bluuebunny/crossref_metadata_2025 huggingface dataset:
Reliability of perturbation theory in general relativity
Authors: Damour Thibault , Schmidt Bernd
Published: July 2002

The relation between perturbation theory and exact solutions in general relativity is tackled by investigating the existence and properties of smooth one-parameter families of solutions. On the one hand, the coefficients of the Taylor expansion (in the parameter) of any given smooth family of solutions necessarily satisfy the hierarchy of perturbation equations. On the other hand, it is the converse question (does any solution of the perturbation equations come from Taylor expanding some family of exact solutions ?) which is of importance for the mathematical justification of the use of perturbation theory. This converse question is called the one of the ‘‘reliability’’ of perturbation theory. Using, and completing, recent results on the characteristic initial value problem, the local reliability of perturbation theory for general relativity in vacuum is proven very generally. This result is then generalized to the Einstein–Yang–Mills equations (and therefore, in particular, to the Einstein–Maxwell ones). These local results are then partially extended to global ones by: (i) proving the existence of semiglobal vacuum space-times (respectively, Einstein–Yang–Mills solutions) which are stationary before some retarded time u0, and radiative after u0, and which admit a smooth conformal structure at future null infinity; and (ii) constructing smooth one-parameter families of such solutions whose Taylor expansions are of the ‘‘multipolar post-Minkowskian’’ type which has been recently used in perturbation analyses of radiative space-times.
Redefinition of position variables and the reduction of higher-order Lagrangians
Authors: Damour Thibault , Schäfer Gerhard
Published: July 2002

Single-time Lagrangians are treated in this paper, describing the dynamics of systems of point particles, which are given as formal power series in some ordering parameter and which may contain higher time derivatives in all terms but the leading one. An efficient method for eliminating the higher time derivatives directly on the Lagrangian level is presented. This method clarifies the meaning of using the lower-order equations of motion in higher-order terms in a Lagrangian. The method consists of an iterative use of ‘‘contact’’ transformations in the jet prolongation of the extended configurations space and is called ‘‘the method of redefinition of position variables.’’ Several examples from electrodynamics and relativistic gravity are treated explicitly.
Continual classical Heisenberg models defined on graded su(2,1) and su(3) algebras
Authors: Makhankov V. G. , Pashaev O. K.
Published: July 2002

Continual integrable Heisenberg models are constructed on real subalgebras of the superalgebra spl(2/1). Two Heisenberg models are shown to exist on the compact subalgebra uspl(2/1)≊su(2/1). One of these, SU(2/1)/S(U(2)×U(1)), is gauge equivalent to SU(2) nonlinear vector Schrödinger equation (NLSE) expressed in odd Grassman variables, the other, SU(2/1)/S(L(1/1)×U(1)), to ‘‘super’’ NLSE which is invariant under global supersymmetry transformations of SL(1/1). Also constructed are a Heisenberg model on the noncompact subalgebra ospu(1,1/1), with higher nonlinearities, and its gauge equivalent analog. Hamiltonian structure and classical solutions are studied and the possible connection of the given models with a version of the Hubbard one is discussed.
Gravitational perturbations of type-D vacuum space–times with cosmological constant
Authors: Torres del Castillo G. F.
Published: July 2002

It is shown that in a type-D vacuum space–time with cosmological constant, the maximal spin weight components of the Weyl spinor perturbations, which obey separable decoupled equations, satisfy certain differential relations that are equivalent to the Teukolsky–Starobinsky identities fulfilled by the separated functions. It is also shown that the real and imaginary parts of the Starobinsky constants can be obtained from these relations.
Period lengths of cellular automata on square lattices with rule 90
Authors: Kawahara Yasuo , Kumamoto Satoru , Mizoguchi Yoshihiro , Nohmi Masaya , Ohtsuka Hiroshi , Shoudai Takayoshi
Published: July 2002

This paper studies two-dimensional cellular automata ca−90(m,n) having states 0 and 1 and working on a square lattice of size (m−1)×(n−1). All their dynamics, driven by the local transition rule 90, can be simply formulated by representing their configurations with Laurent polynomials over a finite field F2={0,1}. The initial configuration takes the next configuration to a particular configuration whose cells all have the state 1. This paper answers the question of whether the initial configuration lies on a limit cycle or not, and, if that is the case, some properties on period lengths of such limit cycles are studied.
Some reductions of the self-dual Yang–Mills equations to integrable systems in 2+1 dimensions
Authors: Chakravarty S. , Kent S. L. , Newman E. T.
Published: July 2002

A reduction of the self-dual Yang–Mills (SDYM) equations is studied by imposing two space–time symmetries and by requiring that the connection one-form belongs to a Lie algebra of formal matrix-valued differential operators in an auxiliary variable. In this article, the scalar case and the canonical cases for 2×2 matrices are examined. In the scalar case, it is shown that the field equations can be reduced to the forced Burgers equation. In the matrix case, several well-known 2+1 integrable equations are obtained. Also examined are certain transformation properties between the solutions of some of these 2+1 equations.
On solutions of constrained KP equations
Authors: Loris Ignace , Willox Ralph
Published: July 2002

