in an infinite domain. The flow is assumed to be uniform at infinity upstream and the range of Reynolds numbers extends from 1 to 60. The Navier-Stokes equations are replaced by a set of finite difference equations and the numerical solution is obtained by means of an iteration method. Conditions at “infinity” are applied by matching to Imai's asymptotic solution. The results are compared with those of other analytical and numerical computations as well as with experiments. In particular, the discussion is concerned with the drag, the base pressure, the shape of the standing vortices, and some formulas suggested for large Reynolds numbers. Excellent agreement with recent experiments of Acrivos, Leal, Snowden, and Pan is obtained.
Numerical Studies of a Viscous Liquid past a Circular Cylinder
Authors: Takaisi Yorisaburo
Published: March 2004

In the study of the steady two-dimensional flows past a circular cylinder in an infinite extent, the two sets of boundary conditions at infinity for the perturbed stream function and the vorticity, which are generally used, are examined numerically on the basis of Navier-Stokes equations. It is confirmed that, for sufficiently small Reynolds number, if points far enough from the cylinder are taken as inner mesh points, then the boundary conditions have little influence on the results, and the drag coefficients approach the values calculated by Imai's formula rather than those calculated based on Oseen's theory.
Numerical Integration of the Navier-Stokes Equations for Steady Two-Dimensional Flow
Authors: Dennis S. C. R. , Chang Gau-Zu
Published: March 2004

A summary is given of a numerical method of solving steady-flow problems for the symmetrical motion of a viscous fluid past a fixed cylinder in two dimensions. The stream function and vorticity are used as dependent variables. Two features which have not previously been mentioned are considered. The first is concerned with the convergence of the iterative procedure which is used to obtain successive approximations to the stream function and vorticity. The second is the method of approximating the equation which governs the vorticity by finite-difference schemes. The latter is discussed in the light of recent suggestions that approximations whose accuracy is demonstrably lower than that of the usual central-difference scheme should be used in order to secure a matrix which is diagonally dominant. It is shown that the diagonally dominant system can be used while still retaining the higher accuracy of central differences. The results of some illustrative calculations are given for flow past a finite flat plate for Reynolds numbers up to 200, and for flow past elliptic cylinders of various ratios of major to minor axes at Reynolds number 40.
Steady, Viscous Flow within a Circular Boundary
Authors: Kuwahara Kunio , Imai Isao
Published: March 2004

The steady two-dimensional flow of a viscous incompressible fluid within a circular vessel with prescribed wall velocity is studied both analytically and numerically in order to see how the flow pattern varies with the Reynolds number R. First, an algorithm to determine the Stokes' type successive approximation for any stage of approximation from the preceding one, when the wall velocity is given as a Fourier series, is established and carried out on a digital computer to the eighth approximation (correct to R8). Second, a finite-difference method is applied to solve the Navier-Stokes' equation numerically. Three typical cases of flow pattern are treated: flow without separation, flow consisting of two symmetric recirculating regions of semicircular form, and flow consisting of two unsymmetrical recirculating regions. It is found that the Stokes' type successive approximation is convergent for R below 32. It is also found that for larger Reynolds number the flow pattern agrees well with Batchelor's uniform vorticity model.