bluuebunny/crossref_metadata_2025 huggingface dataset:
Cooper pairing of two-dimensional electrons in a quantizing magnetic field and the fractional quantum Hall effect
Authors: Pashitskiı̆ E. A.
Published: July 2002

A brief review of the current state of the theory of fractional quantum Hall effect (FQHE) is given along with the assumption of possible connection between the experimentally observed features of the Hall resistance RH of a two-dimensional (2D) electron system in a strong quantizing magnetic field for a fractional filling factor of the lowest Landau level ν=q/(2n+1) with q⩾2, which cannot be described by the Laughlin wave function antisymmetric relative to pair transpositions, and the Cooper pairing of 2D electrons. It is assumed that the electron–electron attraction essential for Cooper pairing can be due to the interaction of 2D electrons with the surface acoustic waves (2D phonons) and the surface 2D plasmons localized near the crystal interfaces (heterojunctions) in the vicinity of inversion layers in the metal–insulator–semiconductor (MIS) structures and heterostructures. The coexistence of coupled electron pairs and unpaired electrons under the FQHE conditions must lead to peculiarities of RH for values of ν described by the Halperin relation following from the symmetry properties of the “mixed” wave function of pairs (bosons) and electrons (fermions). This relation makes it possible in principle to describe all experimental data on FQHE. The summation of “ladder” diagrams diverging according to a power law for T→0 leads to a Bethe–Salpeter-type equation for the vertex part of the electron–electron interaction for a 2D system in a quantizing magnetic field taking into account electron–electron and electron–hole pairing in the Cooper and zero-sound channels. This equation is used to calculate the critical temperature Tc of the phase transition to the state with coupled Cooper pairs and to prove that the value of Tc in the ultra-quantum limit is independent of the effective mass of electrons, i.e., on the 2D density of states. The phase diagram of the 2D system is constructed for the variable electron concentration and magnetic field. It is shown that the region of Cooper pairing of 2D electrons in the case of strong attraction almost coincides with the FQHE region for ν<1, while the region of electron-hole pairing with the formation of charge-density waves (CDW) is expelled to the region with ν>1, which is in accord with the experimental data concerning the CDW-induced features of the longitudinal resistance Rxx for ν=(2n+1)/2 with n⩾2.
NMR study of the low-temperature phase of vanadium dioxide
Authors: Boyarskiı̆ L. A. , Gabuda S. P. , Kozlova S. G.
Published: July 2002

The magnetic shielding and quadrupole interaction constants of V51 nuclei in the low-temperature (nonconducting) phase of vanadium dioxide are determined by magnetic resonance on the V51 nuclei. It is shown that the metal–insulator transition in VO2 is accompanied by a change in the sign of the magnetic shielding constant and by an electronic transition 2V4+→V3++V5+, which is accompanied by a charge ordering in the cation sublattice.
High-frequency impedance of layered conductors in a high magnetic field
Authors: Peschanskiı̆ V. G. , Kozlov I. V. , Jiasemides K.
Published: July 2002

The propagation of electromagnetic waves in layered conductors is investigated theoretically for low temperatures, where it is extremely important to take into account the energy quantization of the charge carriers by the magnetic field. The quantum kinetic equation for the statistical operator is used to calculate the quantum oscillations of the surface impedance over a wide range of frequencies ω.
Rayleigh–Taylor instability of a continuously stratified magnetofluid under a general rotation field
Authors: Dávalos-Orozco L. A. , Aguilar-Rosas J. E.
Published: July 2002

The Rayleigh–Taylor instability of a continuously stratified magnetofluid under a general rotation field and a vertically stratified horizontal magnetic field is investigated. The upper bound for the growth rate of the perturbation is found and corrections to that obtained by Chakraborty [Phys. Fluids 25, 743 (1982)] are given. The theory predicts the formation of rolls appearing in natural rotating convection and magnetoconvection.
Bow flows in water of finite depth
Authors: Vanden-Broeck Jean-Marc
Published: July 2002

Free-surface flow past the bow of a ship in water of finite depth is considered. The bow is assumed to be a semi-infinite two-dimensional, flat-bottomed body with a vertical front. The problem is solved numerically by series truncation for various values of the Froude number F. It is shown that there are splashless flows for 1.22<F<(2)1/2.
Image processing of cylinder wake generation
Authors: Massons J. , Gavaldà Jna. , Díaz F. , Solé Ll.
Published: July 2002

In the present study, image processing techniques are applied to the chronophotographic visualizations of a cylinder wake generation. The flow patterns obtained by means of tracer particles are digitalized and processed in order to characterize the flow. This characterization is carried out by determining the evolution of the geometric parameters governing the wake, together with the streamfunction, vorticity, and pressure distributions. The present study reaches the moment of shedding of the first pair of vortices.
Nonlinear evolution and breaking of interfacial Rayleigh–Taylor waves
Authors: Oron Alexander , Rosenau Philip
Published: July 2002

