bluuebunny/crossref_metadata_2025 huggingface dataset:
Fibonacci graphs possessing identical matching polynomials
Authors: El-Basil Sherif , Kr̆ivka Pavel , Trinajstić Nenad
Published: July 2002

A sequence of Fibonacci graphs is defined. A special case of Fibonacci graphs, i.e., those with identical matching polynomials, is discussed and conditions under which they appear are given. The appearance of Fibonacci graphs with identical matching polynomials may have some implications in statistical physics.
Charged perfect fluid in rigid rotation
Authors: Chakraborty S. K. , Bandyopadhyaya N.
Published: July 2002

This paper is a continuation of the work of Bonnor and Raychaudhuri on a charged dust distribution in rigid rotation in general relativity. Here the authors are concerned with the similar problem of a charged perfect fluid with nonvanishing pressure. As in Raychaudhuri’s work, symmetry-independent reduction of Einstein–Maxwell equations is undertaken. Certain assumptions in Raychaudhuri’s paper regarding the inheritance by the electromagnetic field of the symmetry resulting from the rigidity of the motion are justified.
Scalar formalism for quantum electrodynamics
Authors: Hostler Levere C.
Published: July 2002

A set of Feynman rules, similar to the rules of scalar electrodynamics, is derived for a full quantum electrodynamics based on the relativistic Klein–Gordon–type wave equation {ΠμΠμ+m2+ie σ ⋅ (𝒞 +iB)}φ =0, Πμ ≡−i ∂μ−eAμ, for spin- 1/2 particles [J. Math. Phys. 23, 1179 (1982); J. Math. Phys. 24, 2366 (1983)]. In this equation, φ is a 2×1 Pauli spinor and σa, a=1,2,3, are the usual 2×2 Pauli spin matrices. The irreducible self-energy parts are compared to those of conventional quantum electrodynamics.
The most general magnetized Kerr–Newman metric
Authors: Bretón Baez Nora , García Díaz Alberto
Published: July 2002

The complete magnetic generalization of the Kerr–Newman (KN) metric obtainable by applying a Harrison transformation to the Ernst potentials determined for an arbitrary linear combination of the two Killing vectors of the seed KN metric is derived.
Imparting rotation to a Bianchi type II space-time
Authors: Rebouças M. J. , d’Olival J. B. S.
Published: July 2002

A generalization of Batakis’s procedure for imparting vorticity to a Bianchi type II space-time is considered. A Bianchi type II rotating model is presented. The limiting case of zero rotation is a known vacuum solution.
Renormalization schemes and renormalization group functions in Yang–Mills theories with massive fermions
Authors: Caprasse H. , Hans M.
Published: July 2002

The connection between renormalization schemes (RS’s) and the renormalization group (RG) functions for a massive Yang–Mills theory is investigated. The RS’s are defined in a manner independent of the regularization procedure. The RS transformations are defined in such a way that it is clear that they form a group. It is shown that to a given set of RG functions corresponds an infinite number of RS’s. The subgroup of RS transformations which leave invariant the (mass-shell) MS-RG functions is carefully described. Gauge invariance, regularity of the theory when m→0 and mass decoupling are imposed and the corresponding indeterminations of RS’s are given. It is seen that a RS which fulfills simultaneously the above conditions does not exist.
The Vaidya–Patel solution with Robertson–Walker metric as a rotating inflationary scenario
Authors: Grön Öyvind , Soleng Harald H.
Published: July 2002

The Vaidya–Patel solution of a rotating homogeneous fluid in the presence of a Maxwellian source-free electromagnetic field is interpretated as an inflationary scenario with a gauge field with local U(1) symmetry, a vacuum energy, and a rotating perfect fluid. An explicit solution is found to be expressible in terms of known solutions representing the radiation filled Robertson–Walker universe with a cosmological term. In the case that the rotating fluid is radiation, the discussion of the model is considerably simplified. How the time scale of transition into a pseudo-de Sitter stage, as observed by an observer following the rotating fluid, is affected by vorticity is also studied.
Some results from a Mellin transform expansion for the heat kernel
Authors: Malbouisson A. P. C. , Simão F. R. A. , Ferraz de Camargo Fo. A.
Published: July 2002

In the case of a differential operator containing a gauge field, coefficients of a new heat kernel expansion obtained in a preceding paper (A. P. C. Malbouisson, M. A. R. Monteiro, and F. R. A. Simão, CBPF-NF-024/88, to be published in J. Math. Phys.) are calculated. The prior expansion allows it to be shown that the meromorphic structure of the generalized zeta function is much richer than was known previously. Also, an application to anomalies is done, resulting in a general formula for the arbitrary dimension D. The special cases D=2 and D=3 are investigated.
Covariant quantization of gauge theories in the framework of extended BRST symmetry
Authors: Batalin I. A. , Lavrov P. M. , Tyutin I. V.
Published: July 2002

