bluuebunny/crossref_metadata_2025 huggingface dataset:
Effects of a poloidally asymmetric ionization source on toroidal drift wave stability and the generation of sheared parallel flow
Authors: Ware A. S. , Diamond P. H.
Published: July 2002

The effects of a poloidally asymmetric ionization source on both dissipative toroidal drift wave stability and the generation of mean sheared parallel flow are examined. The first part of this work extends the development of a local model of ionization-driven drift wave turbulence [Phys. Fluids B 4, 877 (1992)] to include the effects of magnetic shear and poloidal source asymmetry, as well as poloidal mode coupling due to both magnetic drifts and the source asymmetry. Numerical and analytic investigation confirm that ionization effects can destabilize collisional toroidal drift waves. However, the mode structure is determined primarily by the magnetic drifts, and is not overly effected by the poloidal source asymmetry. The ionization source drives a purely inward particle flux, which can explain the anomalously rapid uptake of particles which occurs in response to gas puffing. In the second part of this work, the role poloidal asymmetries in both the source and turbulent particle diffusion play in the generation of sheared mean parallel flow is examined. Analysis indicates that predictions of sonic parallel shear flow [v∥(r)∼cs] are an unphysical result of the assumption of purely parallel flow (i.e., v⊥=0) and the neglect of turbulent parallel momentum transport. Results indicate that the flow produced is subcritical to the parallel shear flow instability when diamagnetic effects are properly considered.
Dielectric tensor operator of hot plasmas in toroidal axisymmetric systems
Authors: Brunner S. , Vaclavik J.
Published: July 2002

Kinetic theory is used to develop equations describing dynamics of small-amplitude electromagnetic perturbations in toroidal axisymmetric plasmas. The closed Vlasov–Maxwell equations are first solved for a hot stationary plasma using the expansion in the small parameter εe=ρ/L, where ρ is the Larmor radius and L a characteristic length scale of the stationary state. The ordering and additional assumptions are specified so as to obtain the well-known Grad–Shafranov equation. The dielectric tensor of such a plasma is then derived. The Vlasov equation for the perturbed distribution function is solved by the expansion in the small parameters εe and εp=ρ/λ, where λ is a characteristic wavelength of the perturbing electromagnetic field. The solution is obtained up to the first order in εe and the second order in εp. By integrating the resulting distribution function over velocity space, an explicit expression for the tensor is derived in the form of a two-dimensional partial differential operator. The operator is shown to possess the proper symmetry corresponding to the energy conservation law.
Effect of equilibrium radial electric field on trapped-particle stability in tandem mirrors
Authors: Kesner Jay , Lane Barton
Published: July 2002

A low-beta tandem-mirror trapped-particle instability theory is developed for arbitrary azimuthal mode number including the effects of radial equilibrium electric fields. A stability window is seen to exist for inward-pointing electric fields even when passing electrons bounce beyond passing ions. This stability window can persist at zero radial electric field when the instability drive is sufficiently small. The theory also predicts the possibility of an additional instability when E×B rotation is present: a rotationally driven trapped-particle mode.
Large probes in tokamak scrape-off plasmas. Analytic model for the collisionless scrape-off plasma
Authors: Stangeby P. C.
Published: July 2002

When large probes are used to measure plasma properties in tokamak scrape-off layers, the presence of the probe influences the plasma being measured. A theory is presented for probe interpretation which makes it possible to infer undisturbed values of Te, Ti, ne, etc. The first requirement in such an analysis is for analytic models of the scrape-off layer, which can then be modified to allow for the presence of the probe. The present work gives such a model for the collisionless scrape-off layer, and criteria are stated governing its applicability. Such models may be of use for other applications, e.g., predictions of power loading to limiter surfaces, the magnitude of wall sputtering, etc.
Three-dimensional magnetohydrodynamic studies of the reversed-field pinch
Authors: Schnack D. D. , Caramana E. J. , Nebel R. A.
Published: July 2002

Three-dimensional computational studies of nonlinear resistive megnetohydrodynamic (MHD) instabilities in the reversed-field pinch are presented. It is found that multihelicity mode coupling effects alter the evolution of m=1 modes from that obtained in single helicity. Strong mode coupling to m=0 and m=2 is observed. Magnetic island overlap results in stochastic field lines. At low values of the pinch parameter this is confined to the central region of the pinch; for larger values the stochasticity may extend to the wall. Healing of outer flux surfaces is observed as modes peak and relax. Decay of positive toroidal flux is retarded. Impact on confinement is discussed, and connection is made with experimental observations.
Nonlinear destabilization of tearing modes
Authors: Murtaza G. , Shukla P. K. , Yu M. Y.
Published: July 2002

It is shown that a spectrum of stationary electrostatic fluctuations can destabilize the tearing modes. Since the growth of this nonlinear instability is rapid, it can affect the plasma confinement in magnetic fusion devices.
Absorption of waves in the second harmonic resonance layer
Authors: Imre Kaya , Weitzner Harold
Published: July 2002