The nonlinear evolution of interfacial waves separating liquids of different viscosity and density (Rayleigh–Taylor instability) in a 2-D channel is studied. Using a new approach, which accounts for large gradients, the nonlinear evolution of the interface, y=εA(τ,ξ),ε≪1, is shown to be governed by the regularized Kuramoto–Sivashinsky equation Aτ +βAAξ+{αA+γAξξ/ (1+ε4A2ξ)3/2}ξξ=0, where the constants α,β, and γ are determined at equilibrium, ξ is the slow coordinate along the channel, ξ=ε(x−c0t), and τ=ε2t. It is shown numerically that for ε2≥0.1β linearly unstable waves (while always of finite amplitude) are propelled by convection toward breaking in a finite time.
Growth of disturbances in a laminar boundary layer at Mach 3
Authors: Demetriades Anthony
Published: July 2002

The development of the disturbances preceding transition has been measured in the laminar boundary layer over an adiabatic flat plate at a stream Mach number of 3. The disturbances causing transition were found to begin growing at all frequencies, in a region long before the velocity profile departed from that given by laminar theory. This growth is monotonic and not predicted by classical linear stability theory. In addition, evidence was gathered that the first-mode instability predicted by this linear theory is also present, but that it plays a very minor role in the transition process.
Kinetic energy generated by the incompressible Richtmyer–Meshkov instability in a continuously stratified fluid
Authors: Saffman P. G. , Meiron D. I.
Published: July 2002

The problem of calculating the kinetic energy created by impulsive acceleration of an incompressible continuously stratified fluid is formulated. Solutions are obtained for small density perturbations and a particular profile for various Atwood numbers and length scales. The kinetic energy is reduced when the undisturbed density variation is more diffuse.
Chaotic dynamics of heavy particle dispersion: Fractal dimension versus dispersion coefficients
Authors: Wang Lian-Ping , Burton Thomas D. , Stock David E.
Published: July 2002

The chaotic dynamics of Lagrangian motion of particles in a steady Arnold–Beltrami–Childress (ABC) flow and a pseudoturbulence are investigated and the Lyapunov exponents and fractal dimensions of particle trajectories for different particle inertia and particle drift velocity are computed. The dispersion process of particles could be characterized by the fractal dimension and dispersion coefficients. The interesting behavior of fractal dimension of particle motion in ABC flow suggested the similarity of particle motion in ABC flow and in a mixing layer. The relationship between particle dispersion coefficient and fractal dimension was nearly linear for the pseudoturbulence.
Gallery of Fluid Motion
Authors: Reed Helen L.
Published: July 2002

This article displays winning photographs from the seventh Annual Fluid Mechanics Photo Contest held at the November 1989 meeting of the American Physical Society, Division of Fluid Dynamics, Palo Alto, California.
Mechanism for instability of fluid flow down an inclined plane
Authors: Hsieh D. Y.
Published: July 2002

The mechanism of the instability of a fluid flowing down an inclined plane is clarified by the recognition that the Reynolds number can also be interpreted as the Froude number.
Free-stream turbulence: A limitation on fractal descriptions of open-flow systems
Authors: Schneider Steven P.
Published: July 2002

Cylinder wake velocity measurements were made at Reynolds number 100 with varying levels of free-stream turbulence. The Grassberger–Procaccia (G–P) correlation function, which is often used for estimating fractal dimension, was computed for these data, and also for data obtained by adding random noise to the iterations of the Henon map. A comparison of the two plots shows that the free-stream turbulence acts as a highly random external noise source. Since free-stream turbulence determines the details of the smaller flow scales, no low-order dynamical system will be able to model all the scales in this open flow.
Low Reynolds number flow in and above asymmetric, triangular cavities
Authors: Chebbi B. , Tavoularis S.
Published: July 2002

The flow in and above asymmetric triangular cavities, simulating the scales on the surface of butterfly wings, has been studied in a special recirculating channel, filled with glycerol or water, using flow visualization and laser-Doppler velocimetry. The separation and reattachment points as well as the shape of the recirculation region are determined for different Reynolds numbers and angles of attack.
On the accurate calculation of vortex shedding
Authors: Anderson Christopher R. , Greengard Claude , Greengard Leslie , Rokhlin Vladimir
Published: July 2002

The issue of accuracy and convergence for numerical calculations in situations in which the exact solution of the Navier–Stokes equations (under the imposed initial and boundary conditions) is unstable is discussed. If one relies on roundoff error or truncation error (or the randomness of a stochastic scheme) in order to perturb the computed solution away from the unstable one, then the computed result cannot be accurate. Instead, one must explicitly provide perturbations in order to compute accurately flows of physical interest. Computational results for flow past an impulsively started cylinder are presented.
Faxén’s theorem for a circular cylinder in compressible flow with arbitrary slip
Authors: Weisenborn A. J. , ten Bosch B. I. M.
Published: July 2002

In this paper a derivation of the Faxén theorem for a circular cylinder moving unsteadily through a compressible fluid in arbitrary motion with arbitrary slip is presented. This theorem is a generalization of the Faxén formula for incompressible flow and the no-slip condition, derived by Varley and Zhou [Physica A 127, 363 (1984)].
On the asymmetry of structures in turbulent boundary layers
Authors: Choi W. C. , Guezennec Y. G.
Published: July 2002