The quantization rules for gauge theories in the Lagrangian formalism are formulated on the basis of the requirement of an extended BRST symmetry. The independence of the S matrix to the choice of a gauge is proved. The Ward identities are derived, and the existence theorem for the solutions of the generating equations within the given formalism is proved. Rank 1 gauge theories are considered as an example.
Noncommutative geometry, chiral anomaly in the quantum projective [sl(2,C)-invariant] field theory and jl(2,C)-invariance
Authors: Juriev Denis
Published: July 2002

The quantum projective [sl(2,C)-invariant] field theories with chiral anomaly [with noncommuting holomorphic and antiholomorphic sl(2,C)-symmetries] are considered. The underlying noncommutative geometry is described. It is shown that such theories are invariant with respect to the BL (Borel–Lie) algebra jl(2,C), the central extension of the double sl(2,C)+sl(2,C). The jl(2,C)-invariant quantum projective field theories are classified: it is proved that the jl(2,C)-primary fields are characterized by their weights (λ,μ̄), the corresponding fusion rules are trivial [Vλ,μ̄][Vλ′,μ̄′]= [Vλ+λ′,μ̄+μ̄′] (though the primary fields are not mutually local) and so the category of the jl(2,C)-invariant quantum projective field theories’ (QPFT)-operator algebras is isomorphic to the category of R2-graded associative algebras. The explicit form of the jl(2,C)-primary fields is found.
Existence and uniqueness of the universal W algebra
Authors: Figueroa-O’Farrill José M. , Ramos Eduardo
Published: July 2002

A precise definition of the universal (classical) W algebra for the Wn series is given and its existence and uniqueness are proved. The main observation is that there is a natural reduction from Wn to Wn−1 that allows us to define the universal W algebra as an inverse limit. This universal W algebra is, in a sense, the smallest W algebra from which all Wn can be obtained by reduction. These results extend to other W algebras obtained by reducing the Gel’fand–Dickey brackets, as well as to W superalgebras obtained from the supersymmetric Gel’fand–Dickey brackets.
U(2) as the electroweak gauge group
Authors: LaChapelle J.
Published: July 2002

Using the fiber bundle formalism, the consequences of taking U(2) instead of SU(2)×U(1) as the electroweak gauge group are studied. This choice motivates using electric charge as the defining characteristic of particles: isospin and hypercharge quantum numbers are not assigned to particles. This in turn leads to a definition of matter fields in which quarks and leptons transform by the same U(2) representation; the representation being determined by electric charge quantum numbers only. As a result, all matter fields have equivalent coupling constants. Indeed, in this model, quarks have integer charge. Nevertheless, the quark and lepton currents as well as the gauge boson mass ratio are identical with the Standard Model predictions.
Dyonic black holes in dilaton gravity
Authors: Cheng Guang-Jiun , Lin Wei-Fu , Hsu Rue-Ron
Published: July 2002

An exact solution of the low-energy string theory representing static, spherical symmetric dyonic black holes is found. The solution is labeled by their mass, electric charge, magnetic charge, and asymptotic value of the scalar dilaton. Some interesting properties of the dyonic black holes are studied.
Multifold Kepler systems—Dynamical systems all of whose bounded trajectories are closed
Authors: Iwai Toshihiro , Katayama Noriaki
Published: July 2002

According to the Bertrand theorem, the Kepler problem and the harmonic oscillator are the only central force dynamical systems that have closed orbits for all bounded motions. In this article, an infinite number of dynamical systems having such a closed orbit property are found on T*(R3−{0}) by applying a slightly modified Bertrand’s method to a spherical symmetric Hamiltonian with two undetermined functions of the radius. Actually, for any positive rational number ν, there exists a Hamiltonian system with the closed orbit property just mentioned, which system will be called the ν-fold Kepler system. Each of the systems is completely integrable and further allows the explicit expression of trajectories. The bounded trajectories in the configuration space R3−{0} may have self-intersection points. Moreover, the ν-fold Kepler system is reducible to a two-degrees-of-freedom system, which is completely integrable and gives rise to flows on the two-torus for bounded motions. If ν is allowed to take irrational numbers, any flow is shown to be dense in the torus. In conclusion, on the analogy of the Kepler problem, the Runge–Lenz-like vector for the ν-fold Kepler system is touched upon.
Affine projection-tensor geometry: Lie derivatives and isometries
Authors: Gowdy Robert H.
Published: July 2002

The generalized projection-tensor geometry introduced in an earlier article is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous article and obtain fully projected decompositions of Lie derivatives of the projection-tensor field, the metric, and the projected parts of the metric. These results are applied to the analysis of space–times with isometries. The familiar cases of space–times with isotropic group orbits—cosmological models and spherical symmetry—are discussed as illustrations of the results.
Determinants of Laplacians, the Ray–Singer torsion on lens spaces and the Riemann zeta function
Authors: Nash Charles , O’Connor Denjoe
Published: July 2002

Explicit expressions are obtained for the determinants of the Laplacians on zero- and one-forms for an infinite class of three dimensional lens spaces L(p,q). These expressions can be combined to obtain the Ray–Singer torsion of these lens spaces. As a consequence an infinite class of formulas is obtained for the Riemann zeta function ζ(3). The value of these determinants (and the torsion) grows as the size of the fundamental group of the lens space increases and this is also computed. The triviality of the torsion for just the three lens spaces L(6,1), L(10,3), and L(12,5) is also noted.
Axially symmetric solutions for SU(2) Yang–Mills theory
Authors: Singleton D.
Published: July 2002