Absorption caused by relativistic broadening of quasiperpendicular incident waves within the second cyclotron harmonic layer is investigated in an inhomogeneous electron plasma. The resonance region is treated by a boundary layer analysis, and field equations valid in this region are derived by solving the rescaled (with respect to the parameter η which is the ratio of the thermal speed and the speed of light) linearized relativistic Vlasov equation. The geometrical optics solutions valid in the nonresonant region are evaluated near the resonance, and they are connected to the asymptotic forms of the inner solutions. The energy conservation theorems appropriate for this problem allow the evaluation of fractional transmitted and reflected energy, and thus distinguish between the energy mode converted to the quasielectrostatic (relativistic Bernstein) mode and that absorbed by the plasma (which does not exist for the purely perpendicular propagation and nonrelativistic case). Numerical methods are developed which enable one to handle the computation of the excessively stiff differential equations in the high-field side. The three fundamental scattering problems are then evaluated numerically for various values of electron density and the product of electron temperature and scale length for the variation of the magnetic field for the case of perpendicular propagation. It is found that, unlike the mode coupling, the transmission of the X mode is not affected by the relativistic corrections. In the case of high-field side incidence, the reflection is still zero as predicted in the nonrelativistic approach. However, in contrast to the zero absorption in the nonrelativistic case, there is significant absorption caused by relativistic broadening, particularly in the case of low-field side incidence.
Backward wave oscillators with rippled wall resonators: Analytic theory and numerical simulation
Authors: Swegle John A. , Poukey James W. , Leifeste Gordon T.
Published: July 2002

In this paper, a comprehensive theoretical treatment is developed for backward wave oscillators composed of a relativistic electron beam guided by a strong magnetic field through a slow wave structure consisting of a cylindrical waveguide with a sinusoidally varying wall radius. This analysis, equally applicable to traveling wave tube operation, includes both a linearized theory of small-amplitude perturbations and numerical simulations of the saturated, large-amplitude operating regime. The variation of device operating characteristics with system parameters is examined in detail. Comparisons of the analytic and numerical results with experiments and additional calculations show excellent agreement and justify a high degree of confidence in the validity of the theory.
Nearly perpendicular wave propagation at the fundamental electron-cyclotron resonance
Authors: Imre Kaya , Weitzner Harold
Published: July 2002

Waves propagating nearly perpendicular to the equilibrium magnetic field across the fundamental cyclotron resonance layer are studied by a boundary layer analysis for a weakly relativistic, inhomogeneous Vlasov plasma. The plasma is assumed to be perpendicularly stratified. It is found that the wave energy associated with the ordinary mode transmitted through the layer is independent of the relativistic corrections and is given by a geometrical optics formula. It is also found that there is no reflected energy associated with this mode when it is incident from the high-field side. These results are the same as the nonrelativistic case with purely perpendicular propagation. Relativistic effects produce a significant reduction of the reflection coefficient for low-field side incidence from the nonrelativistic value. Correspondingly, for this mode there is a considerable increase in the absorption rate for sufficiently high, but moderate, electron density and temperature.
Forced magnetohydrodynamic turbulence in a uniform external magnetic field
Authors: Hossain Murshed , Vahala George , Montgomery David
Published: July 2002

Two-dimensional dissipative magnetohydrodynamic turbulence is randomly driven at small spatial scales and is studied by numerical simulation in the presence of a strong uniform external magnetic field. A novel behavior is observed which is apparently distinct from the inverse cascade that prevails in the absence of an external magnetic field. The magnetic spectrum becomes dominated by the three longest-wavelength Alfvén waves in the system allowed by the boundary conditions: those which, in a box size of edge 2π, have wavenumbers (kx,ky) =(1,0),(1,1), and (1,−1), where the external magnetic field is in the x direction. At any given instant, one of these three modes dominates the vector potential spectrum, but they do not constitute a resonantly coupled triad. Rather, they are apparently coupled by the smaller-scale turbulence.
Stability of transverse monopole oscillations in periodic beam–beam focusing
Authors: Takayama Ken
Published: July 2002

The stability of the transverse monopole oscillation is considered in contrarotating, reciprocally pinched, cylindrically symmetric beams bunched in the moving direction. The problem is reduced to coupled and time-dependent ordinary second-order linear differential equations for the perturbed beam envelope functions. The equations are solved exactly and the self-consistent stability condition for transverse monopole oscillations is derived to first order.
Thermoconvective waves in a binary mixture
Authors: Bhattacharyya S. N. , Gupta A. S.
Published: July 2002