Turbulence-producing events in the buffer region of a turbulent boundary layer were found to be associated with a significant probability of a nonzero spanwise velocity component at the time of maximum Reynolds stress. The conditional structures were reconstructed for various levels of spanwise velocity perturbations using the stochastic estimation. The resulting fields exhibit a marked asymmetry with one dominating vortical structure instead of a pair of counter-rotating ones.
Linearized geometrical-dynamics treatment of the stability of converging shocks
Authors: Book David L.
Published: July 2002

The approximation of geometrical shock dynamics has been used to study the stability of radially converging shocks of arbitrary initial strength. The equations of motion are linearized about the symmetric solution, using the shock Mach number as the independent variable, and solved numerically. Perturbations with angular dependence given by pure cylindrical (in two-dimensional) or spherical (in three-dimensional) harmonics exhibit damped oscillatory behavior for all but the lowest mode numbers. Relative to the decreasing shock radius R, however, they grow without bound. The solutions can be approximated by hypergeometric functions. The limiting behavior as R→0 is found using the asymptotic properties of the latter.
Inverse energy cascade in a nearly two-dimensional turbulence
Authors: Nakauchi Norihiko , Oshima Hiroshi , Saito Yoshio
Published: July 2002

Spectral structures of homogeneous axisymmetric turbulence subjected to a uniform magnetic field B0 and a randomly stirred two-dimensional force fed in a narrow band of wavenumbers is studied, using the energy spectrum equation that is closed by the eddy-damped quasinormal Markovian (EDQNM) approximation. When the interaction parameter N=σB20L/(ρ0u) is large (where σ is the electric conductivity, ρ0 the uniform fluid density, L the integral scale, and u the root mean square velocity), the existence of the inverse energy cascade toward large scales with a k−5/3 energy spectrum and the enstrophy cascade toward small scales with k−3 energy spectrum are observed in the evolution of the energy of velocity components transverse to B0. The energy of the velocity components parallel to B0 shows a k−1 energy spectrum, which agrees with the k−1 variance spectrum predicted by Lesieur and Herring [J. Fluid Mech. 161, 77 (1985)] for a passive scalar convected by two-dimensional isotropic turbulence. This is of great interest because it is found that in the limit of two-dimensional turbulence the equation for the parallel velocity components is reduced to the same equation as that for a passive scalar convected by two-dimensional isotropic turbulence.
A representation for the temperature field near the stagnation region in oblique stagnation flow
Authors: Lyell M. J.
Published: July 2002

Oblique stagnation flow has been the subject of previous work. In this Brief Communication, attention is restricted to the case in which the flow is steady, inviscid, and two dimensional. A general solution to the thermal field valid in the region of the stagnation point, which formally exhibits x dependence, is sought. Such a solution is obtained and then compared to the well-known similarity solution for temperature in the case in which the flow field is normal plane stagnation flow.
On the linear laws of thermodynamics of irreversible processes for slightly rarefied gas flows
Authors: Liu Guangjun
Published: July 2002

In rarefied gas flows the thermoviscous coupling phenomenon appears, and it cannot be described by ordinary, linear, irreversible thermodynamics. In this paper the formulas for the momentum and thermal fluxes in the slightly rarefied gas flows have been deduced by the use of the linearized 13-moment equations of Grad, and the thermoviscous coupling terms have been obtained. These formulas are expressed in the form of irreversible thermodynamics and the generalized linear laws and Onsager reciprocal relationship are given. The formula of entropy production has also been derived.
Shear flow coherent structures via Karhunen–Loève expansion
Authors: Rajaee Mojtaba , Karlsson Sture K. F.
Published: July 2002

The method of snapshots for Karhunen–Loève expansion has been applied to two-dimensional, two-component hot-wire data from the first pairing region of a weakly perturbed free shear layer. Almost 90% of the fluctuation energy is captured by the first four modes. The first and the second modes contain almost equal amounts of energy, as do the third and the fourth, and the time dependence for each pair is very nearly sinusoidal with the odd modes leading in phase by π/2.
Kinetic theory for mixtures of polyatomic gases of rough spherical molecules
Authors: Rodbard M. G. , Kremer G. M.
Published: July 2002

A kinetic theory for a mixture of ν-polyatomic gases of perfectly rough, perfectly elastic, and rigid spherical molecules is developed. A macroscopic state of the mixture is characterized by 16ν+1 fields of partial densities, partial velocities, partial pressure tensors, partial translational heat fluxes, partial rotational heat fluxes, and temperature of the mixture. The generalized laws of Fick, Fourier, and Navier–Stokes are obtained from an iteration method akin to the Maxwellian procedure. As an application, the transport coefficients for binary mixtures of CH4–CF4, CH4–CD4, and CD4–CF4 are determined.
Microbubble skin friction reduction on an axisymmetric body under the influence of applied axial pressure gradients
Authors: Clark H. , Deutsch S.
Published: July 2002