We derive solutions of general Wronskian form for the (vector) constrained KP hierarchies. As one explicit example we discuss rational solutions. In order to introduce our method, we give a direct, elementary proof of the existence of Wronskian solutions for the l-modified KP hierarchies (l:0,1,…).
The Kowalewski top: A new Lax representation
Authors: Tsiganov A. V.
Published: July 2002

The 2×2 monodromy matrices for the Kowalewski top on the Lie algebras e(3), so(4), and so(3,1) are presented. The corresponding quadratic R-matrix structure is the dynamical deformation of the standard R-matrix algebras. Some tops and Toda lattices related to the Kowalewski top are discussed.
A nonlinear deformed su(2) algebra with a two-color quasitriangular Hopf structure
Authors: Bonatsos D. , Daskaloyannis C. , Kolokotronis P. , Ludu A. , Quesne C.
Published: July 2002

Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as 𝒜q+(1). This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0,1,2,… . To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed by proceeding in two steps. In the first one, a variant and extension of the deforming functional technique is introduced: variant because a map between two deformed algebras, suq(2) and Aq+(1), is considered instead of a map between a Lie algebra and a deformed one, and extension because use is made of a two-valued functional, whose inverse is singular. As a result, the Hopf structure of suq(2) is carried over to 𝒜q+(1), thereby endowing the latter with a double Hopf structure. In the second step, the definition of the coproduct, counit, antipode, and ℛ-matrix is extended so that the double Hopf algebra is enlarged into a new algebraic structure. The latter is referred to as a two-color quasitriangular Hopf algebra because the corresponding ℛ-matrix is a solution of the colored Yang–Baxter equation, where the “color” parameters take two discrete values associated with the two series of finite-dimensional representations.
Normalization integrals of orthogonal Heun functions
Authors: Becker Peter A.
Published: July 2002

A formula for evaluating the quadratic normalization integrals of orthogonal Heun functions over the real interval 0⩽x⩽1 is derived using a simple limiting procedure based upon the associated differential equation. The resulting expression gives the value of the normalization integral explicitly in terms of the local power-series solutions about x=0 and x=1 and their derivatives. This provides an extremely efficient alternative to numerical integration for the development of an orthonormal basis using Heun functions, because all of the required information is available as a by-product of the search for the eigenvalues of the differential equation.
Casimir invariants and characteristic identities for gl(∞)
Authors: Gould M. D. , Stoilova N. I.
Published: July 2002

A full set of (higher-order) Casimir invariants for the Lie algebra gl(∞) is constructed and shown to be well defined in the category OFS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(∞) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)].
Geometrical evaluation of star products
Authors: Zachos Cosmas
Published: July 2002

The geometric picture of the star product based on its Fourier representation kernel is utilized in the evaluation of chains of star products and the intuitive appreciation of their associativity and symmetries. Such constructions appear even simpler for a variant asymmetric product, and carry through for the standard star-product supersymmetrization.
Nonlinear viscous fingering in miscible displacement with anisotropic dispersion
Authors: Zimmerman W. B. , Homsy G. M.
Published: July 2002

The effect of anisotropic dispersion on nonlinear viscous fingering in miscible displacements is examined. The formulation admits dispersion coefficient-velocity field couplings (i.e., mechanical dispersivities) appropriate to both porous media and Hele–Shaw cells. A Hartley transform-based scheme is used to numerically simulate unstable miscible displacement. Several nonlinear finger interactions were observed. Shielding, spreading, tip splitting, and pairing of viscous fingers were observed here, as well as in isotropic simulations. Multiple coalescence and fading were observed in simulations with weak lateral dispersion, but not for isotropic dispersion. Transversely and longitudinally averaged one-dimensional concentration histories demonstrate the rate at which the mixing zone broadens and the increase in lateral scale as the fingers evolve when no tip splitting occurs. These properties are insensitive to both the dispersion anisotropy and the Peclet number at high Peclet number and long times. This suggests the dominance of finger interaction mechanisms that are essentially independent of details of the concentration fields and governed fundamentally by pressure fields.
Pitot–static tube response at very low Reynolds numbers
Authors: Chebbi B. , Tavoularis S.
Published: July 2002

The response of Pitot–static tubes in the very low Reynolds number range (Re<1) has been investigated experimentally in a closed circuit glycerine channel. The disturbance of the flow by the tube presence has also been investigated by mapping the velocity field around the tube using laser Doppler anemometry. Finally the yaw sensitivity of pressure tubes at very low Re has been determined and compared to that at high Re.
Exact solution of a restricted Euler equation for the velocity gradient tensor
Authors: Cantwell Brian J.
Published: July 2002