The propagation of undamped transverse thermal waves in a layer of binary mixture is investigated. It is shown that when the thermal diffusivity KT is equal to the mass diffusivity KS, such waves do not exist. But when KT>KS, these waves may exist provided the layer is heated from below (such that thermohaline instability does not occur) and the concentration of the solute in the mixture decreases vertically upward. The analysis also reveals the interesting result that when KT<KS, undamped waves can propagate even if the layer is heated from above provided the concentration increases vertically upward. It is further shown that as in a homogeneous fluid, weakly damped low-frequency waves can propagate and the regions in the parameter space where such propagation is possible are delineated. High-frequency waves are shown to be always strongly damped.
A nonlinear diocotron mode
Authors: Prasad S. A. , Malmberg J. H.
Published: July 2002

A perturbation procedure for the construction of a nonlinear diocotron mode of an infinite length cylindrical pure electron plasma column is presented. The plasma is modeled as a cold fluid executing E×B drift in a strong axial magnetic field. The mode has no axial variation and depends on θ (azimuthal angle) and t (time) through the combination θ−Ωt. Thus the potential and the density are stationary in the frame rotating with angular frequency Ω. In this frame, the potential satisfies the relation ∇2φ=F(φ) where F is a function of φ only. This equation is solved perturbatively to determine a nonlinear mode supported by a cylindrically symmetric equilibrium density profile. The properties of the mode depend only on the offset of the plasma column from the axis of the bounding conducting cylinder and the frequency of the mode is larger than the value predicted by linear theory by an amount roughly proportional to the square of the offset.
The combined Rayleigh, Kelvin–Helmholtz problem
Authors: Chimonas G.
Published: July 2002

Stability characteristics of a model tilted shear flow are studied. The model allows a formulation that can be readily solved for all orientations of the shear from the Rayleigh case through to the Kelvin–Helmholtz case. It is found that any tilt away from the strict Kelvin–Helmholtz situation destabilizes the flow, no matter how large the Richardson number. The transition from the Rayleigh limit to the Kelvin–Helmholtz limit proceeds smoothly, with the stability curves displaying a characteristic pattern of evolution.
Steady flow past sudden expansions at large Reynolds number. Part I: Boundary layer solutions
Authors: Milos Frank S. , Acrivos Andreas
Published: July 2002

In the steady laminar flow past a sudden channel expansion at large Reynolds number R, the longitudinal length scale of the separated eddy typically increases linearly with R whereas the transverse length scale is O(1). If these trends were to continue indefinitely, the equations of motion in the bulk flow would reduce to the boundary layer equations as R→∞. Previous investigators obtained steady finite difference solutions to the latter for all values of the expansion ratio when the inlet velocity profile was parabolic; however, when the inflow was uniform, numerical instabilities were encountered below a certain value of the expansion ratio. In the present work these instabilities are avoided through the use of a global Newton method, and uniform inflows to several sudden expansion geometries are considered. In each case steady solutions are found only above a critical value of the expansion ratio where the pressure gradient becomes singular near the reattachment point. These results suggest that for uniform inflows and smaller values of the expansion ratio, the eddy length will no longer increase linearly with R when the latter is sufficiently large.
Macroscale particle simulation of relativistic electron beam injection into a magnetized plasma channel
Authors: Tanaka Motohiko , Sato Tetsuya
Published: July 2002

A large-scale particle simulation of an intense relativistic electron beam injection into a longitudinally periodic and magnetized, three-dimensional plasma channel is performed with application to the steady-state current drive of tokamaks. It is found that the electromagnetically beam-induced electric field uniformly decelerates the beam electrons and generates a plasma return current as far as the injection continues. The beam electrons are decelerated also by the scaler potential field especially before the beam path becomes closed. A net longitudinal current, and hence the azimuthal magnetic field, is formed in the vicinity of the beam path after the return current has reached a steady force–balance equilibrium with the electric field and anomalous friction. The net saturation current is independent of the injection beam current and is scaled as Inet∼(γ2−1)1/2, where γ=(1−v2b/c2)−1/2 and vb is the velocity of the electron beam. For γ≫1, a macroscale helical instability develops and prevents the net current from reaching the level given by the aforementioned scaling. This instability is suppressed by application of a strong longitudinal magnetic field, which recovers the net current of the previous scaling.
Saturated tearing modes in toroidal geometry
Authors: Bateman Glenn , Morris R. N.
Published: July 2002

A quasilinear method is developed for determining saturated tearing mode magnetic island widths in axisymmetric toroidal plasmas with arbitrary cross-sectional shape, aspect ratio, or plasma pressure (beta). The method is applied to compute magnetic island widths in force-free toroidal plasmas with aspect ratio as low as 2.0 and elongation between 1.0 and 2.0. It is found that current suppression within the magnetic island strongly increases the saturated width while current peaking reduces width. The effects of current profile, geometry, and harmonic mixing are also studied.
Resistive-heating instability of a compressible, force-free plasma
Authors: Sparks L. , Van Hoven G.
Published: July 2002

The thermal stability of a resistive, force-free plasma in a two-dimensional, slab geometry is investigated numerically. Linearly unstable modes that arise as an energetic consequence of Ohmic heating are examined in relation to the dynamic magnetic-tearing instability. Plasma compression is found to give rise to a set of unstable thermal modes not seen in previous incompressible studies. Such modes can occur in parameter regimes where no purely growing tearing mode exists.
Flow structures in the developing region of a symmetric wake and an unsymmetric wake
Authors: Miau Jiun-Jih , Karlsson Sture K. F.
Published: July 2002