The influence of both a favorable and an adverse applied axial pressure gradient on microbubble-induced skin friction reduction was examined. An 87 mm diameter, 632 mm long model equipped with a 273 mm long cylindrical force balance was employed. Experiments were carried out in a 305 mm diameter water tunnel, at free-stream speeds of 4.6, 7.6, 10.7, 13.7, and 16.8 m/sec. Air was injected at rates as high as 12×10−3 m3/sec. Measurement of the static pressure along the body with gas injection demonstrated that gas injection did not alter the pressure gradient and that the flow remained axisymmetric. Reductions in skin friction for the zero pressure gradient case agreed well with the earlier results of Deutsch and Castano [Phys. Fluids 29, 3590 (1986)]. The adverse-gradient-induced separation of the boundary layer for speeds at and above 7.6 m/sec, for air injection rates in excess of 5.0×10−3 m3/sec. The favorable gradient strongly inhibited the drag reduction mechanism [47].
Recurrence and chaotic behavior resulting from nonlinear interaction between long and short waves
Authors: Yoshinaga Takao , Wakamiya Mamoru , Kakutani Tsunehiko
Published: July 2002

Long time asymptotic behavior resulting from nonlinear interaction between long and short waves is examined numerically by using the Fourier expansion method. A slightly modulated short wave is adopted as an initial condition. The results exhibit recurrence or chaotic motion, depending upon the magnitude of the control parameters involved in the governing equations. It is found that the chaotic motion is possible, even in a case for which only a single unstable mode exists in the Fourier modes.
Experimental study of the wavelength selection in a pentagonal vessel in Bénard convection
Authors: Cerisier P.
Published: July 2002

Experiments on Bénard convection are performed on silicon oil in a pentagonal vessel. Initially, a perfect convective hexagonal pattern is imposed with such an orientation that one side wall causes the appearance of orientation disorder, while the other four side walls do not perturb the pattern. The disorder first appears close to this wall and then, in the whole pattern. The amount of disorder and the wavelength are studied for the transient and the permanent states. The time evolution of the pattern depends on the distance to the threshold, but very slow or very fast evolutions are exhibited for particular values of this parameter. It is found that the final state is independent of initial conditions.
Convergence of Galerkin solutions using Karhunen–Loève expansions of inhomogeneous 1-D turbulence
Authors: Park S. B. , Sung H. J. , Chung M. K. , Adrian R. J.
Published: July 2002

The rate of convergence of the Karhunen–Loève expansion of an inhomogeneous, instantaneous random field is compared with that of Fourier expansion in relation to the Reynolds number. The model turbulence is generated by solving the Burgers’ equation with random forcing. The coefficients of the Fourier expansion are determined by a Galerkin solution scheme. The results show obvious superiority of the Karhunen–Loève expansion, especially for high Reynolds number flows.
Application of the principle of breaking ocean waves to mixing technology
Authors: Doman Michael
Published: July 2002

Turbulent mixing in the multiphase system of breaking ocean waves and whitecaps is known to play an important role in the mass exchange between ocean and atmosphere. Thus engineering applications to this naturally occurring dynamic exchange process appear to be of interest in various areas of applied mixing technology. Starting from the fact that ocean waves break after having reached their point of instability, a three-dimensional collapsible swivel mechanism (CSM) was developed for simulating by mechanical means the highly dynamic movement of breaking ocean waves. The CSM, employing reversion kinematics of a six-link spatial kinematic chain, has been realized in the construction of a new mixing technology (called swing mixer) that can either move the fluid by the use of mixing tools in a vessel (stirrer principle) or by moving the entire vessel (shaker principle). A first description of swing mixers has recently been given.1 A special characteristic of swing mixers is their three-dimensional reversing motion, the forward and backward paths being nonsuperimposable mirror images of one another. During the mixing process in swing mixers, the efficient mixing principle of repeated stretching and folding2 also takes place in the third dimension. Details of the mixing technology of swing mixers will be discussed together with some suggestions as to how spatial and temporal changes in the concentration may be determined with the help of CCD cameras in a given multiphase system agitated by swing mixers.
On creeping flow between a source and a sink in the presence of a sphere
Authors: Smith S. H.
Published: July 2002

Through analyzing a simple solution of the axisymmetric Stokes equations for slow viscous flow, it is possible to show how placing a finite body between a source and sink tends to expand the domain through which the exchange of mass takes place, whereas placing it on the same side tends to contract this domain.
Statistical and eddy structure approaches to turbulent mixing
Authors: Hunt J. C. R. , Malik N. A. , Perkins R. J.
Published: July 2002

For industrial and environmental purposes there is a need for broad concepts and general models to describe many types of mixing processes and situations. These concepts arise from exact conversation results,1 and the similarity of the velocity fields and the particle displacements in turbulent fields at high Reynolds number, especially in the presence of shear. However, the design and control of mixing, like other kinds of turbulent problems, is usually improved by considering quasideterministic models of how turbulent eddies affect the process. Such models are changing with new computations and experimental studies of turbulence structure. Mixing involves continuously bringing together volumes of fluid with different concentrations on small enough scales to effect mixing between molecules.

