bluuebunny/crossref_metadata_2025 huggingface dataset:
Renormalization group analysis of anisotropic diffusion in turbulent shear flows
Authors: Rubinstein Robert , Barton J. Michael
Published: July 2002

The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity–scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.
Some effects of swirl on turbulent mixing layer development
Authors: Mehta R. D. , Wood D. H. , Clausen P. D.
Published: July 2002

An experimental study has been conducted to investigate the effects of swirl on the streamwise development of an axisymmetric turbulent mixing layer. The initial boundary layer was tripped well upstream of the lip. All three mean velocities and the six independent components of the Reynolds stress tensor were measured using a rotatable cross-wire probe for three swirl numbers (0, 0.2, and 0.4). The zero swirl case was found to develop as expected, with a linear growth rate and the peak Reynolds stresses approaching constant asymptotic levels. The results show that the swirling mixing layer is affected by the angular momentum instability over almost the whole layer. The effect of the instability is to increase all the peak Reynolds stresses within the mixing layer, with the peaks increasing monotonically with swirl number. The largest increases occurred in the spanwise normal stress and the two secondary shear stresses. A part of the increase in the turbulence stresses is attributed to ‘‘extra’’ production through terms activated by the angular momentum instability. The thickness and growth rate for the lower swirl rate were found to be comparable to the zero swirl case, while those for the higher swirl rate were increased significantly, in line with the increased Reynolds stresses. This nonmonotonic behavior of the mixing layer growth rate is attributed to the effects of a favorable pressure gradient in the core flow.
Experimental study of controlled tip disturbance effect on flow asymmetry
Authors: Degani David , Tobak Murray
Published: July 2002

The effect on the asymmetric mean flow observed on pointed bodies of revolution at incidence of changing the size and location of a controlled disturbance as well as changes in angle of attack and flow conditions are evaluated experimentally. Flow visualization and side-force measurements are carried out for a generic ogive-cylinder body inclined at high angle of attack in a low-speed wind tunnel. For all angles of attack tested (30°–60°), minute changes in the size or location of the controlled disturbance result in finite changes in the asymmetric flow field, even to the extent of reversing the sign of the side force or becoming almost symmetric. The process is reversible; returning the wire to an original position likewise restores the corresponding flow field and mean side force. The variation of side force with continuous variation of a perturbation’s size or location remains continuous and single valued, even in the incidence range of 50° to 60°, where ‘‘bistable’’ behavior of the asymmetric flow field is observed.
On energy transfer in resonant bubble oscillations
Authors: Feng Z. C. , Leal L. G.
Published: July 2002

In this paper, energy transfer mechanism due to resonant interactions of bubble shape and volume deformation modes is studied. In the process, a number of recent investigations that have focused on specific sets of initial conditions are generalized. Using phase-space analysis and a reduction of the mode dynamics equations to an integrable Hamiltonian, two types of resonant interactions are considered. The first is the so-called one–two resonance, when the natural frequency of the breathing mode is twice (or approximately twice) that of a shape mode. In this case, it is found that there is nearly always a continuous, periodic exchange of energy between the shape and volume modes. However, there exists a particular class of initial conditions, that was the subject of most earlier studies, for which the energy transfer is one way, from the shape mode to the volume mode. The second type of resonant interaction occurs when the natural frequency of the breathing mode is approximately equal to that of the shape mode. Here, it is found that periodic energy exchange can take place if equilibrium shape of the bubble is nonspherical due, for example, to a surface pressure distribution or a steady extensional flow. The analysis of the one–two resonance case is used to explain the stability of an oscillating spherical bubble to small perturbations of shape. It is found that instability of small volume oscillations can lead to large shape oscillation.
Effect of mass-ratio dependence of the force law for tracer diffusion in shear flow
Authors: Garzó V. , López de Haro M.
Published: July 2002

The Boltzmann–Lorentz equation for Maxwell molecules is used to analyze the effect of mass dependence of the force law for tracer diffusion in uniform shear flow. An observed mass dependence of intermolecular forces suitable for disparate mass binary mixtures is explicitly considered. A comparison with earlier results is carried out.
Hydrodynamic expansion of exploding-foil targets irradiated by 0.53 μm laser light
Authors: Drake R. P. , Phillion D. W. , Estabrook Kent , Turner R. E. , Kauffman R. L. , Campbell E. M.
Published: July 2002