By casting the Yang–Mills–Higgs equations of an SU(2) theory in the form of the Ernst equations of general relativity, it is shown how the known exact solutions of general relativity can be used to give similar solutions for Yang–Mills theory. Thus all the known exact solutions of general relativity with axial symmetry (e.g., the Kerr metric, the Tomimatsu–Sato metric) have Yang–Mills equivalents. In this paper we only examine in detail the Kerr-like solution. It will be seen that this solution has surfaces where the gauge and scalar fields become infinite, which correspond to the infinite redshift surfaces of the normal Kerr solution. Unlike the Kerr solution, our solution apparently does not have any intrinsic angular momentum, but rather appears to give the non-Abelian field configuration associated with concentric shells of color charge. Several possible physical consequences of these axial symmetric Yang–Mills field configurations are discussed.
Spectral transform and solitons for the three-wave coupling model with nontrivial boundary conditions
Authors: Doktorov E. V.
Published: July 2002

A nonlinear three-wave coupling model with nontrivial boundary conditions is analyzed in the framework of the inverse spectral transform. Spectral data are determined and their evolution is derived. It is shown that there exists mutual cancellation of divergences of the scattering matrix elements in branching points on the plane of a spectral parameter. A regular dark-soliton-type solution is obtained.
A new Hamilton operator for a massive relativistic particle with spin one in a generalized Heisenberg/Schrödinger picture
Authors: Frick Rudolf A.
Published: July 2002

We consider a particular four-dimensional generalization of the transition from the Heisenberg to the Schrödinger picture. The space–time independent expansion with respect to the unitary irreducible representations of the Lorentz group is applied, as Fourier transformation in the Heisenberg picture, to the states of a massive relativistic particle. A new Hamilton operator has been found for such a particle with spin one.
Maximal sign-invariants of quasilinear parabolic equations with gradient diffusivity
Authors: Galaktionov Victor A. , Posashkov Sergey A.
Published: July 2002

We consider quasilinear parabolic equations with gradient diffusivity ut=div(|∇u|σ∇u)+f(u), x∈RN, t>0, where σ≠−1 is a fixed constant and f(u) is a given smooth function. We also study quasilinear parabolic equations with a gradient-dependent coefficient ut=h(|∇u|)Δu+f(u), with a smooth function h(p). For both classes of equations we derive first-order sign-invariants, i.e., first-order operators preserving their signs on the evolution orbits {u(⋅,t),t>0}. We give a complete description of (maximal) sign-invariants of prescribed structures. As a consequence, we construct new exact solutions of some quasilinear equations.
Information gain within nonextensive thermostatistics
Authors: Borland Lisa , Plastino Angel R. , Tsallis Constantino
Published: July 2002

We discuss the information theoretical foundations of the Kullback information gain, recently generalized within a nonextensive thermostatistical formalism. General properties are studied and, in particular, a consistent test for measuring the degree of correlation between random variables is proposed. In addition, minimum entropy distributions are discussed and the H-theorem is proved within the generalized context.
On Verma bases for representations of sl(n,C)
Authors: Raghavan K. N. , Sankaran P.
Published: July 2002

Conjectural bases for irreducible representation spaces of simple Lie algebras, due to Verma, have been described by Li, Moody, Nicolescu, and Patera. In this paper the basis conjecture for the algebras of type An is established.
Probability amplitude dynamics for a two-level system
Authors: Boyd John K.
Published: July 2002

The time-dependent probability amplitudes are determined for a two-level system without invoking the rotating wave approximation. A new analytic solution is obtained in the limit of small ratio of Rabi frequency to driver frequency. An analytic solution is also obtained in the limit of large ratio of Rabi frequency to driver frequency for a restricted range of parameters. The form of this solution guides the selection of parameters that cause substantial changes in the character of the solution. The dependence on parameter values is studied numerically for the transition probability and the coherent spectrum.
Low-temperature acoustic characteristics of the amorphous alloy Zr41.2Ti13.8Cu12.5Ni10Be22.5
Authors: Gaiduk A. L. , Bezuglyi E. V. , Fil V. D. , Johnson W. L.
Published: July 2002

The temperature dependences of the sound velocity v and attenuation α of high-frequency (50–160 MHz) sound in the bulk amorphous alloy Zr41.2Ti13.8Cu12.5Ni10Be22.5 are studied at helium temperatures in the normal and superconducting states. The alloy is characterized by a relatively small constant C determining the intensity of interaction between an elastic wave and two-level systems. The density of states of the latter systems is estimated. The peculiarities in the variation of v during the superconducting transition point to the possibility of a gapless superconductivity in a narrow temperature interval near Tc.
Dynamics of inviscid truncated model of two-dimensional turbulent shear flow
Authors: Kaneda Yukio , Gotoh Toshiyuki , Bekki Naoaki
Published: July 2002