The Lagrangian statistical analysis of the displacements of fluid elements enables joint moments of concentration to be calculated in terms of initial concentration distributions in the absence of diffusion and reaction.2 This macromixing analysis in conjunction with simple concepts of small-scale mixing leads to models and a new understanding for many mixing processes, e.g., concentration fluctuations, simple chemical reactions, and the effects of varying the mean shear, the velocity spectra and the molecular diffusivity.3–7 Since extreme pollution concentrations and many complex chemical and physical processes can only be understood in a given scalar field, rather than from statistics of scalar fields, it is necessary to understand and model where and how mixing occurs in a single realization of the flow. This requires computing and/or measuring the evolving velocity and scalar fields in turbulent flows. Recent direct numerical simulations8–10 and kinematic simulations,11,12 i.e., velocity fields constructed from random Fourier modes, with observed or idealized two-point, two-time Eulerian and Lagrangian spectra, have shown (i) how surface areas expand exponentially, and volumes elongate only slightly;8,13 (ii) how scalar surfaces are deformed quite differently in different characteristic regions of turbulent flows; viz., vortical, eddy regions (rolling up into ‘‘fractal’’ surfaces), convergent–divergent, stagnating regions (stretching out, and nonfractal), and streaming regions (where tendrils form);14 (iii) how large volumes of matter disperse in particular events (which cannot be obtained from ensemble average statistics obtained from stochastic models based on displacements of one or two particles).15
Cavitating flow of a fluid with surface tension past a circular cylinder
Authors: Vanden-Broeck Jean-Marc
Published: July 2002

The effect of surface tension on the cavitating flow past a circular cylinder is considered. The problem is solved numerically for various values of the Weber number α and of the angular position γ of the separation points. It is shown that the angle β between the free surface and the surface of the cylinder is determined uniquely by specifying the values of α and γ.
A study of the effect of aspect ratio on vortex shedding behind circular cylinders
Authors: Lee T. , Budwig R.
Published: July 2002

The vortex shedding mode of circular cylinders at several aspect ratios is examined via spanwise flow visualization and hot-wire anemometry. For aspect ratios greater than 60 the shedding mode and shedding frequency results of previous investigators are compared with present results on cylinders with and without end modifications. For aspect ratios less than 60 the effects of rectangular endplates on vortex shedding are examined. The results reveal that nearly parallel shedding is generated in the wake of cylinders with appropriate endplates. The characteristics of this shedding are reported and a model is proposed to account for the production of nearly parallel shedding by the proximity of endplates.
Density gradient stabilization of the Richtmyer–Meshkov instability
Authors: Mikaelian Karnig O.
Published: July 2002

Numerical and analytical results on the growth rate of the Richtmyer–Meshkov (RM) instability in continuous density profiles are presented, and this paper relates them to the Rayleigh–Taylor (RT) instability by treating the shock as an instantaneous acceleration of incompressible fluids. Most of this work is in the linear regime, where it is found that density gradient stabilization is even more effective for the RM instability than for the RT instability. Recent experimental results are discussed and a numerical simulation of a shock-tube experiment with a continuous density profile between two gases is presented.
The role of the inviscid model for the long-wave instability of an inclined liquid layer
Authors: Smith Marc K.
Published: July 2002

The inviscid model used by Hsieh [Phys. Fluids 8, 1785 (1965); Phys. Fluids A 2, 1145 (1990)] for the study of the long-wave instability of an inclined liquid layer is shown to be equivalent to an approximate method for estimating the onset of the instability from the full viscous equations of motion. This implies that the mechanism of the instability is associated with a viscous flow as described by Smith [J. Fluid Mech. 217, 469 (1990)]; not an inviscid flow, as concluded by Hsieh.
On the stability of a cellular flow under a solidifying surface
Authors: Riahi D. N.
Published: July 2002

Nonlinear solutal convection in the melt under a planar solidifying surface is investigated in the limit of small segregation k and for cases where the amplitude of motion is not restricted to be small. In contrast to the small-amplitude case, it is found that there is no subcritical instability and that squares can be the only stable flow pattern for a significant range of amplitudes that widens as k decreases or as Péclet number z∞ increases. All the other flow structures are unstable with the exception of down-hexagons, which can be stable only in a narrow range of small amplitudes. This later range of amplitudes is independent of k, but it reduces in size as z∞ increases.
Numerical studies of transverse curvature effects on transonic flow stability
Authors: Macaraeg M. G. , Daudpota Q. I.
Published: July 2002

A numerical study of transverse curvature effects on compressible flow temporal stability for transonic to low supersonic Mach numbers is presented for axisymmetric modes. The mean flows studied include a similar boundary-layer profile and a nonsimilar axisymmetric boundary-layer solution. The effect of neglecting curvature in the mean flow produces only small quantitative changes in the disturbance growth rate. For transonic Mach numbers (1–1.4) and aerodynamically relevant Reynolds numbers (5000–10 000 based on displacement thickness), the maximum growth rate is found to increase with curvature—the maximum occurring at a nondimensional radius (based on displacement thickness) between 30 and 100.
On the continuum equations for dispersed particles in nonuniform flows
Authors: Reeks M. W.
Published: July 2002