An experiment is reported in which several diagnostics were used to study the hydrodynamic expansion of exploding-foil targets. The CH targets, 1–3 μm thick, were irradiated with 3–4 kJ of 0.53 μm laser light in 1 nsec pulses. The electron density was diagnosed using the transmission and scattering of light at the laser frequency, the scattering of light at 3/2 of the laser frequency, the spectrum of Raman-scattered light, the x-ray spectrum from doped targets, and the image of the ultraviolet bremsstrahlung emission from the plasma. The measurements were consistent with one another, but generally were not consistent with two-dimensional computer simulations. The targets burned through later and took longer after burnthrough to reach quarter-critical density than predicted. This discrepancy may be a consequence of excessive profile steepening caused by the local, heat-transport model used in the simulation.
The source-driven dissipative nonlinear Schrödinger model of resonance absorption
Authors: Larroche Olivier , Pesme Denis
Published: July 2002

A source-driven dissipative nonlinear Schrödinger (NLS) equation is numerically studied, characterized by a nonlinearity parameter and a dissipative length, governing the generation of finite-amplitude, localized electrostatic plasma waves by resonance absorption of light in an inhomogeneous plasma. It is shown that as the nonlinearity parameter is increased a transition to chaos occurs through a quasiperiodic scenario. In the chaotic regime, it is shown from statistical diagnostics that as the dissipation length is increased, the system shifts from a convective regime governed by the competition between pumping and convection of the waves due to the inhomogeneity to a dissipative regime governed by the competition between pumping and a scale-length-dependent absorption mechanism, which approximately models Landau damping. The scaling laws obtained show that the turbulent state can be described in both regimes as a set of NLS solitons, interacting through the pumping and damping mechanisms.For a vanishing density gradient, the system admits a homogeneous limit, which is found to be chaotic and dissipative.
Radiation guiding and efficiency enhancement in the cyclotron autoresonance maser
Authors: Kleva Robert G. , Levush Baruch , Sprangle P.
Published: July 2002

The effect of the electron beam on the propagation of the radiation beam in a cyclotron autoresonance maser (CARM) is investigated. It is shown that the natural tendency of the radiation beam to spread diffractively can be overcome and the radiation beam can be focused because of its interaction with the electron beam. The radiation beam can be transported without defocusing following wave saturation only if the Doppler-shifted wave frequency is slightly larger than the gyrofrequency. Efficiencies in excess of 70% can be attained through the use of a tapered magnetic field. The effect of thermal spreads in the pitch angle and energy of the electrons on the guiding of the radiation beam and the efficiency of the CARM is investigated. The CARM is much more sensitive to spreads in pitch angle than to spreads in energy. If the spread in pitch angle becomes too large, typically a few percent, then the instability is quenched.
Theory and application of complex geometric optics in inhomogeneous magnetized plasmas
Authors: Bravo-Ortega Armando , Glasser Alan H.
Published: July 2002

A new treatment is presented of geometric optics in inhomogeneous magnetized plasmas with non-Hermitian dielectric tensors. Previous treatments assume either that the dielectric tensor is nearly Hermitian or that the frequency is nearly real. This is done in order to restrict the values of space-time coordinates along a ray to real values. This work eliminates this restriction and gives a new interpretation of the meaning of complex-valued coordinates, and shows that it extends the range of validity of the theory. This derivation is fully covariant, eliminating the special role played by the time in previous derivations. A new numerical treatment of the amplitude equation, which may be more convenient than ray tracing, is suggested. An application of the method of complex ray tracing to lower hybrid wave propagation in a tokamak is introduced.
The effects of impurity ions on the scattered light spectrum of a plasma
Authors: DeSilva A. W. , Baig T. J. , Olivares I. , Kunze H.-J.
Published: July 2002