The velocity gradient tensor satisfies a nonlinear evolution equation of the form (dAij/dt)+AikAkj− (1/3)(AmnAnm)δij=Hij, where Aij=∂ui/∂xj and the tensor Hij contains terms involving the action of cross derivatives of the pressure field and viscous diffusion of the velocity gradient. The homogeneous case (Hij=0) considered previously by Vielliefosse [J. Phys. (Paris) 43, 837 (1982); Physica A 125, 150 (1984)] is revisited here and examined in the context of an exact solution. First the equations are simplified to a linear, second-order system (d2Aij/dt2)+(2/3)Q(t)Aij=0, where Q(t) is expressed in terms of Jacobian elliptic functions. The exact solution in analytical form is then presented providing a detailed description of the relationship between initial conditions and the evolution of the velocity gradient tensor and associated strain and rotation tensors. The fact that the solution satisfies both a linear second-order system and a nonlinear first-order system places certain restrictions on the solution path and leads to an asymptotic velocity gradient field with a geometry that is largely but not wholly independent of initial conditions and an asymptotic vorticity which is proportional to the asymptotic rate of strain. A number of the geometrical features of fine-scale motions observed in direct numerical simulations of homogeneous and inhomogeneous turbulence are reproduced by the solution of the Hij=0 case.
Three-dimensional optimal perturbations in viscous shear flow
Authors: Butler Kathryn M. , Farrell Brian F.
Published: July 2002

Transition to turbulence in plane channel flow occurs even for conditions under which modes of the linearized dynamical system associated with the flow are stable. In this paper an attempt is made to understand this phenomena by finding the linear three-dimensional perturbations that gain the most energy in a given time period. A complete set of perturbations, ordered by energy growth, is found using variational methods. The optimal perturbations are not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbation to grow by as much as three orders of magnitude. It is suggested that excitation of these perturbations facilitates transition from laminar to turbulent flow. The variational method used to find the optimal perturbations in a shear flow also allows construction of tight bounds on growth rate and determination of regions of absolute stability in which no perturbation growth is possible.
Analysis of vibration-dissociation-recombination processes behind strong shock waves of nitrogen
Authors: Boyd Iain D.
Published: July 2002

Computations are presented for the relaxation zone behind strong, one-dimensional shock waves of nitrogen. The numerical results are compared with existing experimental data. It is indicated that the derivation of chemical rate coefficients must account for the degree of vibrational nonequilibrium in the flow. A nonequilibrium chemistry model is employed together with equilibrium rate data to compute successfully the flow in several different nitrogen shock waves. The analysis is performed with the direct simulation Monte Carlo method (DSMC). The DSMC code is vectorized for efficient use on a supercomputer. The code simulates translational, rotational, and vibrational energy exchange, and dissociative and recombinative chemical reactions. A new model is proposed for the treatment of three-body recombinative collisions in the DSMC technique, which usually simulates binary collision events. The new formulation represents improvement over previous models in that it can be employed with a wide range of chemical rate data, does not introduce into the flow field troublesome pairs of atoms that may recombine upon further collision (pseudoparticles), and is compatible with the vectorized code.
Oscillatory Stokes flow in periodic porous media
Authors: Chapman A. M. , Higdon J. J. L.
Published: July 2002

The unsteady Stokes equations for the microscopic flow in model porous media subject to an oscillatory pressure gradient are solved. The media consist of periodic lattices (SC, BCC, FCC) of spheres ranging from dilute systems with isolated spheres to highly concentrated consolidated media with overlapping spheres. Detailed results are presented for the dynamic permeability and comparisons are made with previously published results, asymptotic limits, and approximate theories. The wave speed and attenuation rate for acoustic waves are evaluated.
The dynamics of shock accelerated light and heavy gas cylinders
Authors: Jacobs J. W.
Published: July 2002

Experiments have been carried out in which a cylindrical volume of a gas, that is either lighter or heavier than its surroundings, is impulsively accelerated by a weak shock wave. Laminar jets of helium or sulphur hexafluoride (SF6) are used to produce the cylinders, and planar laser-induced fluorescence is used to visualize the flow. It is found that the vorticity deposited on the boundary of the SF6 cylinder by the interaction with the shock wave, separates from the heavy gas to form a pair of vortices, which subsequently wrap the SF6 around them. This process is quite different from what is observed in the light gas experiments, which showed a small amount of helium to remain with the vorticity, eventually becoming part of the vortex cores. Centrifugal forces combined with differences in the rates of the diffusion of vorticity in the two gases are given as possible reasons for these differences. Measurement of the initial downstream velocity for a heavy gas cylinder is found to agree well with a theory based on two simple models. But, because diffusion causes the light gas jet density to be significantly greater than that of pure helium, the theory overpredicts the measured velocity of the light gas experiments. The final translational velocities for both light and heavy gas experiments are not accurately predicted by the model, and measurements of the vortex spacing are found to be significantly larger than those indicated by this theory. These differences are likely caused by the theory’s inability to accurately describe the viscous nonuniform flow.
Streamwise vortex meander in a plane mixing layer
Authors: LeBoeuf Richard L. , Mehta Rabindra D.
Published: July 2002