A conditional sampling technique was designed and employed to determine the ensemble-averaged flow structures in the developing region of a symmetric wake (r=1.0) and an unsymmetric wake (r=0.5). It was found that at a velocity ratio of 0.5 the large scale structure, which was observed from a reference frame traveling with its phase speed, is initially confined in the high-speed stream, elongated in the stream direction, and is shaped elliptically. As the flow convects downstream it grows in the cross-stream direction, as well as tilting toward the wake center, and then evolves into a nearly circular shape. Results for a velocity ratio of 1.0, corresponding to the case of a 2-D wake flow, show that two rows of counter-rotating vortices develop in two streams originating in the linear instability region. Similar to the case for r=0.5, these vortices grow, as well as tilt, when the flow convects them downstream. However, the growth rate of these flow structures is slower than that of the case for r=0.5.
Plasma heating through a supercritical oblique collisionless shock
Authors: Lembège B. , Dawson J. M.
Published: July 2002

Electron and ion dynamics are investigated through particle simulation of a supercritical oblique collisionless shock. As θ deviates from 90°, ions are accelerated and trapped in the electrostatic wells and later become detrapped; this results in strong ion heating perpendicular to B0. Below a critical angle θte electrons are strongly energized along B0, and heated. A large parallel electron current builds up and induces new transverse electromagnetic components in the ramp of the shock. For weaker angles, ion heating vanishes below a second critical angle θti.
Diamagnetic drift effects on ion Bernstein mode propagation in a plasma slab
Authors: Ferraro R. D. , Fried B. D.
Published: July 2002

A one-dimensional infinite-order differential equation that describes the propagation of small amplitude electrostatic waves through a uniformly magnetized inhomogeneous plasma slab is derived. The spatially varying coefficients of the equation may be written in terms of an arbitrary density profile function provided that the velocity space distribution of the equilibrium is Maxwellian and the plasma is charge neutral. Ion Bernstein waves with frequencies between the first and second ion cyclotron harmonics and wavelengths along the density inhomogeneity larger than the ion Larmor radius are adequately modeled by truncating the differential equation at second order. Using a single mode electrostatic antenna to investigate the role of the diamagnetic drift on Bernstein wave propagation, a wavenumber dependence in the position of the low density cutoff for propagation is found, resulting in a preferential coupling of the antenna to waves with moderate kz∥ B propagating antiparallel to the ion diamagnetic drift. Moderate levels of Bernstein wave activity inside the plasma are demonstrated for an antenna located in the evanescent region.
Halo formation and hollowing in relativistic electron beams
Authors: Hubbard Richard F. , Lampe Martin , Slinker Steven P. , Joyce Glenn
Published: July 2002

A relativistic electron beam propagating through dense gas may evolve into a variety of current density profiles Jb(r) depending on the beam temperature T and plasma current profile Jp(r). Four broad classes of equilibria are discernible in particle simulations: (1) Bennett-like or compact, (2) core and halo, (3) on-axis hollowed, and (4) off-axis hollowed. The qualitative features of each class are reproduced in a simple analytical model that assumes an isothermal beam and a Bennett plasma current profile and iterates about an initial ansatz of a Bennett beam current profile. Bennett-like equilibria are produced when the return current fraction f is small or when T/TB=1−f, where TB=eIb/2c is the Bennett temperature. For T/TB >1−f and moderate or high f, the equilibrium consists of a compact core surrounded by a halo, which may contain most of the beam current. In extreme cases (T/TB≫1−f and f close to unity) an off-axis density minimum occurs. (This is also referred to as off-axis hollowing.) For T/TB<1−f  and moderate or high f, the beam core is broader than the plasma current profile, and on-axis hollowing results. Simulations with the ultrarelativistic sarlac simulation code [Bull. Am. Phys. Soc. 31, 1429 (1986); Phys. Fluids 29, 3056 (1986)] exhibit all of these types of equilibria. sarlac also treats transverse beam distortion arising from the resistive hose instability. Hose instability growth appears to be strongly enhanced when halos are generated.
The electrostatic two-stream instability driven by slab-shaped and cylindrical beams injected into plasmas
Authors: Galvez Miguel , Borovsky Joseph E.
Published: July 2002

An electrostatic linear analysis is performed for a finite-width electron or ion beam streaming along a strong magnetic field in the presence of a homogeneous background plasma. The linear fluid equations have been solved as a boundary value problem for planar and cylindrical beam shapes, and the dispersion which results as an eigenvalue problem is solved numerically without approximation as a function of the electron beam width. The solution gives unstable modes for any beam width and the dispersion relation shows different branches. There is a branch in both configurations that represents the most unstable mode, and the wavelength of this unstable mode for the cylindrical beam is larger than the corresponding wavelength for the most unstable mode of the slab-shaped beam.
Stability of a layer of viscous magnetic fluid flow down an inclined plane
Authors: Renardy Y. , Sun S. M.
Published: July 2002