The method of classical statistical mechanics is applied to an inviscid truncated model system of two-dimensional turbulent shear flow. The idea of canonical equilibrium distribution is extended to treat a time-dependent Liouville equation governing the evolution of probability distribution function in the phase space. Results of numerical simulations supporting the theoretical conjectures based on the canonical distribution are shown.
Wall vortex induced by and moving with a confined vortex pair
Authors: Yamada Hideo , Honda Yuhichi
Published: July 2002

A wall vortex was found, which was induced by, and moved together with, a confined vortex pair, near the parallel plates between which the confined vortex pair was traveling. The generation of the wall vortex can be attributed to the boundary layer separation that was caused by the characteristic flow field of the vortex pair itself.
Large-eddy simulations of excitation effects on a VTOL upwash fountain
Authors: Rizk Magdi H. , Menon Suresh
Published: July 2002

The responses of an upwash fountain to various azimuthal and axisymmetric excitations, applied at the exits of its neighboring jets, are investigated. Kinematic arguments are used to determine the interactions of large-scale structures in the fountain and the effects of these interactions on the fountain’s characteristics. Numerical simulations of a row of impinging jets, which contain the essential features of twin jets impinging on the ground, are used to simulate the hovering configuration of a vertical takeoff and landing (VTOL) aircraft. The flow is assumed to be governed by the time-dependent, incompressible Navier–Stokes equations. The large-eddy simulation approach is followed. Distinct fountain characteristics are shared among the cases in which azimuthal perturbations are applied at both jet exits in the same direction. These include a high fountain spreading rate, a strong lateral interaction with the neighboring jets, and a weak upload at the aircraft’s undersurface. A strong similarity in fountain characteristics also exists for the cases of axisymmetric forcing and azimuthal forcing in opposite directions at the two jet exits. The similar characteristics here include a low fountain spreading rate and a strong upload at the aircraft’s undersurface.
Irregular reflections of weak shock waves in polyatomic gases
Authors: Honma Hiroki , Henderson L. F.
Published: July 2002

In this paper experiments with weak shocks in carbon dioxide are described. The incident shocks were arranged to reflect off the sloping surfaces of rigid ramps of various corner angles. Regular and Mach reflectionlike phenomena were observed, but because the incident shocks were so weak, all the waves in the reflecting systems showed evidence of either partial or complete dispersion. Consequently, the wave systems were different from the classical perfect gas theory systems described by the von Neumann theory. These wave systems were named ‘‘dispersed irregular reflections.’’
Convective regimes in reactive fluid media due to the interaction with catalytic surfaces
Authors: Viljoen Hendrik J. , Gatica Jorge E. , Hlavacek Vladimir
Published: July 2002

Reactive fluid media enclosed in a cavity with a catalytic surface are analyzed. Nonisothermal chemical reactions on this surface can lead to convective instabilities. A simplified model is developed by using a low-order truncation of a Fourier-type expansion and employing the Galerkin method. A linear stability analysis is presented and it is shown that, under certain conditions, the marginal curve for the onset of oscillatory instabilities can lie below that for monotonic ones. The stability of the convective modes is studied by nonlinear stability analysis and it is shown how they can evolve into periodic and nonperiodic motion patterns. Numerical results are provided to support and confirm analytical predictions.
Eckhaus instabilities in generalized Landau–Ginzburg equations
Authors: Riley David S. , Davis Stephen H.
Published: July 2002

The effect of Eckhaus instabilities is shown to be mitigated by an increase in order of a Landau–Ginzburg equation.
Soret-driven convection coupled to the morphology of a solid–liquid interface
Authors: Hadji Layachi , Schell Mark
Published: July 2002

The importance of Soret-driven convection in solidification processes is illustrated through an analysis of the coupling between convective currents and the deformations in a solid–liquid interface. The interface appears on freezing an upper portion of a layer of a dilute binary fluid. The presence of the interface and the amount of the solid strongly affect the stability properties of the liquid mixture and, in turn, the state of the liquid determines the patterns formed on the interface. Marginal stability curves are constructed by plotting the critical Rayleigh number and the critical wave number against the thickness of the solid layer. At small values of a positive separation ratio, increases in the thickness of the solid layer are found to have a destabilizing effect, the static state becomes unstable at smaller values of the Rayleigh number, whereas at larger values for the separation ratio this effect disappears. As the separation ratio is increased, a change of slope at zero thickness in the solid layer, from negative to positive, occurs in the plots of the critical wave number. For the case of a sufficiently large separation ratio, a weakly nonlinear analysis leads to the prediction of a bifurcation diagram that is characterized by two regions of bistability. A stable stationary convective structure consisting of down-hexagons appears through a subcritical bifurcation and for a small range of Rayleigh numbers coexists with the static state. Squares become stable at higher Rayleigh numbers and for a small parameter range coexist with down-hexagons. These stationary structures, down-hexagons and squares, are imprinted as patterns on the solid–liquid interface through the action of the convective currents. It is deduced that down-hexagons appear as a result of the coupling of the convective motion in the melt with the deformations in the interface and do not occur in the absence of solidification.
Time-resolved flow field in a rectangular chamber containing a sinusoidally oscillating piston
Authors: Kurzweg U. H. , Zhao A. X.
Published: July 2002