Previous measurements in a two-stream plane mixing layer have shown that the mean streamwise vorticity decays monotonically with downstream distance such that it is absent in the far-field (self-similar) region [J. H. Bell and R. D. Mehta, J. Fluid Mech. 239, 213 (1992); AIAA J. 28, 2034 (1990)]. It was not clear at that time if this measured decay reflected the diffusion of the instantaneous streamwise vorticity or was a result of increasing vortex meander within the mixing layer. The present experimental study was conducted in order to determine the existence of streamwise vortex meander in a mixing layer, and if present, its significance on the measured properties. The dependence of the velocity cross-correlation on the fixed probe location was shown to be a good indicator of the stationarity of the streamwise vortex location. The cross-correlation measurements obtained here indicate that spanwise meander is negligible, although transverse apparent meander (normal to the plane of the mixing layer) was indicated. The transverse meander, exemplified by the elliptical shape of the mean streamwise vorticity contours, was expected, since the streamwise vorticity in the braid region is essentially inclined, with respect to the streamwise direction. These conclusions were supported by results of estimated spanwise profiles of the transverse velocity component. The balance of evidence suggests that the measured mean streamwise vorticity decay is representative of the decay of the vorticity rather than an artifact of meander.
Thermocapillary motion in a spinning vaporizing droplet
Authors: Lozinski David , Matalon Moshe
Published: July 2002

The thermocapillary motion generated within a spinning vaporizing droplet is described. Rotation induces a swirling flow in the surrounding gas. This in turn establishes a nonuniform vapor concentration and temperature at the droplet surface. An internal circulation is thus created from the interfacial temperature gradients. This internal motion, described in the limits of small Reynolds and Marangoni numbers, appears as a pair of toroidal vortices. Depending on whether the gaseous Lewis number, Le, is less than or greater than one, the temperature along the surface peaks at either the poles or the equator of the droplet. Consequently, the direction of the internal circulation is from the poles to the equator or vice versa.
A practical nonlocal model for electron heat transport in laser plasmas
Authors: Epperlein E. M. , Short R. W.
Published: July 2002

A brief review of nonlocal heat-flow models is presented. Numerical difficulties associated with their implementation, as recently demonstrated by Prasad and Kershaw [Phys. Fluids B 1, 2430 (1989)], are discussed and a simple solution is proposed. A new nonlocal heat-flow formula is developed, based on numerical simulations of the decay of linearized thermal waves, using the electron Fokker–Planck code spark. The formula is tested by modeling the full implosion of a CH shell driven by 351 nm laser irradiation. Results are shown to be in good agreement with spark simulations.
Nonstationarity of a two-dimensional quasiperpendicular supercritical collisionless shock by self-reformation
Authors: Lembege Bertrand , Savoini Philippe
Published: July 2002

Two-dimensional electromagnetic particle simulations evidence a self-reformation of the shock front for a collisionless supercritical magnetosonic shock propagating at angle θ0 around 90°, where θ0 is the angle between the normal to the shock front and the upstream magnetostatic field. This self-reformation is due to reflected ions which accumulate in front of the shock and is observed (i) in both electric and magnetic components, (ii) for both resistive and nonresistive two-dimensional shocks, and (iii) over a cyclic time period equal to the mean ion gyroperiod measured downstream in the overshoot; resistive effects may be self-consistently included or excluded for θ0≂90° according to a judicious choice of the upstream magnetostatic field orientation. The self-reformation leads to a nonstationary behavior of the shock; however, present results show evidence that the shock becomes stationary for θ less than a critical value θr, below which the self-reformation disappears. Present results are compared to previous works where one/two-dimensional hybrid and particle codes have been used, and to experimental measurements.
A theory of two-stream instability in two hollow relativistic electron beams
Authors: Uhm Han S.
Published: July 2002

Stability properties of two-stream instability of two hollow electron beams are investigated. The equilibrium configuration consists of two intense relativistic hollow electron beams propagating through a grounded conducting cylinder. Analysis of the longitudinal two-stream instability is carried out within the framework of the linearized Vlasov–Maxwell equations for the equilibrium distribution function, in which beam electrons have a Lorentzian distribution in the axial momentum. Dispersion relation of the longitudinal two-stream instability is derived. Stability criteria from this dispersion relation indicate that the normalized velocity difference Δβ between the beams should be within a certain range of value to be unstable. Growth rate of the instability is a substantial fraction of the real frequency, thereby indicating that the longitudinal two-stream instability is an effective means of beam current modulation. Transverse instability of hollow electron beams is also investigated. Dispersion relation of the coupled transverse oscillation of the beams is derived and numerical investigation of this dispersion relation is carried out. Growth rate of the kink instability is a substantial fraction of the diocotron frequency, which may pose a serious threat to the two-stream klystron.
Kinetic theory of a whistler-pumped free electron laser
Authors: Sharma Anamika , Tripathi V. K.
Published: July 2002