The continuum equations of a dispersed phase of solid, noncolliding particles in a nonuniform turbulent gas flow are derived from a kinetic equation for the transport of the average phase space density 〈W(v,x,t)〉 for particles with velocity v and position x at time t. The crucial feature of this equation is the form given for the phase space diffusion current j representing the net acceleration of a particle from interactions with turbulent eddies. This is based on Kraichnan’s Lagrangian history direct interaction approximation which gives j=−[(∂/∂v)⋅μ+(∂/∂x)⋅λ+γ]〈W(v,x,t)〉, where μ, λ, and γ are dispersion tensors dependent upon displacements in the velocity and position of a particle about v,x in times of order of the time scale of the fluctuating aerodynamic driving force. Most important these tensors are affected by spatial variations in the mean carrier flow velocity and external force as well as inhomogeneities in the carrier phase turbulence; γ is zero for homogeneous turbulence. This form for j is invariant under a random Galilean transformation. The dispersed phase momentum and energy equations deduced from the kinetic equation contain local gradient forms for the net fluctuating interphase force (per unit volume) and its rate of working. The former contains in general an asymmetric stress component (which adds to the particle Reynolds stress) as well as a body force dependent upon inhomogeneities in the turbulence. Conditions are examined under which the mass and momentum equations reduce to a convection–diffusion equation. The convection velocity in this case is the local carrier flow velocity plus a drift velocity proportional to local gradients of the turbulence (zero if the particles follow the flow). The diffusion coefficient is linearly related to the pressure/mean density of the dispersed phase via the particle response time. It is shown to be influenced by the local mean shearing of the carrier flow. Conditions are derived when this contribution can be ignored, the diffusion coefficient reducing to the form for homogeneous turbulence.
A study of repeated vortex mergers in a forced quasi-2-D shear flow
Authors: Manin D. Yu.
Published: July 2002

A detailed analysis of a forced two-dimensional (2-D) shear flow with bottom friction is presented based on a numerical integration of the governing equation. The regime being analyzed features two vortices merging periodically, but with frequency decreasing in time. The slow symmetrization of the solution is shown to be responsible for the elongation of the period between mergers. A simple two-mode dynamical system is proposed as a model for mode interaction. An explanation is proposed for oscillatory regimes observed previously by different authors in laboratory experiments with quasi-2-D shear flows.
Discrete-velocity collision dynamics for polyatomic molecules
Authors: Goldstein David B.
Published: July 2002

A multispeed discrete-velocity molecular model of a rarefied gas is developed which permits quantitatively accurate simulation of mixtures of molecules of different mass which have both translational and internal rotational energies. In particular, the molecules are represented as having three discrete velocity components and a single discrete internal energy that does not directly affect the translational motion. During binary collisions, rotational and translational kinetic energies are exchanged according to a phenomenological model. Results are presented for the thermal relaxation to equilibrium of mixtures of H2 and Ne, N2 and O2, and N2 and CO2. Good agreement is found with the corresponding continuous-velocity results.
The Ginzburg–Landau equation for interfacial instabilities
Authors: Pierce R.
Published: July 2002

A coherent method for pursuing a numerical multiple scales analysis of an interface problem is presented. Finding numerical boundary conditions for the homogeneous adjoint problem and evaluation of surface terms in the inhomogeneous solvability criteria is reduced to one singular value decomposition. The method is applied to derive the complex Ginzburg–Landau equation for plane Poiseuille flow with compliant walls of finite thickness. The wall model is simple yet unprecedented in that the wall response is maintained as an independent variable throughout the wall thickness. Only small amplitude states are considered, but this type of analysis is a necessary prerequisite to the study of three-dimensional instability of finite-amplitude states in the presence of compliant walls. The effect of variations in wall thickness on the coefficients is briefly explored.
Two-headed detonation in reactive particle-oxidizing gas flow
Authors: Zhang F. , Grönig H.
Published: July 2002

The structure and the propagation mechanism of stable two-headed detonation waves in a heterogeneous cornstarch particle–oxygen mixture have been studied in a circular tube 141 mm in diameter. Pressure transducers and double response gauges responding to both the shock and combustion front have been used for observations in a 0.5 m long test section, which has 32 gauge positions arranged on four circumferences. The results show that at the detonation wave front, two Mach triple-point configurations exist on the periphery. The collision of the two triple points leads to an overdriven wave followed by a transient decay, which requires continual regeneration by collisions for sustained propagation. The trajectory of the two triple points form a single cell, whose width is equal to π times the tube diameter. Degeneration of a transient two-headed mode results in one kind of onset mechanisms of a stable single-headed spin.
Diffusion from a point source in a time-dependent unbounded extensional flow
Authors: Krishnan Gokul P. , Leighton David T.
Published: July 2002

In this paper, the solution for diffusion from a point source in a time-dependent pure extensional flow is presented. The convective diffusion equation is shown to separate for this flow field, and the resulting reduced equations can be solved exactly for arbitrary time dependence. Both planar and uniaxial extensional flows are examined.
The dependence of the dissipation on rotation
Authors: Ristorcelli J. R. , Lumley J. L.
Published: July 2002

A form of the evolution equation for the dissipation showing the effects of rotation is derived directly from the Navier–Stokes equations. Rotation affects the dissipation if the flow is inhomogeneous or compressible. This is due to the fact that pressure scales with inverse Rossby number and certain pressure correlations usually neglected have to be retained when Re Ro≊1. The term reflecting the effects of rotation on the dissipation is a volume integral of the two-point velocity correlation similar in structure to the ‘‘rapid-pressure’’ correlation appearing in the second-moment equations. Some of its properties are indicated.
Vortex dipoles impinging on circular cylinders
Authors: Orlandi P.
Published: July 2002