The periodic laminar flow of an incompressible fluid existing within a rectangular chamber when one of the walls is oscillated sinusoidally, and, where fluid can enter and leave the chamber through a small orifice in the stationary wall opposite to the oscillating surface, is examined numerically using a newly developed iterative algorithm (SIMPLE-TP) valid for incompressible and time-periodic flows. Results indicate the presence of a high-velocity jet emanating from the orifice during that portion of the oscillation cycle when the wall recedes from the orifice and also show the presence of at least one counter-rotating vortex pair during all parts of the oscillation cycle.
Optimal large eddy simulation in one dimension
Authors: Humi Mayer
Published: July 2002

How the optimal choice of the filter function in large eddy simulations is related to the spectrum of the turbulent flow is shown. A new formula for the subgrid residuals, which ensures that the exact and filtered flow have the same energy decay profile, is also derived.
Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation
Authors: Loyalka S. K. , Hamoodi S. A.
Published: July 2002

The existence of a minimum in the cylindrical Poiseuille flow of a rarefied gas has been known since the experiments of Knudsen [Ann. Phys. 4, 75 (1909)]. Previously, the phenomenon has been studied with models of the Boltzmann equation, but results for the Boltzmann equation itself have not been reported. In the present paper, proceeding from recent studies, first the SN numerical algorithm for solving the linearized Boltzmann equation for the cylindircal geometry is outlined. Then, explicit numerical results for a rigid sphere gas and the boundary condition of diffuse specular reflection are obtained. The results show a minimum of the flow rate, and generally, provide a good description of the experimental data.
On long-wave instability of thin-film flow on curved beds
Authors: Eagles P. M.
Published: July 2002

The steady flow on a curved bed of large radius of curvature is perturbed by fixed-frequency waves. The frequency is small, commensurate with the magnitude of the curvature of the bed and the perturbations are of the long-wave type. A streamwise growth rate is calculated and several examples are given showing that the flow is theoretically unstable even for very small Reynolds numbers, in contrast to the classical theories of Benjamin [J. Fluid Mech. 2, 554 (1957)] and Yih [Phys. Fluids 8, 812 (1965)] for plane inclined beds.
Complex cavities: Are two dimensions sufficient for computation?
Authors: Koseff Jeffrey R. , Prasad Ajay K. , Perng Chinyuan , Street Robert L.
Published: July 2002

A two-dimensional numerical solution of the flow in a lid-driven cavity with a cutoff is compared with a physical experiment of the same flow. The Reynolds number of the flow is 3200. The results show that whereas the numerical solution is steady, the physical flow is unsteady and oscillates between three different flow modes. The oscillation is ascribed to unsteady three-dimensional structures in the flow.
Fourth-order Lagrangian of short waves riding on long waves
Authors: Zhang Jun
Published: July 2002

Applying the variational principle, a fourth-order wave-action conservation and second-order dispersion relation of a short-wave train riding on a long wave are derived from its fourth-order Lagrangian. The modulated nonlinear Schrödinger equation describing the evolution of short waves on long waves is obtained through the combination of the wave-action conservation and dispersion relation, and is identical to the previous derivation through a WKB perturbation method. The relationship between a Schrödinger equation and a Lagrangian is explored, revealing that their solutions for a steady short-wave train are generally different in accuracy except for the leading order.
On the viscosity of nondegenerate reacting gases
Authors: Ferrari L. , Russo G. , Fuschini E.
Published: July 2002

The viscosity of a nondegenerate molecular gas A, in equilibrium with its dissociation products B and C (having comparable masses) is considered. In contrast with the usual van der Waals corrections to Maxwell’s formula, a new term is found, which decreases with pressure and increases with temperature. The prevalence of these effects on van der Waals corrections and its experimental observability are studied. It is shown that alkaline molecules, at pressures of order 10−2 Torr, and temperatures below 103 K, should be good candidates to display the effect of a gaseous viscosity decreasing with the square root of the pressure.
Gallery of Fluid Motion
Authors: Reed Helen L.
Published: July 2002

This article displays winning photographs from the eighth Annual Fluid Mechanics Photo Contest held at the November 1990 meeting of the American Physical Society, Division of Fluid Dynamics, Cornell University, Ithaca, New York.
The effect of heat addition on slightly compressible flow: The example of vortex pair motion
Authors: Moore D. W. , Pullin D. I.
Published: July 2002