A kinetic formalism of mode coupling in a whistler-pumped free electron laser (FEL) is developed. The analysis includes the effect of finite space charge field of the electron beam. Kinetic effects appear through the beam plasma susceptibility in the coupling coefficient. For a Gaussian distribution in beam axial momentum, the growth rate of FEL instability falls off rapidly with increasing momentum spread. The growth rate is also a sensitive function of pump frequency and plasma density. Feasibility of this device in the low-current Compton regime is also examined.
Nonlinear instability at the interface between two viscous fluids
Authors: Hooper A. P. , Grimshaw R.
Published: July 2002

Co-current flow of two viscous fluids in a channel is linearly unstable to long wavelength disturbances. The weakly nonlinear evolution of this instability is examined. It is shown that, because of surface tension and nonlinear effects, the interface can either return to its original undisturbed state or evolve to some finite amplitude steady state.
Simulations of the single-mode, bump-on-tail instability
Authors: Denavit J.
Published: July 2002

The nonlinear saturation of the single-mode, bump-on-tail instability is studied by numerical solutions of the Vlasov equation. Modes close to marginal stability are found to saturate with a field amplitude E∝Δ2, where the small parameter Δ=2(ω−ω′)/ω′ defines the difference between the mode frequency ω and the frequency ω′ of the marginally stable mode. This scaling agrees with O’Neil’s theory [Phys. Fluids 14, 1204 (1971)] of the two-stream instability, and does not confirm the time asymptotic analysis of Simon and Rosenbluth [Phys. Fluids 19, 1567 (1976)], which predicts larger amplitudes with E∝Δ1/2.
Microwave studies of a tunable free-electron laser in combined axial and wiggler magnetic fields
Authors: Fajans J. , Bekefi G. , Yin Y. Z. , Lax B.
Published: July 2002

Measurements of narrow-band (Δω/ω≤0.02) microwave emission from a tunable (7≤ω/2π≤21 GHz) Raman, free-electron laser operating in a single TE11 waveguide mode are reported. Approximately 100 kW of rf power has been observed at an electronic efficiency of 12%, and ∼1 MW of rf power has been generated at a reduced efficiency of 8%. Frequency, gain, and rf power measurements have been carried out for various values of the guide magnetic field, below, above, and near to the resonance between the cyclotron frequency of the guide magnetic field and the frequency associated with the periodic wiggler magnetic field. The results are in very good agreement with the predictions of three-dimensional free-electron laser theory.
Numerical simulation of double-diffusive Marangoni convection
Authors: Bergman T. L.
Published: July 2002

Marangoni convection is important in a variety of physical systems and occurs as a result of surface tension gradients at a liquid free surface. In general, liquid surface tension varies with temperature and species concentration in a binary fluid. If the temperature and concentration distributions make opposing contributions to the overall surface tension gradient at a free surface, convective motion, as well as heat and mass transfer within the system, is shown to depend on double-diffusive effects. This situation is analogous to double-diffusive natural convection, in that convection may occur, even though the overall surface tension difference along the free surface suggests stagnant fluid conditions.
Convective and absolute instability of a viscous liquid jet
Authors: Leib S. J. , Goldstein M. E.
Published: July 2002

The effect of viscosity on the capillary instability of a liquid jet is examined. The critical Weber number for convective instability is determined as a function of Reynolds number and comparison is made with the inviscid limit. It is shown that certain waves that are neutral in the inviscid case exhibit growth for finite Reynolds numbers.
Linear stability theory of two-layer fluid flow in an inclined channel
Authors: Tilley B. S. , Davis S. H. , Bankoff S. G.
Published: July 2002

The linear stability of the two-layer flow of immiscible, incompressible fluids in an inclined channel is considered. In the long-wave limit, mechanisms for linear instability, and the consequences of competition between mechanisms, are identified. For arbitrary wave numbers, air–water and olive oil–water systems are considered, in order to determine the influence of the channel thickness and the mean interfacial height on the stability of the flow. This paper characterizes those physical situations in which the primary instability is to long-wave interfacial disturbances. The odd Orr–Sommerfeld shear mode within the water layer, which is necessarily stable in plane Poiseuille flow, is found to grow and even be the dominant mode of instability for the olive oil–water system. The consequences beyond linear stability are discussed.
Experimental study of streaming flows associated with ultrasonic levitators
Authors: Trinh E. H. , Robey J. L.
Published: July 2002

Steady-state acoustic streaming flow patterns have been observed during the operation of a variety of resonant single-axis ultrasonic levitators in a gaseous environment and in the 20–37 kHz frequency range. Light sheet illumination and scattering from smoke particles have revealed primary streaming flows which display different characteristics at low and high sound pressure levels. Secondary macroscopic streaming cells around levitated samples are superimposed on the primary streaming flow pattern generated by the standing wave. These recorded flows are quite reproducible, and are qualitatively the same for a variety of levitator physical geometries. An onset of flow instability can also be recorded in nonisothermal systems, such as levitated spot-heated samples when the resonance conditions are not exactly satisfied. A preliminary qualitative interpretation of these experimental results is presented in terms of the superposition of three discrete sets of circulation cells operating on different spatial scales. These relevant length scales are the acoustic wavelength, the levitated sample size, and finally the acoustic boundary layer thickness. This approach fails, however, to explain the streaming flow-field morphology around liquid drops levitated on Earth. Observation of the interaction between the flows cells and the levitated samples also suggests the existence of a steady-state torque induced by the streaming flows.
The effects of permeability heterogeneity on miscible viscous fingering: A three-dimensional magnetic resonance imaging analysis
Authors: Fernandez Erik J. , Grotegut Chad A. , Braun George W. , Kirschner Kenneth J. , Staudaher John R. , Dickson Matthew L. , Fernandez Veronica L.
Published: July 2002