This paper concerns the linear stability of a layer of viscous magnetic fluid flow down an inclined plane under the influence of gravity and a tangential magnetic field. The stability of a magnetic fluid in a three-dimensional space is first reduced to the stability of the flow in a two-dimensional space by using Squire’s transformation. The stability of long waves and short waves is analyzed asymptotically. The stability of waves with intermediate length is obtained numerically. It is found that the magnetic field has a stabilizing effect on both the surface and shear modes and can be used to postpone the instability of such flows.
Interaction of surface gravity waves on a nonuniformly periodic seabed
Authors: Nayfeh Ali H. , Hawwa Muhammad A.
Published: July 2002

The interaction of surface gravity waves on a nonuniformly periodic seabed is considered. The method of multiple scales is used to analyze the interaction leading to two coupled-mode equations. The power reflection coefficient is used as an indicator to evaluate the filter action of the bottom corrugation. The results show that the modes are strongly coupled when the Bragg resonant condition is satisfied. The characteristics of the filtration are found to be enhanced by imposing special types of amplitude and phase modulated periodic nonuniformities, including amplitude taper and chirped periodic variations.
One-dimensional models for slender axisymmetric viscous liquid jets
Authors: García F. Javier , Castellanos Antonio
Published: July 2002

A one-dimensional analysis of slender axisymmetric viscous liquid jets is considered. A set of one-dimensional models is derived by substituting a truncated Taylor series in the radial coordinate into the Navier–Stokes equations and boundary conditions at the interface. The relative error, defined as the order of magnitude of the neglected terms divided by the order of the retained ones, is small if the dimensionless wave number k is small enough. The Lee slice model is generalized to take into account viscosity, the relative error being k2. A new model having a parabolic radial dependence for the axial velocity is developed, with a relative error k4. The Cosserat model comes from the introduction of the mean axial velocity into the previous one, but an inconsistency arises from neglecting some viscous terms of the same order as those retained. A new model for the mean axial velocity is derived. It conserves the same inertial contribution but avoids the above-mentioned problem by estimating the involved terms instead of neglecting them. Therefore the relative error is k4 for any value of viscosity. Linear stability analysis is performed for the infinite jet. Results are compared with the exact linear solution given by Lord Rayleigh. The main features predicted in the derivation of the one-dimensional models manifest themselves in the linear case.
Reynolds number similarity of orthogonal decomposition of the outer layer of turbulent wall flow
Authors: Liu Z.-C. , Adrian R. J. , Hanratty T. J.
Published: July 2002

Experimental evidence is presented to show that in the outer region of wall-bounded turbulent flow, both the eigenfunctions and the eigenvalue spectra of the one-dimensional proper orthogonal decomposition have forms that are independent of Reynolds number when scaled by the wall friction velocity and the outer length scale.
Inclusion of lubrication forces in dynamic simulations
Authors: Sangani Ashok S. , Mo Guobiao
Published: July 2002

A new method is described for incorporating close-field, lubrication forces between pairs of particles into the multiparticle Stokes flow calculations. The method is applied to the suspensions of both spherical as well as cylindrical particles, and results computed by the method are shown to be in excellent agreement with the exact known results available in the literature.
A numerical study of free-surface turbulence in channel flow
Authors: Pan Y. , Banerjee S.
Published: July 2002

Direct numerical simulations of open-channel flow indicate that turbulence at the free surface contains large-scale persistent structures. They are ‘‘upwellings’’ caused by impingement of bursts emanating from the bottom boundary; ‘‘downdrafts’’ in regions where adjacent upwellings interact, and whirlpool-like ‘‘attached vortices’’ which form at the edge of upwellings. The attached vortices are particularly long-lived in the sense that once formed, unless destroyed by other upwellings, they tend to interact with each other and dissipate only slowly. If turbulence generation at the bottom wall is turned off by changing the boundary condition to free slip, then the upwellings (related to bursts) and downdrafts no longer form. The dominant structures at the free surface become the attached vortices which pair, merge, and slowly dissipate. In the central regions, as expected, the structure remains three dimensional throughout the decay process. Near the free surface, the structure appears to be quasi- two dimensional, as indicated by quantitative measures such as energy spectra, interwave number energy transfer, invariants of the anisotropy tensor, and length scales. In the decaying case, the quasi-two-dimensional region increases in thickness, with decay time, though the structure in the central regions of the flow remains three dimensional.
Vibrational energy conservation with vibration–dissociation coupling: General theory and numerical studies
Authors: Olejniczak Joseph , Candler Graham V.
Published: July 2002