Measurement of the scattered light spectrum from hydrogen plasmas containing small amounts of heavy impurity ions confirms the predictions of theory that the low-frequency ion-acoustic scattered light feature consists of the normal profile due to scattering from a pure hydrogen plasma, with a narrow peak superimposed that is attributed to the impurity. The intensity of the impurity peak scales as the square of a mean charge Z*. Measurements are reported for electron densities of 1–3×1018 cm−3 and electron temperatures ranging from 10 to 80 eV.
Spiky Langmuir solitons in a dense ultrarelativistic electron–positron plasma
Authors: Mofiz U. A. , Mamun A. A.
Published: July 2002

Spiky and short-duration Langmuir solitons are found to exist in an ultrarelativistic electron–positron plasma. Nonlinear Landau damping and pulsar radiation are discussed.
Simulations of rf-driven sheath formation in two dimensions
Authors: Riyopoulos S. , Grossmann W. , Drobot A. , Kress M.
Published: July 2002

The results from two-dimensional particle simulations of sheath formation around periodic metal arrays placed inside magnetized plasmas and driven by oscillating voltages are reported. The main goal is the modeling of the plasma interaction with the Faraday bars surrounding the antennas during ion cyclotron tokamak heating. The study of the time-averaged potentials shows that the two-dimensional sheath structure depends on both the sheath length-to-thickness ratio and the inclination of the magnetic lines. The equipotential surfaces form closed, nested cells between adjacent bars. When the magnetic lines are nearly perpendicular to the potential gradients, the ion motion is dominated by the E×B drift, and ion streamlines form vortices around the equipotentials. At larger inclinations of the magnetic lines, the flow decouples from the equipotentials and ion transport is mainly along the potential gradients. The critical angle for the transition from vortex circulation to field aligned flow is computed. The effects of the cross-field ion transport on the sheath properties are discussed. It is shown that the sheath length and the magnetic line inclination affect the sheath scaling in the two-dimensional case. The one-dimensional theory results are recovered in the limit of high length-to-thickness ratio and large inclination of the magnetic lines.
Nonlinear analysis of a magnicon output cavity
Authors: Hafizi B. , Gold S. H. , Manheimer W. M. , Sprangle P.
Published: July 2002

A nonlinear analysis of the wave–particle interaction in the output cavity of a frequency-doubling magnicon amplifier is presented. The cavity is immersed in an axial magnetic field, wherein electrons interact with a rotating TM210 mode via a gyroresonant mechanism. The electron equations of motion and the wave equation for the radio-frequency (rf) field are derived and expressed in terms of scaled variables in order to study the general scaling of the output cavity. Single-electron, time-dependent simulation of the interaction in the cavity is performed to assess the accessibility and stability of high-efficiency states for an X-band magnicon. Results from multielectron, steady-state simulation are presented to show the effect of spreads in electron-beam radius, energy, and transverse momentum on the efficiency.
Near-forward scattering of laser light*
Authors: Batha S. H. , Baldis H. A. , Bradley K. S. , Drake R. P. , Estabrook Kent , Johnston T. W. , Montgomery D. S. , Procassini R. J.
Published: July 2002

Near-forward scattering of laser light in a plasma, in regimes relevant to future inertial-confinement-fusion (ICF) experiments, has been investigated experimentally. The intensity scaling of stimulated Raman scattering (SRS) forward scattering at one angle was measured from a low-Z plasma. It was found that the intensity threshold and scaling were consistent with convective theory. Forward SRS saturated at a relatively low intensity. In a second experiment using Ti plasmas, absolutely calibrated, time-resolved stimulated Brillouin scattering (SBS) spectra from up to seven different angles were measured simultaneously. It was found that the angular dependence of the scattered energy was qualitatively consistent with convective theory. The spectra provided the first evidence of near-forward SBS. Contrary to previous estimates, near-forward SBS was shown to be more efficient than oblique backscattering and may be an important effect for ICF.
Suppression of turbulent fluctuations in tokamaks
Authors: Shaing K. C.
Published: July 2002

It is shown that the criterion for the suppression of turbulent fluctuations in tokamaks is not simply the shear of the radial electrical field. The shear of the parallel flow must be taken into account. One of the most efficient ways to influence turbulence fluctuations through the shear of the angular frequency is to fix the parallel flow and change the poloidal E×B rotation.
Two-fluid equations for low-n singular modes in the low-frequency regime
Authors: Zheng L.-J.
Published: July 2002