The three-dimensional evolution of the viscous fingering instability has been visualized directly with magnetic resonance imaging (MRI). Miscible displacement of thin solute bands by aqueous solvent was investigated in packed beds of 30 μm chromatographic particles. Fingering behavior into samples of glycerol and a protein, bovine serum albumin (BSA), with viscosity ratios ranging from 1 to approximately 4, were compared. The three-dimensional morphology and dynamics of fingers were monitored to approximately millimeter spatial resolution using MRI. Linear and nonlinear fingering behavior were observed. Permeability heterogeneities with length scales on the order of the finger wavelength induced complex three-dimensional fingering patterns. Sample and column boundary effects on fingering dynamics were also noted. The differences in fingering behavior observed between albumin and glycerol samples are consistent with the wavelength predictions of linear stability analysis and the large differences in molecular diffusivity.
Multiscalar mapping closure for mixing in homogeneous turbulence
Authors: Valiño Luis
Published: July 2002

A new methodology to use mapping closures for the mixing of several scalars in homogeneous turbulence is explained. The main idea is the unidimensional mapping for each scalar, with the cross-dissipation handled by a joint reference field. A restricted and a general closure are described. A Monte Carlo code based on a fractional step technique has been developed. As an example, the segregated double-delta two-scalar mixing is analytically and numerically solved and predictions are shown.
Different approximations of shallow fluid flow over an obstacle
Authors: Nadiga B. T. , Margolin L. G. , Smolarkiewicz P. K.
Published: July 2002

Three different sets of shallow water equations, representing different levels of approximation are considered. The numerical solutions of these different equations for flow past bottom topography in several different flow regimes are compared. For several cases the full Euler solutions are computed as a reference, allowing the assessment of the relative accuracies of the different approximations. Further, the differences between the dispersive shallow water (DSW) solutions and those of the highly simplified, hyperbolic shallow water (SW) equations is studied as a guide to determining what level of approximation is required for a particular flow. First, the Green-Naghdi (GN) equations are derived as a vertically-integrated rational approximation of the Euler equations, and then the generalized Boussinesq (gB) equations are obtained under the further assumption of weak nonlinearity. A series of calculations, each assuming different values of a set of parameters—undisturbed upstream Froude number, and the height and width of the obstacle, are then presented and discussed. In almost all regions of the parameter space, the SW and DSW theories yield different results; it is only when the flows are entirely subcritical or entirely supercritical and when the obstacles are very wide compared to the depth of the fluid that the SW and DSW theories are in qualitative and quantitative agreement. It is also found that while the gB solutions are accurate only for small bottom topographies (less than 20% of the undisturbed fluid depth), the GN solutions are accurate for much larger topographies (up to 65% of the undisturbed fluid depth). The limitation of the gB approximation to small topographies is primarily due to the generation of large amplitude upstream propagating solitary waves at transcritical Froude numbers, and is consistent with previous analysis. The GN approximation, which makes no assumptions about the size of the nonlinearity, is thus verified to be a better system to use in cases where the bottom topographies are large or when the bottom topographies are moderate but the flow transcritical.
Gas transport across an air/water interface populated with capillary waves
Authors: Saylor J. R. , Handler R. A.
Published: July 2002

An experimental study of gas transport across an air/water interface, populated by a field of standing capillary waves is presented. The experiments were conducted in a small tank containing distilled water, enriched with carbon dioxide. The capillary waves were of the Faraday type, generated by providing a small vertical vibration to the water tank. The frequency of excitation was varied from 200 to 400 Hz, giving wavelengths from 3.62 to 2.26 mm (linear estimate). The gas transport rate across the interface increased by almost two orders of magnitude as the wave slope was increased from zero to slightly above 0.2 m/m. A unique aspect of these experiments is that capillary waves were isolated from the obfuscating effects of turbulence, aerosol generation, and other phenomena typically present in wind/wave tunnel experiments. Consequently the large enhancement in gas transfer was due to the effects of capillary waves alone, demonstrating their importance in gas exchange processes. The maximum mass transfer coefficients obtained in these experiments are not achieved in typical wind/wave tunnel experiments below wind speeds of 10 m/s.
Experiments characterizing nonlinear shear layer dynamics in a supersonic rectangular jet undergoing screech
Authors: Walker Steven H. , Thomas Flint O.
Published: July 2002