Vortex pairs interacting with a circular cylinder have been simulated by the numerical simulation of the two-dimensional Navier–Stokes equation in the vorticity streamfunction formulation. The interaction with a cylinder with a diameter equal to the diameter of the dipole has been simulated in the inviscid case with free-slip boundaries. This case has been considered as a way to perturb the initial dipole, which splits into two vortices that rejoin at a different location on the cylinder depending on the initial displacement of the cylinder from the centerline of the primary vortex pair. By the scatter plots it was shown that the Lamb dipole after the perturbation relaxes to its initial k2ψ functional relationship. The case of no-slip interaction has been considered when the cylinder is two orders of magnitude smaller than the dipole. The same features observed in the experiment of Homa et al. [J. Fluid Mech. 197, 571 (1988)] are obtained by the numerical simulations, that is a thin vorticity layer is generated at the cylinder, it rolls up and forms dipolar and tripolar structures, depending on the initial displacement of the cylinder from the centerline of the incoming dipole. Scatter plots of the vortex pair formed by the primary and secondary vorticity show a linear distribution similar to that of the Lamb dipole. The dependence on the Reynolds number has been investigated.
Vortex drift. II: The flow potential surrounding a drifting vortical region
Authors: Rott Nicholas , Cantwell Brian
Published: July 2002

The potential flowfield surrounding a vortical flow domain is investigated. The vortical region is restricted to a three-dimensional finite domain in an unbounded incompressible viscous fluid that is at rest at infinity. The vector streamfunction of the flow is obtained by the integrals over the given vorticity field, expressing the Biot–Savart law. In the approach proposed here, the asymptotic vector streamfunction in the far field is expressed by integrals that represent the moments of the vorticity vector field. The asymptotic far-field potential is then determined by an integration that is analogous to the procedure well known in two dimensions, where the conjugate potential is found in the case that the streamfunction is known. In three dimensions, no general formula was found but an explicit expression for the asymptotic potential was constructed for the far-field dipole and quadrupole. The integrability conditions that permit the determination of the potential from the vector streamfunction are interpreted as the consequence of the requirement that the underlying vorticity field has to be source free. The asymptotic potentials are discussed first using only the inherent symmetries of the general dipole and the quadrupole fields. The results are then specialized to the case of axial symmetry. It will be shown that (i) the dipole strength is invariant and that (ii) the strength of the flow quadrupole remains constant while it moves together with the dipole with the drift speed already postulated in Part I. The role of the pressure in the flow generating process is also briefly noted.
Normalization based on the active motion in a turbulent boundary layer
Authors: Antonia R. A. , Anselmet F. , Fulachier L.
Published: July 2002

A comparison between the inner regions of self-preserving turbulent boundary layers over an impervious wall and a porous surface with a uniform moderate suction rate indicates that, in each case, the relevant velocity and length scales are those of the ‘‘active’’ motion. There is close agreement between the two flows for velocity and temperature variances and longitudinal heat fluxes when the measurements are conditioned on only the negative part of the Reynolds shear stress and are normalized by the scales of the active motion
Pulsatile flow in a rotating straight pipe: I. Analysis of the fluid motion inside a nutation fluid damper
Authors: Lei U. , Ho C. F.
Published: July 2002

Rigorous analysis shows that the spin synchronous mode fluid motion inside a nutation fluid damper on board of a spinning satellite can be modeled as an incompressible, laminar pulsatile flow in a circular straight pipe. The pipe rotates with constant angular velocity ω_ about an axis perpendicular to its own axis. The distance between the rotation axis and the pipe axis is much greater than a, the pipe’s radius. The flow is driven by a three-dimensional harmonic oscillation of the pipe wall with frequency Ω and amplitude w′0, and is governed by three-dimensionless parameters: RΩ(=Ωa2/ν), Δ(=ω/Ω), and A( = w′0/Ωa), where ν is the kinematic viscosity of the fluid. Both the asymptotic analysis and the numerical calculation have been carried out for RΩ=0.1–1000 and Δ=0–2 under A≪1. It is found that the rotating effect increases the energy dissipation significantly in comparison with the result of the pulsatile straight pipe flow in an inertia frame (the previous theory for the nutation damper). For Δ=1.5, the energy dissipation in a rotating pipe flow is 5.43 times that in a ‘‘stationary’’ pipe flow for large RΩ, which agrees with the previous experiment. A steady stream is induced by the convective effect for finite values of A. Such steady motion is consisted of axial counter flows together with pairs of counter-rotating vortices in the cross-sectional plane.
Vorticity dynamics and scalar transport in separated and reattached flow on a blunt plate
Authors: Tafti Danesh
Published: July 2002

Two-dimensional calculations are performed for a Reynolds number of 1000 and an effective Prandtl number of unity to study the dynamics of large-scale spanwise vortices with a passive scalar field in a separation and reattaching flow over a blunt plate. A triple decomposition technique is used to isolate the quasiperiodic fluctuations related to the large-scale vortices shed from the separated shear layer. Three vortex shedding modes are identified in the reattachment zone, two of which involve partial pairings. The coherent vortices shed from the reattachment zone have a dominating effect on scalar transport, and act as ‘‘large-scale mixers’’ by entraining wall scalar around their upstream periphery and free-stream scalar on their lower downstream edge. There is a definite relationship between the phase-averaged perturbations (due to the presence of coherent vortices) in the wall friction factor and wall scalar transport with their respective time mean maximums. On the other hand, although there does exist an explicit spatial relationship between the instantaneous stagnation point and instantaneous location of maximum wall scalar transport, there is no such relationship in the mean between the two locations, except that both are dependent on the vorticity dynamics in the reattachment region.
The Burnett equations for a Lorentzian mixture
Authors: Uribe F. J. , García Colín L. S.
Published: July 2002