The effect of a point heat source on the two-dimensional irrotational flow of a slightly compressible nonviscous and nondiffusive fluid is studied. Heat is added at a constant rate and with a prescribed spatial distribution. The Mach number M is assumed small and the governing equations are solved to order M2 by a generalization of the Rayleigh–Janzen expansion. The interaction between entropy variations produced by the heat source and the pressure field generates a wake consisting of a vortex sheet and a dipole sheet extending downstream of the heat source, and this in turn perturbs the flow at order M2. A general result is that if heat is added where the gas is compressed by the flow, the impulse directed against the free stream is increased and vice versa. Cross-stream impulse is produced if the heat source is not on the axis of symmetry (if any) of the flow. This would result in a lifting force if a cylinder is providing the perturbation to the free stream. When heat is added on the downstream dividing streamline of a symmetrical flow the order M2 velocity field at infinity is that due to an apparent mass source and it is shown that the required flux of mass and momentum is supplied from infinity via the wake. Detailed calculations are performed for the case of the self-propagation of a symmetrical vortex pair, where heat is added downstream of the rearward stagnation point. The resultant increase in the pair impulse is shown to lead to a slow increase in the vortex pair separation.
The role of dissipation fluctuations on the generation of structures and the Kuramoto–Shivashinsky equation
Authors: Tur A. V. , Yanovsky V. V.
Published: July 2002

Using the Burgers equation as an example, it is shown that accounting for Gaussian fluctuations of dissipation leads to the Kuramoto–Shivashinsky equation. A generalized Kuramoto–Shivashinsky equation is derived and a mechanism of generation of structures due to dissipation fluctuations is investigated.
The effect of wall compliance on the Goertler vortex instability
Authors: Denier J. P. , Hall P.
Published: July 2002

The stability of the flow of a viscous incompressible fluid over a curved compliant wall to longitudinal Goertler vortices is investigated. The compliant wall is modeled by a particularly simple equation relating the induced wall displacement to the pressure in the overlying fluid. Attention is restricted to the large Goertler number regime; this regime being appropriate to the most unstable Goertler mode. The effect of wall compliance on this most unstable mode is investigated.
Stretching, folding, and alignment along Lagrangian orbits
Authors: Tabor M.
Published: July 2002

The stirring and mixing of passive scalars is determined by the geometry of the Lagrangian orbits followed by the advected particles. The efficiency of these processes depends on the ‘‘stretching and folding’’ of a local element (line, area, and volume). This deformation is determined by the nature of the local straining field and the degree of alignment of the advected element with the straining directions. Various ways of quantifying the dynamics of the straining field, that are valid for both three-dimensional flows and dynamical systems in general, are proposed. One of the simplest is a quantity termed the persistence of strain, σ2, which is defined as σ2= 1/2 Tr(A2), where A is the tangent map of the flow. This is shown to provide a compact quantification of the relative strengths of the straining and rotational components of the flow along a Lagrangian path. This, in turn, leads to the concept of a ‘‘strain history’’ of a fluid particle for which we can also compute a ‘‘stretch–fold’’ radio χ, that provides an average measure of these effects along an orbit. The quantity σ2 is closely related to the curvature of an orbit and this suggests a study of the curvature κ and torsion τ of particle trajectories. Further information is provided by extending the definition of Lyapunov exponents ins such a way as to include complex eigenvalue information that is traditionally discarded from the tangent map during the computation of these exponents. This provides additional information about the orientation and alignment of the advected element. These considerations are especially important when considering the fate of small deformable bodies, such as polymers, in flow fields with rapidly fluctuating strain rates.
Chaotic mixing of a viscous fluid in a screw impeller mixer
Authors: Khakhar D. V. , Sridhar G.
Published: July 2002

Several studies on model systems1,2 have established the potential utility of the theory of chaotic systems for the analysis of mixing in laminar flow fields. Here we present an application of the theory to the mixing, under creeping flow conditions, in a screw impeller mixer, which is used in a number of industrial mixing operations. The flow in the system was found to comprise five main components: (i) unidirectional flow in the annulus; (ii) turning slow flow in the lower compartment; (iii) double helical motion in the screw element; (iv) helical motion in the upper part of the draft tube; and (v) turning flow in the upper compartment. Under creeping flow conditions, the flow is independent of the rotational speed of the impeller, thus mixing can be altered only by changing the system geometry. The flow is time independent with respect to a frame of reference fixed on the impeller, and can be considered to be a more complicated version of that in the partitioned pipe mixer.3 Streak lines of the flow are invariant to 2π rotations of the impeller, and illustrate the stretching and folding of material lines by the flow. The development of a streak line starting in the annulus was studied experimentally using a fluorescent tracer dye. Each streak line was found to be segmented into an infinite number of loops each starting at a point on the impeller blade. Each loop in turn was found to be wrapped toroidally around the draft tube. Poincaré sections were obtained by noting the points of intersection of a tracer particle trajectory with a horizontal plane. The coordinate system was fixed either on the tank or on the impeller. Experimentally obtained Poincaré sections were chaotic but showed no structure in either case indicating a well mixed-system to the resolution of the measurements. Studies are currently underway with impellers of varying pitch and length to study their effect on the quality of mixing in terms of Poincaré sections and the extent of stretching of a streak line loop in each rotation of the impeller.
Anomalous diffusion and patchiness generated by Lagrangian chaos in shallow tidal flows
Authors: Pasmanter R. A.
Published: July 2002