Braginskii’s two-fluid equations are employed to obtain the eigenmode equations governing low-n singular modes in toroidal geometry. Collisional effects are neglected. The equilibrium electric field is taken into account. The frequency of the modes is assumed to be lower than that of the ion acoustic wave along the magnetic field lines. In this low-frequency regime it is shown that the pressure of the ion fluid tends to be constant along the magnetic field lines, as also does that of the electron fluid, and the parallel electric field tends to vanish. The finite-gyroradius (FGR) effect is recovered by taking into consideration the diamagnetic drift velocity and the gyroviscosity of the ion fluid. The results show that the toroidal effect gives rise not only to the so-called apparent mass effect, but also to an enhancement of the FGR and equilibrium electric field effects. The toroidicity-induced FGR and equilibrium electric field effects are shown to be even more important than those exhibited in the cylindrical equilibrium model.
Transverse mode solitons in a hot ultrarelativistic electron–positron plasma
Authors: Mofiz U. A. , Mamun A. A.
Published: July 2002

Intense short-duration transverse mode solitons are found to exist in a ultrarelativistically hot electron–positron plasma and its relation with the pulsar radiation in discussed.
One-dimensional Vlasov–Maxwell equilibria
Authors: Greene John M.
Published: July 2002

The purpose of this paper is to show that the Vlasov equilibrium of a plasma of charged particles in an electromagnetic field is closely related to a fluid equilibrium, where only a few moments of the velocity distribution of the plasma are considered. In this fluid equilibrium the electric field should be calculated from Ohm’s law, rather than the Poisson equation. In practice, only one-dimensional equilibria are treated, because the symmetry makes this case tractable. The emphasis here is on gaining a better understanding of the subject, but an alternate way of doing the calculations is suggested. It is shown that particle distributions can be found that are consistent with any reasonable electromagnetic field profile.
Generic ballooning in anisotropic pressure toroids
Authors: Cooper W. Anthony
Published: July 2002

The ballooning mode equation for three-dimensional toroidal configurations with anisotropic plasma pressure is derived from the Kruskal–Oberman energy principle. The Mercier criterion is evaluated for nonaxisymmetric systems with shear (stellarators). This theory can determine spatially localized neutral beam injection effects on ballooning-interchange stability.
Thermal equilibrium of a cryogenic magnetized pure electron plasma
Authors: Dubin Daniel H. E. , O’Neil T. M.
Published: July 2002

The thermal equilibrium correlation properties of a magnetically confined pure electron plasma (McPEP) are related to those of a one-component plasma (OCP). The N-particle spatial distribution ρs and the Helmholtz free energy F are evaluated for the McPEP to O(λ2d/a2), where λd is the thermal de Broglie wavelength and a is an interparticle spacing. The electron gyromotion is allowed to be fully quantized while the guiding center motion is quasiclassical. The distribution ρs is shown to be identical to that of a classical OCP with a slightly modified potential. To O(λ2d/a2) this modification does not affect that part of F which caused by correlations, as long as certain requirements concerning the size of the plasma are met. This theory is motivated by a current series of experiments that involve the cooling of a magnetically confined pure electron plasma to the cryogenic temperature range.
Study of the influence of the proximity of a moving solid wall on bubble dynamics
Authors: Ligneul P.
Published: July 2002

The presence of nearby surfaces influences the behavior cavitation bubbles in a complex manner. To understand this influence, nine experiments were performed with spark-generated bubbles in contact with a rotating cylinder in both distilled water and polymer solution. It was shown that the presence of the wall increases the bubble life cycle when compared to the case of a bubble in unbounded fluid. The effect of the polymer as well as the wall–bubble interface disturbance is shown to reduce this life cycle. A correction for the lengthening effect is introduced and shown to give reasonable results for the bubble in distilled water as well as polymer solution. The utility of the characterization scheme used in the present analysis is demonstrated by these results.
Particle simulation on radio frequency stabilization of flute modes in a tandem mirror. I. Parallel antenna
Authors: Kadoya Yutaka , Abe Hirotada
Published: July 2002