It is shown that for a binary mixture of dilute gases characterized by the Boltzmann equation the Burnett contribution for the fluxes can be evaluated without solving the integrodifferential equations for the corrections to the distribution function to third order in the Chapman–Enskog method. The conservation equations can be closed knowing only the second-order solution (in the Chapman–Enskog method) to the Boltzmann equation which is well known. By considering a trace component of light particles in a heavy gas (Lorentz approximation) all the higher-order transport coefficients for the soft-sphere model can be evaluated and from these results an estimation of the Burnett corrections to the Navier–Stokes regime is given. Other pertinent results of this calculation are also discussed.
Stochastic electron beams in the ion-focused regime
Authors: O’Brien K. J.
Published: July 2002

In this paper the concept of a stochastic electron beam is introduced. A stochastic electron beam is one for which the transverse dynamics is chaotic. Utilizing adiabatic orbits, the resonance overlap condition for transition to stochasticity in a particular electron beam system, the ‘‘triple-Bennett configuration,’’ is derived. The tangent map is derived and used to state conditions for strong orbit instability and the resulting exponential decay of phase correlations. The dependence of the K entropy on the strength ε of the nonaxisymmetry of the triple-Bennett configuration is investigated numerically. Implications for the suppression of the ion-hose instability in the ion-focused regime are briefly discussed.
The behavior of acceleration waves in radiation magnetogasdynamic flow
Authors: Shankar Rama , Prabhu S. S.
Published: July 2002

The method of characteristics is used to study the propagation of acceleration waves in a radiation magnetogasdynamic flow, which is induced by the motion of a piston advancing with a finite acceleration into a constant state of rest. The analysis assumes an azimuthal magnetic field produced by a constant current flowing along the axis. The characteristic solutions have been obtained in the neighborhood of leading forward characteristics. The critical values of the initial amplitude and critical time for breakdown of an acceleration wave at the cusp of the envelope of intersecting forward characteristics have been obtained. It has been shown that the effect of coupling of the radiation and the magnetic field on compression waves, which are emanating from piston movement, is to slow down the motion of a breakdown point, and thus to increase the cylindrical shock formation time, while the effect on expansion waves is to enhance the decay rate.
Experimental studies of the rotational stability of a tandem mirror with quadrupole end cells
Authors: Severn G. D. , Hershkowitz N. , Breun R. A. , Ferron J. R.
Published: July 2002

It is demonstrated that the radial electric field in the Phaedrus Tandem Mirror [Plasma Physics and Controlled Nuclear Fusion Research 1984 (IAEA, Vienna, 1985), Vol. 2, p. 265] can be altered using plasma potential control rings (PPC rings) situated at each end of the device, and the azimuthal plasma rotational velocity may thus be varied. Low-frequency (ω≪ωci), low azimuthal mode number (m=−1 and m=−2) instabilities driven by E×B rotation are observed and shown to be in qualitative agreement with the theory of Freidberg and D’Ippolito [Phys. Fluids 26, 2657 (1983)], and Phillips [Phys. Fluids 27, 1783 (1984)] for the case when Phaedrus is operated as a conventional tandem mirror with minimum-‖B‖ end cells.
An estimate of the ion orbit loss rate in tokamaks
Authors: Shaing K. C.
Published: July 2002

The ion orbit loss rate in the edge region of a tokamak is estimated from an orbit-averaged Coulomb collision operator. The mechanism of the ion orbit loss in a tokamak is qualitatively different from that of the electron loss in a mirror machine, because ion orbit loss in a tokamak results from the coupling between the configuration-space diffusion and the velocity-space scattering, while the electron loss in a mirror machine results from the velocity-space scattering. Despite this difference, the magnitudes of the ion orbit loss rate in a tokamak estimated from these two concepts are similar. Because the ion orbit loss flux is related to the plasma viscosity, it represents a loss of poloidal momentum.
Circular magnetic macroparticle accelerator to reach thermonuclear ignition
Authors: Winterberg F.
Published: July 2002

A circular magnetic macroparticle accelerator for impact fusion, making use of the skin effect in the accelerator ring, is proposed. The macroparticle can be either a ferromagnetic or magnetized superconducting projectile. If the accelerator ring consists of a good conductor, then the magnetic field of a rapidly moving projectile has no time to penetrate into the conductor. As a result, the magnetic field of the projectile generates a virtual mirror image in the conductor, repelling the projectile with the same force as the force generated by the magnetic field of the projectile itself, and thereby counteracting the centrifugal force. Since under the condition of the skin effect, the conductor behaves like a perfect diamagnetic, the projectile can be accelerated in a stable orbit if the cross section of the conductor forms a trough.