As a simplified model of the currents generated by a tidal wave propagating over a shallow region with bottom irregularities, i.e., the Wadden Sea in The Netherlands, we used a two-dimensional incompressible flow, periodic both in space and time. In previous work we have reported that the paths of passive particles advected by nonrandom, laminar, 2-D tidal flows are often chaotic if the spatial inhomogeneity and time dependence are not negligible. Moreover, the numerical calculations showed that the deterministic advection of particles by such a velocity field leads to the following. (1) Patchiness, i.e., parts of the solute cloud that (in the absence of diffusion) do not disperse at all. Different patches may drift with different velocities. These patches coexist with the chaotic areas described next. (2) Chaotic paths with properties similar to those of random walks; i.e., the variance of the solute cloud grows in time like tα. The value of α depends upon the parameters that characterize the flow, e.g., 0≤α≤1 if there is no permanent homogeneous component of the velocity field, otherwise 0≤α≤2. When all paths are chaotic, i.e., when no patches are present, then α=1. (3) The residence time of dispersing stuff on the boundaries of the patches (KAM surfaces) is extremely long; this, combined with the abundance of KAM surfaces, leads to the anomalous diffusion reported above and to multifractal structure of the concentration. (4) When the effects of diffusion are taken into account (a) patches become ‘‘leaky’’ and disperse much slower than the rest of the cloud; (b) after a long transient the variance tensor grows linearly in time; and (c) the multifractal structure disappears below a microscopic length scale. The question we addressed next is how to circumvent the lengthy numerical calculations in order to determine the anomalous diffusion exponent α, the size distribution and the location of the nondispersing islands (patches), the area occupied by drifting paths, the effective diffusion coefficient (when irreversible diffusion is included), etc. No general analytic method seems to exist.
Two- and three-dimensional numerical modeling of dispersion and mixing in shallow (tidal) waters
Authors: van Dam G. C.
Published: July 2002

Two main mechanisms can be distinguished in the process of dispersion and mixing of dissolved or suspended matter in shallow waters: (1) vertical current shear and the accompanying vertical mixing and (2) spreading caused by the inhomogeneity and time dependence of the field of horizontal velocities. Both mechanisms have long been recognized and have been investigated by many researchers. The various studies usually concern only one of the two phenomena at a time. This is not necessarily a drawback from a theoretical viewpoint if care is taken that the values of parameters typical for one phenomenon, as derived from field data, are not significantly contaminated by effects caused by the other. In practice this type of error has been rather common. In several cases the existence of the other mechanism than the one described was entirely overlooked or at least neglected. There is an extensive range of time and length scales in which none of the two mechanisms has negligible influence. Most of the field data and many topics of interest are also in the range of simultaneous occurrence.

In order to determine the relative importance of the two mechanisms one needs a mathematical model in which the two phenomena are explicitly modeled in such a way that the entire range of several orders of magnitude is covered with good accuracy. This was established by a three-dimensional numerical model in which the dispersing matter was represented by discrete particles. In this way, no bound is set to spatial resolution; the scale range that can be covered is unbounded at either end. Extension at small scales only requires a consequent decrease of time step length. The second mechanism (horizontal inhomogeneity) can be simulated in two ways, by scaled random walk and by synthetic velocity fields. The first technique is the most economical. The second has the advantage that it is directly related to energy and velocity spectra; it has become more feasible by applying a shifting spectral window. The final results of the two techniques, measured as variances of particle clouds as functions of time, were virtually identical. It was found that only for very short and relatively long times (after instantaneous point release), the mechanism of the horizontal velocity structure prevails.

In the middle of the intermediate range, the vertical shear of the current is entirely dominant. In a basin like the North Sea this dominance occurs at horizontal length scales of a few kilometers and a time scale of a few hours to about one day, depending on the local vertical mixing rate and tidal energy. By adjusting the spectrum of the horizontal velocity structure to the rather extensive set of field data, a theoretical envelope was obtained from the model, enclosing the set of measured curves quite accurately. The resulting energy spectrum agrees well with estimates in the literature.
Reply to comments of Chakraborty and Tuteja
Authors: Dávalos-Orozco L. A.
Published: July 2002

A reply to the comments by Chakraborty and Tuteja [Phys. Fluids A 1, 1600 (1989)] is presented. After a careful review, it was found that their comments are correct. Despite this, the physical conclusions, for H=0, concerning the implications of the problem on natural convection under a horizontal magnetic field remain the same.
Viscous effects on the free surface deformation in thermocapillary flows
Authors: Rivas Damián
Published: July 2002

The free surface deformation caused by thermocapillary flows in a two-dimensional rectangular cavity, in the absence of gravitational forces, is studied. The correction to the flat shape is obtained as a domain perturbation for small capillary numbers. The viscous term in the equation for the free surface correction is retained. It is shown that, even at large Reynolds numbers, the viscous effects can be important and must not be neglected.
Bounds for mobility of foams flowing through porous media
Authors: Miksis Michael J.
Published: July 2002

Variational bounds have been used to estimate the fluid permeability of one-phase flow in porous media. Here an extension of this idea to foam flow in porous media is discussed.
Onset of solutal convection during directional solidification of a binary alloy in a cylinder
Authors: Guérin R. Z. , Billia B. , Haldenwang P.
Published: July 2002