The coupling between vibrational relaxation and dissociation in nitrogen is studied. The conservation of vibrational energy equation is derived and the form of the source terms is determined for physically consistent coupling models. Using a computational fluid dynamics method, the results from three current coupling models are compared to existing experimental interferograms for spherical geometries. It is found that the coupling models of Park, Treanor and Marrone, and Macheret and Rich are able to accurately predict the shock standoff distances and reproduce the experimental interference patterns for these conditions. However, there are differences in the vibrational temperature profiles among the coupling models. The experimental interferograms are not sensitive to these differences, though.
The role of dynamic surface tension in air assist atomization
Authors: Shavit Uri , Chigier Norman
Published: July 2002

Aqueous surfactant solutions were atomized using an air assist atomizer, and the effects of dynamic surface tension on atomization were studied. The solutions differ from one another in their dynamic behavior, but all have the same equilibrium surface tension. The constant equilibrium surface tension was achieved by choosing surfactant concentrations above the critical micelle concentration (CMC). The dynamic change of surface tension in aqueous Tergitol NP-10 solutions of 1.5, 3, 6, 12, and 60 mM was measured using the oscillating jet technique. While atomizing the liquid jet, it was found that frequencies and amplitudes of the flapping motion of the liquid jet increased with surfactant concentration showing that surface tension decreases in the region between the nozzle exit and breakup. The length of the intact liquid jet was found to be insensitive to surfactant concentration, suggesting that, due to sudden increase of surface area, surface tension is near its initial value in the breakup region. Measurements in the spray region show a strong influence of the dynamic change of surface tension on drop size. Finally, using an analysis based on a critical Weber number, the actual time average of surface tension was estimated at an axial location of 1.5× the intact length downstream from the nozzle exit, and an overall profile of surface tension as a function of axial location was proposed.
A geometrical interpretation of force on a translating body in rotational flow
Authors: Wells John C.
Published: July 2002

Some recent results for the force on a translating rigid three-dimensional body in incompressible flow, in which the integration is over the vorticity field rather than surface pressure, are interpreted from a point of view that distinguishes changes of fluid impulse directly attributable to the vorticity field from those due to its image system in the body. An expression is first derived geometrically for a sphere in inviscid fluid; the flow is taken to consist of discrete vortex loops whose change in impulse, and that of the image system in the sphere, are calculated via their projected areas. As an example, the force on a sphere due to an infinite line vortex is calculated exactly. To generalize the geometrical derivation to bodies of any shape, a reciprocal theorem is proved concerning the impulse of the image system of a dipole. This yields the inviscid form of a result derived mathematically by Howe [J. Fluid Mech. 206, 131 (1989)]. Physical interpretations of the various terms in Howe’s expression are offered, and the relationship to a very similar independent result by Chang [Proc. R. Soc. London Ser. A 437, 517 (1992)] is discussed.
Rotating flow past a sliced cylinder
Authors: Foster M. R. , Davies P. A.
Published: July 2002

Depending upon the relative sizes of the parameters of the problem, rotating flow of a vertically confined fluid past an asymmetric object—in this case a circular cylinder with top sliced at an angle—may induce flow inside the Taylor column, driven by the viscous stresses in the column wall. The motion is along the constant-depth contours, which are not closed in such a situation. We show from theoretical considerations that so long as the angle of the slice is bigger than the one-quarter power of the Ekman number, E, such an interior motion in the column does occur. In general, the motion consists of two eddies over the obstacle. A series of case study laboratory experiments is presented in support of the analysis, to show the effect of the slice orientation and magnitude on the flow over such a bump, and to illustrate the nature of the flows which are generated when inertial effects are dominant.
Transient growth in compressible boundary layer flow
Authors: Hanifi Ardeshir , Schmid Peter J. , Henningson Dan S.
Published: July 2002

The potential for transient growth in compressible boundary layers is studied. Transient amplification is mathematically associated with a non-orthogonal eigenvector basis, and can amplify disturbances although the spectrum of the linearized evolution operator is entirely confined to the stable half-plane. Compressible boundary layer flow shows a large amount of transient growth over a wide range of parameter values. The disturbance size is here measured by a positive definite energy like quantity that has been derived such that pressure-related transfer terms in its evolution equation mutually cancel. The maximum of the transient growth is found for structures which are independent of the streamwise direction and is found to scale with R2. This suggests that the transient growth originates from the same lift-up mechanism found to give large growth in incompressible shear flows. The maximum growth is also found to increase with Mach number. In compressible flow, disturbances that experience optimal transient growth can be excited naturally by a non-linear interaction of oblique unstable first mode waves. Thus, a triggering of transient growth may account for the difference in timescales between the fast oblique breakdown process and traditional secondary instability.
On some exact solutions of the relativistic Navier–Stokes equations
Authors: Granik A. , Chapline G.
Published: July 2002