Jet screech is the result of a resonant aeroacoustic feedback loop. In modern high-performance aircraft jet screech has given rise to in-flight sonic fatigue failure of nozzle components. For this reason, jet screech has been the focus of numerous investigations. However, the prediction of screech amplitude has been a very elusive goal. A primary objective of the work to be reported is to experimentally characterize the nonlinear instability wave development in the shear layer of a rectangular supersonic jet undergoing screech. Hot-film probes are used to measure the instability wave development in the jet shear layers along a constant Mach number ray. Higher-order polyspectral techniques are employed to determine resonant nonlinear phase locking between multiple instability modes. A detailed comparison of the “inner loop” hot-film measurements with “outer loop” acoustic measurements is made. Such a comparison reveals the importance of incorporating nonlinear effects into a jet screech amplitude prediction method.
Vortex crystals from 2D Euler flow: Experiment and simulation
Authors: Schecter D. A. , Dubin D. H. E. , Fine K. S. , Driscoll C. F.
Published: July 2002

Vortex-in-cell simulations that numerically integrate the 2D Euler equations are compared directly to experiments on magnetized electron columns [K. S. Fine, A. C. Cass, W. G. Flynn, and C. F. Driscoll, “Relaxation of 2D turbulence to vortex crystals,” Phys. Rev. Lett. 75, 3277 (1995)], where turbulent flows relax to metastable vortex crystals. A vortex crystal is a lattice of intense small diameter vortices that rotates rigidly in a lower vorticity background. The simulations and experiments relax at the same rates to vortex crystals with similar vorticity distributions. The relaxation is caused by mixing of the background by the intense vortices: the relaxation rate is peaked when the background circulation is 0.2–0.4 times the total circulation. Close quantitative agreement between experiment and simulation provides strong evidence that vortex crystals can be explained without incorporating physics beyond 2D Euler theory, despite small differences between a magnetized electron column and an ideal 2D fluid.
On the onset of convective instabilities in cylindrical cavities heated from below. I. Pure thermal case
Authors: Touihri R. , Ben Hadid H. , Henry D.
Published: July 2002

Three-dimensional steady flows are simulated in a circular cylindrical cavity of aspect ratio A=H/D, where H is the height and D the diameter of the cavity. The cavity is heated from below and its sidewalls are considered to be adiabatic. The effect of the geometry of the cavity on the onset of convection and on the structure and symmetries of the flow is analyzed. The nonlinear evolution of the convection beyond its onset is presented through bifurcation diagrams for two typical aspect ratios A=0.5 and A=1. Axisymmetric (m=0) and asymmetric (m=1 and m=2) azimuthal modes [exp (imφ)] are observed. For A=0.5, the axisymmetric solution loses its stability to a three-dimensional solution at a secondary bifurcation point. Better understanding of the mechanisms leading to this instability is obtained by analyzing the energy transfer between the basic state and the critical mode. To study the influence of the Prandtl number on the flow pattern and on the secondary bifurcation, three values of the Prandtl number are investigated: Pr=0.02 (liquid metal), Pr=1 (transparent liquids), and Pr=6.7 (water).
The development of transient fingering patterns during the spreading of surfactant coated films
Authors: Matar Omar K. , Troian Sandra M.
Published: July 2002

The spontaneous spreading of an insoluble surfactant monolayer on a thin liquid film produces a complex waveform whose time variant shape is strongly influenced by the surface shear stress. This Marangoni stress produces a shocklike front at the leading edge of the spreading monolayer and significant film thinning near the source. For sufficiently thin films or large initial shear stress, digitated structures appear in the wake of the advancing monolayer. These structures funnel the oncoming flow into small arteries that continuously tip-split to produce spectacular dendritic shapes. A previous quasisteady modal analysis has predicted stable flow at asymptotically long times [Phys. Fluids A 9, 3645 (1997)]. A more recent transient analysis has revealed large amplification in the disturbance film thickness at early times [O. K. Matar and S. M. Troian, “Growth of nonmodal transient structures during the spreading of surfactant coated films,” Phys. Fluids A 10, 1234 (1998)]. In this paper, we report results of an extended sensitivity analysis which probes two aspects of the flow: the time variant character of the base state and the non-normal character of the disturbance operators. The analysis clearly identifies Marangoni forces as the main source of digitation for both small and large wave number disturbances. Furthermore, initial conditions which increase the initial shear stress or which steepen the shape of the advancing front produce a larger transient response and deeper corrugations in the film. Disturbances applied just ahead of the deposited monolayer rapidly fall behind the advancing front eventually settling in the upstream region where their mobility is hampered. Recent findings confirm that additional forces which promote film thinning can further intensify disturbances [O. K. Matar and S. M. Troian, “Spreading of surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures,” Chaos 9, 141 (1999). The transient analysis presented here corroborates our previous results for asymptotic stability but reveals a source for digitation at early times. The energy decomposition lends useful insight into the actual mechanisms preventing efficacious distribution of surfactant.
Transient response of a capsule subjected to varying flow conditions: Effect of internal fluid viscosity and membrane elasticity
Authors: Diaz A. , Pelekasis N. , Barthès-Biesel D.
Published: July 2002