The onset of solutal convection during directional solidification of a binary alloy growing in a cylinder is determined for the axisymmetric and selected nonaxisymmetric flow states. The Tau–Chebyshev projection method is used to solve the system of linearized partial differential equations. The Pb–Tl and Pb–Sn alloy systems are investigated, which, respectively, correspond to k=1.1 and to k=0.3. A critical convective pattern with an azimuthal wave number α=1 is obtained when the aspect ratio β of the cylinder is less than about 6.5. At this value a transition to axisymmetric modes (α=0) is evidenced. Finally, the comparison with previous results for growth in a vertical slot shows the enhancement of the hydrodynamic stability associated to the 3-D confinement by the cylinder.
Experiments on attached flow about sharp edges and its relevance to the Kutta condition
Authors: Auerbach David
Published: July 2002

Experiments on impulsively started flows about sharp edges subtending angles between 150° and 175° show that the flow remains attached for a long time, in seeming contradiction to the Kutta condition. Although certain details of the flow are not understood, comparison of viscous boundary-layer and inviscid vortex growth rates indicate that this behavior may well be due to the starting flow being of an initially viscous nature.
The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies
Authors: Shaw Stephen J. , Duck Peter W.
Published: July 2002

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for Mach numbers 2.8 and 3.8, revealing that curvature and choice of wall conditions both have a significant effect on the stability of the flow. The asymptotic, large azimuthal wave-number solution is obtained for the inviscid stability of the flow and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented.
Taylor vortices between elliptical cylinders
Authors: Schumack Mark R. , Schultz William W. , Boyd John P.
Published: July 2002

Critical parameters (Reynolds number and wave number) signaling the onset of Taylor vortices are calculated for the flow between ‘‘elliptical’’ cylinders. The spinning inner cylinder is circular; the stationary outer cylinder is composed of two circular arcs and is similar to an ellipse. It is shown that increasing ellipticity destabilizes the flow and increasing eccentricity stabilizes the flow. The spectral element method is used to calculate the base flow and to solve the linear stability problem.
The ‘‘onion vortex’’: An adiabatic, steady-state flow of a perfect gas in the infinite domain
Authors: Moses Harry E. , Sandri Guido v. H.
Published: July 2002

This Brief Communication gives a new exact solution of the nonlinear adiabatic equations of fluid flow for a perfect gas in infinite three-dimensional domain that is not the trivial constant flow. The temperature of the gas is an arbitrary function of the radius. The velocity of the gas can be described by considering concentric spheres, one for each value of the radius, which rotate about the same fixed axis through the common center of the spheres, the angular velocity of each sphere being dependent upon the temperature at the radius. The velocity of the gas at a point is then that of the sphere at that point. The nature of this flow suggests that it be named an ‘‘onion vortex.’’ It is shown that onion vortices for the same temperature distribution have an additive property, which is surprising in the context of nonlinear equations.
A weakly nonlinear theory based explanation for wave interactions in rotating channel flow
Authors: Singer Bart A.
Published: July 2002

A weakly nonlinear wave-interaction theory is used to explain the decay of linearly unstable oblique waves in rotating channel flow at low Reynolds number. At the low Reynolds number studied, the waves tend to stabilize each other and therefore when no waves are preferentially excited, the linearly most unstable mode reaches a nonlinear amplitude first and causes the stabilization of all competing modes.
On the constitutive relations for dispersed particles in nonuniform flows. I: Dispersion in a simple shear flow
Authors: Reeks M. W.
Published: July 2002

The work presented follows on from a previous study in which a kinetic approach was used to generate the continuum equations for a dilute dispersed phase of noncolliding particles in a nonuniform turbulent flow. Here this approach is used to derive forms for the Reynolds stresses and the fluctuating interphase momentum transfer for particles at equilibrium in a bounded simple shear flow; the combination of the two also gives the total stress and long-term particle diffusion coefficients. These forms are based on equilibrium solutions of a kinetic equation describing the transport of the particle phase space probability density <W(v,x,t)≳ for a particle with velocity v and position x at time t. The crucial constituent of the equation is the form of the phase space diffusion current given here by −(∂/∂v⋅μ+∂/∂x⋅λ+γ)<W(v,x,t)≳, where μ, λ, and γ are tensors whose components depend upon gradients of the local mean carrier flow, as well as particle and carrier flow time scales. While some of the results quoted here can be obtained by more direct means, this approach identifies those contributions arising explicitly from the mean shear gradient kp of the dispersed phase (the viscous contributions) and those arising explicitly from that of the carrier flow. These forms highlight fundamental deficiencies in the traditional use of the Boussinesq approximation, that have hitherto gone unrecognized. The Reynolds stresses for instance are composed of a homogeneous component (as if the carrier flow is homogeneous) and a deviatoric component (due to the mean shear gradient): The Boussinesq approximation ignores the homogeneous components in the shear stresses and accounts only for the viscous contribution in the deviatoric component. For small particles (approaching fluid point motion) the deviatoric Reynolds shear stresses (in the streamwise direction) are proportional to the relative mean shearing between the two phases. For large particles (approaching infinite response time) the normal Reynolds stress in the streamwise direction is proportional to kp2, as is also the corresponding particle diffusion coefficient which is also proportional to particle response time.