The relativistic Navier–Stokes equations following from the first-order theory of Eckart are derived. Exact analytic solutions, which are the generalizations of the well-known nonrelativistic solutions for Couette flow, are found. In particular, it is shown that even in the case when the dissipative coefficients are constant the temperature distribution influences the velocity distribution. The relativistic generalization of the classical Busemann theorem is found for the case of dissipative coefficients varying with temperature. For almost every type of these flows the velocity and temperature profiles are flattened as compared with respective nonrelativistic profiles.
Nonlinear critical Reynolds number of a stratified plane Poiseuille flow
Authors: Li H.-S. , Fujimura K.
Published: July 2002

The minimum Reynolds number, ReNc, below which all the two-dimensional and monochromatic wave disturbances decay, is studied numerically for a thermally stratified plane Poiseuille flow. The ReNc is found to be sensitive to the change of Prandtl number P. Under unstable stratification with Rayleigh number just below critical, ReNc≂1000 is found for P≤10−3.
Boundary conditions for the lattice Boltzmann method
Authors: Maier Robert S. , Bernard Robert S. , Grunau Daryl W.
Published: July 2002

When the Lattice Boltzmann Method (LBM) is used for simulating continuum fluid flow, the discrete mass distribution must satisfy imposed constraints for density and momentum along the boundaries of the lattice. These constraints uniquely determine the three-dimensional (3-D) mass distribution for boundary nodes only when the number of external (inward-pointing) lattice links does not exceed four. We propose supplementary rules for computing the boundary distribution where the number of external links does exceed four, which is the case for all except simple rectangular lattices. Results obtained with 3-D body-centered-cubic lattices are presented for Poiseuille flow, porous-plate Couette flow, pipe flow, and rectangular duct flow. The accuracy of the two-dimensional (2-D) Poiseuille and Couette flows persists even when the mean free path between collisions is large, but that of the 3-D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3-D low-Reynolds-number flow.
Experimental study of heat and momentum transfer in rotating channel flow
Authors: Matsubara Masaharu , Alfredsson P. Henrik
Published: July 2002

The enhancement of momentum and heat transfer caused by stationary streamwise vortices due to a Coriolis instability in a rotating straight channel is examined. It is shown that the changes in skin friction and Nusselt number depend on changes in the spanwise averaged mean flow and temperature distributions. Hot wire anemometry was used to experimentally determine the streamwise velocity and temperature distributions in a cross stream plane 68 channel widths downstream of the inlet. A technique to accurately compensate the velocity readings for the varying temperature in the channel was developed. It is shown that the streamwise vortices give rise to disturbance profiles which are close to those obtained from linear theory for small rotation numbers and that in this region there is no enhancement of either the averaged momentum or heat transfer. However, even for a disturbance amplitude in the streamwise velocity of the order of 20%, the disturbances are close to linear (both the disturbance distribution and growth rate). In this weakly non-linear region the changes in the mean flow and temperature distributions could be estimated by using the linear eigenfunctions of the disturbances where the amplitude was taken from the measurements. In the fully non-linear (saturated) region the Nusselt number on both the stable and unstable side of the channel was almost twice that at no rotation, however, the skin friction was almost unaffected on the stable side. This shows that the Reynolds analogy between momentum and heat transfer is not valid in this flow situation.
The role of chaotic orbits in the determination of power spectra of passive scalars
Authors: Antonsen Thomas M. , Fan Zhencan , Ott Edward , Garcia-Lopez E.
Published: July 2002

This paper relates properties of the power spectrum of a passive scalar convected by a chaotic fluid flow to the distribution of finite time Lyapunov exponents. The properties considered include the early time evolution of the power spectrum, the late time exponential decay of the scalar variance, and the wave number dependence of the power spectrum in the presence of a source of scalar variance. Theoretical predictions are tested by comparing full numerical solutions of the relevant partial differential equation to solutions of a model system which includes diffusion and involves integrations along the fluid orbits only. The model system is shown to give results in close agreement with the numerical solutions of the full problem. This suggests the possible general utility of the model equations for a broad range of problems involving passive scalar convection.
Direct simulation of concentration creep in a binary gas-filled enclosure
Authors: Papadopoulos Dimitrios H. , Rosner Daniel E.
Published: July 2002

A Cartesian, two-dimensional enclosure containing an isothermal rarefied binary gas mixture is studied as a limiting-case model for actual crystal growth experiments conducted in reduced gravity environments. By employing a microscopic  approach related to the Boltzmann equation, it is demonstrated that in the presence of appreciable partial concentration gradients a steady-state flow pattern develops, driven by kinetic boundary layers adjacent to solid boundaries. In contrast, a macroscopic analysis based on the continuum transport equations and the classical no-slip boundary condition would predict no flow whatsoever. For the case of equal mass species, the velocity scales involved are shown to increase with the disparity in accommodation coefficients, in agreement with expectations based on one-dimensional, linearized Knudsen sublayer theory, while quantitative comparison between simulations and the latter theory reveals significant confinement effects. Simulation of concentration creep in binary mixtures composed of disparate mass species requires an alternative computational procedure, motivated by surface recombination/dissociation reactions. For this case, flow fields and creep coefficient values for a range of mass ratios are also reported. It is concluded that future continuum-level modelling efforts should more fully exploit the detailed information now available from relevant microscopic simulations.
Suction effect on an impulsively started circular cylinder: Vortex structure and drag reduction
Authors: Chu Chin-Chou , Chang Chien-Cheng , Liu Cheng-Chien , Chang Ray-Lin
Published: July 2002