The transient deformation of an axisymmetric capsule freely suspended in a pure straining flow is studied, for sudden or periodic variations of the intensity of the rate of strain. The particle Reynolds number is supposed to be very small and the problem is solved numerically by means of the boundary integral method. In the case of a sudden start of flow, the time response of the capsule can be approximated by an exponential function, and is thus characterized by only two parameters: the equilibrium deformation D∞ and the characteristic response time τs. The respective influence of viscosity ratio, membrane elasticity, and initial particle geometry is analyzed. The dynamic response of the capsule subjected to periodic variations of the rate of strain is also studied. The response time τs appears to be an appropriate parameter to estimate the capsule adaptability to changing flow conditions.
A note on “critical roughness height” and “transitional roughness”
Authors: Bradshaw P.
Published: July 2002

An unrigorous but plausible analysis suggests that the concept of a critical roughness height, below which roughness does not affect a turbulent wall flow, is erroneous. The Oseen approximation implies that the effect of roughness on the additive constant in the logarithmic law of the wall should vary as the square of the roughness Reynolds number (specifically the roughness height in “wall units”). This is an important point in determining whether surfaces used in experiments at high unit Reynolds number can be regarded as hydraulically smooth. Attention is also called to the qualitative difference between Nikuradse’s measurements of friction factor in pipe flow with uniform-size sand-grain roughness in the “transitional” range of Reynolds number and the data correlation in the Moody chart of 1944; the latter was derived from tests on miscellaneous real-life rough surfaces in the 1930s. Nearly all textbooks on elementary fluid dynamics present, but practically none discuss, this difference. Nikuradse’s monodisperse roughness is a very rare case with untypical behavior in the transitional range.
Calculation of the dielectric tensor for a generalized Lorentzian (kappa) distribution function
Authors: Summers Danny , Xue Song , Thorne Richard M.
Published: July 2002

Expressions are derived for the elements of the dielectric tensor for linear waves propagating at an arbitrary angle to a uniform magnetic field in a fully hot plasma whose constituent particle species σ are modeled by generalized Lorentzian distribution functions. The expressions involve readily computable single integrals whose integrands involve only elementary functions, Bessel functions, and modified plasma dispersion functions, the latter being available in the form of finite algebraic series. Analytical forms for the integrals are derived in the limits λ→0 and λ→∞, where λ=(k⊥ρLσ)2/2, with k⊥ the component of wave vector perpendicular to the ambient magnetic field, and ρLσ the Larmor radius for the particle species σ. Consideration is given to the important limits of wave propagation parallel and perpendicular to the ambient magnetic field, and also to the cold plasma limit. Since most space plasmas are well modeled by generalized Lorentzian particle distribution functions, the results obtained in this paper provide a powerful tool for analyzing kinetic (micro-) instabilities in space plasmas in a very general context, limited only by the assumptions of linear plasma theory.
Stabilization of ballooning modes with sheared toroidal rotation
Authors: Miller R. L. , Waelbroeck F. L. , Hassam A. B. , Waltz R. E.
Published: July 2002

Stabilization of magnetohydrodynamic ballooning modes by sheared toroidal rotation is demonstrated using a shifted circle equilibrium model. A generalized ballooning mode representation is used to eliminate the fast Alfvén wave, and an initial value code solves the resulting equations. The s−α diagram (magnetic shear versus pressure gradient) of ballooning mode theory is extended to include rotational shear. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (dΩ/dq, where Ω is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and direct stable access to the second stability regime occurs when this frequency is approximately one-quarter to one-half the Alfvén frequency, ωA=VA/qR.
Theory and simulation of rotational shear stabilization of turbulence
Authors: Waltz R. E. , Dewar R. L. , Garbet X.
Published: July 2002

Numerical simulations of ion temperature gradient (ITG) mode transport with gyrofluid flux tube codes first lead to the rule that the turbulence is quenched when the critical E×B rotational shear rate γE−crit exceeds the maximum of ballooning mode growth rates γ0 without E×B shear [Waltz, Kerbel, and Milovich, Phys. Plasmas 1, 2229 (1994)]. The present work revisits the flux tube simulations reformulated in terms of Floquet ballooning modes which convect in the ballooning mode angle. This new formulation avoids linearly unstable “box modes” from discretizing in the ballooning angle and illustrates the true nonlinear nature of the stabilization in toroidal geometry. The linear eigenmodes can be linearly stable at small E×B shear rates, yet Floquet mode convective amplification allows turbulence to persist unless the critical shear rate is exceeded. The flux tube simulations and the γE−crit≈γ0 quench rule are valid only at vanishing relative gyroradius. Modifications and limits of validity on the quench rule are suggested from analyzing the finite relative gyroradius “ballooning-Schrödinger equation” [R. L. Dewar, Plasma Phys. Controlled Fusion 39, 437 (1997)], which treats general “profile shear” (x variation in γ0) and “profile curvature” (x2 profile variation).