Drag reduction on an impulsively started circular cylinder by surface suction has been investigated with a joint numerical and experimental study. Two suction slots entraining mass with various rates were located symmetrically in a range of angles downstream of the points of zero shear stress. The Reynolds number Re of this study was between 500 and 2000, while the suction coefficient Ṁ varied from 0 to 0.08. Analysis based on the force contributed by fluid elements with nonvanishing vorticity [Chang, Proc. R. Soc. London Ser. A 437, 517 (1992)] has provided a clear view of the physical mechanism causing the drag reduction. For the impulsive flow with surface suction, the initial drag reduction is due to the strengthening of the front boundary layer, while the slender vortices in the near wake due to suction then become the dominant factor in reduction of the drag force in later stages. Close agreements were found between the experimental and numerical results, including streakline flow visualization and surface vorticity measurements on the top of the cylinder. In addition, a parametric study on the slot location, the suction angle, and the width of the suction slot has also been carried out in detail.
The instability of sand ripples under partially standing surface waves
Authors: Mei Chiang C. , Yu Jie
Published: July 2002

We extend recent works on oscillatory flows over rigid ripples and the instability of sand ripples under such flows, by considering the instability of sand ripples under partially standing surface waves over a finite water depth. The variation of unstable ripples within a wavelength of the standing waves and inferences on the ripple distribution over a sand bar are examined. The steady circulation due to the combined effects of waves and ripples are also discussed.
Eulerian analysis of concentration fluctuations in dispersing plumes and puffs
Authors: Thomson David J.
Published: July 2002

A recent analysis of the second-order moments of concentration fluctuations in dispersing plumes and puffs has been reexamined in order to obtain a picture of the budget for the second-order moments. We have compared this picture with the parametrizations of the transport and dissipation of concentration variance in a second-order closure model. The comparison lends support to the form of the second-order closure parametrizations and also provides a constraint on the constants used in the parametrization of the dissipation of concentration variance, thereby providing the means to reduce the number of tunable constants in the model by one. The constraint implies that the constants must differ for area, line and point sources and implies that finding a good parametrization of the dissipation of concentration variance for arbitrary source geometries may be difficult.
Drop breakup in the flow through fixed beds via stochastic simulation in model Gaussian fields
Authors: Mosler Alisa B. , Shaqfeh Eric S. G.
Published: July 2002

Shaqfeh and Koch have shown that the flow through a dilute disordered fixed bed of fibers produces large polymer conformation change beyond a certain critical flow rate [J. Fluid Mech. 244, 17 (1992)]. We now examine the effect of this flow on the shape and breakup of viscous drops. Because the flow through a dilute fixed bed is equivalent to a certain anisotropic Gaussian flow field, we follow our previous paper and reproduce a model of the flow through a spectral expansion where the wave number vectors are chosen from statistical distributions which ensure that the desired velocity field will be realized [Phys. Fluids 9, 1222 (1997)]. We examine the dynamics of model drop shapes, averaged over the Gaussian statistics of the flow field, by synthesizing a large number of flow realizations. The drop surface is modeled using the first, second, and third order small deformation theories which can accurately predict critical conditions in classical strong flows. While the first order model yields a bounded average drop shape for all flow conditions, the second and third order models demonstrate that the flow through fixed beds is indeed “strong” since beyond a certain value of the pore-size capillary number, Ca∼0.15, large average drop deformation occurs and the average drop shape becomes unbounded (“drop breakup”). This critical condition is determined for various viscosity ratios and fixed bed particle volume fractions. Similar to a simple shear flow, we find that there is a critical viscosity ratio, χ∼2.5, beyond which breakup is not observed in the fixed bed for any Ca. In addition, the critical condition is shown to depend heavily on the transient nature of the flow in the bed since approximately half of the flow fields in which drop breakup occurs would not break an initially spherical drop at any Ca if they were steady. For supercritical capillary numbers, we define conditions under which the unbounded drop shapes fragment into smaller droplets and we examine the drop breakup rates as a percentage of the drop population.
Surface waves impinging on a vertical wall
Authors: McHugh John P. , Watt David W.
Published: July 2002

Flow visualization experiments have been performed which consider a solitary wave impinging on a vertical wall. Several stages of motion appear as the incident wave height is increased in subsequent runs. Small amplitude incident waves reflect off the vertical wall without a significant change in shape. Higher wave amplitudes form a liquid sheet at impact, which ascends the vertical wall and has a ridge of fluid at the leading edge. Small waves form behind the ridge, and the ridge may form droplets. Large incident wave amplitudes form spilling breaking waves, which result in much more complicated motion in the ascending sheet, including the formation of spray.