A two- and one-half-dimensional electromagnetic particle code (PS2M) [H. Abe and S. Nakajima, J. Phys. Soc. Jpn. 53, xxx (1987)] is used to study how an electric field applied parallel to the magnetic field affects the radio frequency stabilization of flute modes in a tandem mirror plasma. The parallel electric field E∥ perturbs the electron velocity v∥ parallel to the magnetic field and also induces a perpendicular magnetic field perturbation B⊥. The unstable growth of the flute mode in the absence of such a radio frequency electric field is first studied as a basis for comparison. The ponderomotive force originating from the time-averaged product 〈v∥B⊥〉 is then shown to stabilize the flute modes. The stabilizing wave power threshold, the frequency dependency, and the dependence on ∇‖E∥‖ all agree with the theoretical predictions.
Particle simulations of merging ion rings in resistive plasmas
Authors: Lyster P. M. , Sudan R. N.
Published: July 2002

A numerical study, employing the particle code ringa [Plasma Phys. 23, 521 (1981)], of two ion rings that merge with each other due to their mutual magnetic attraction is presented. It is shown that an ion ring with closed magnetic field lines (field reversed) can be formed by merging two weaker non-field-reversed rings. A rough calculation shows that there is an optimal plasma conductivity σ≊c2/4πaRΩζ1/2 (a and R are the respective axial width and major radius of the ring, Ω is the ion cyclotron frequency in the external magnetic field, and ζ is the field reversal factor of the weaker ring) for which most of the energy of mutual magnetic attraction between the rings is dissipated during the process of merging.
A similarity solution for the Direct Interaction Approximation and its relationship to renormalization-group analyses of turbulence
Authors: Woodruff S. L.
Published: July 2002

The application of Kraichnan’s Direct Interaction Approximation [J. Fluid Mech. 5, 497 (1959)] to the inertial range of Navier–Stokes turbulence is examined. A similarity form valid in the inertial range is presented, along with several approximations permitting explicit solutions. The relationship of the present results to some recent renormalization-group calculations is discussed. It is shown that these renormalization-group calculations misrepresent the Direct Interaction Approximation’s nonlinear interaction and that the addition of an artificial stirring force is unnecessary.
The stability of nonaxisymmetric circular Couette flow with a radial temperature gradient
Authors: Kong Chin-Hwa , Liu I-Chung
Published: July 2002

A numerical solution of linear differential equations governing the stability of the nonaxisymmetric wide-gap circular Couette flow was present in this study. The numerical solution took into account the presence of a radial temperature gradient between the two rotating cylinders. Boussinesq approximation was applied in the analysis so as to examine the interaction of radial temperature difference with the centrifugal potential but neglect the gravity effect. The critical Taylor number and corresponding critical axial and azimuthal wave numbers were shown graphically for various values of radius ratio, ratio of angular velocities of the inner and outer cylinders, and temperature gradient parameter N for Prandtl number 0.7. Not only the critical Taylor number but the oscillatory onset mode of nonaxisymmetric disturbances could be altered by the effects of a temperature gradient, as indicated by the calculated results.
Similarity states of passive scalar transport in buoyancy-generated turbulence
Authors: Chasnov J. R.
Published: July 2002

The mixing of a passive scalar field by turbulence that is generated by buoyancy forces acting on an initial random density field is considered. Various asymptotic similarity states of the passive scalar field with and without a uniform mean passive scalar gradient are determined by dimensional arguments based on exact or near invariants of the density and passive scalar fields. The results of large-eddy numerical simulations are shown to support the derived scaling laws. The large-eddy simulations also demonstrate the different mixing properties of an active and passive scalar field.
Sprays in radially spreading shear-layer flows
Authors: Katoshevski D. , Tambour Y.
Published: July 2002

Two radially spreading adjacent streams, which differ in their radial velocities and thus form a radially spreading shear-layer flow, are considered here. The theory presented by the authors for sprays suspended in unidirectional [Katoshevski and Tambour, Phys. Fluids A 5, 3085 (1993)] shear layers is extended here for radially spreading shear layer flows. The behavior of a multisize (polydisperse) evaporating spray, which is suspended in one of the streams, is studied. The spray spreads in the lateral direction towards the other coflowing stream, resulting in lateral changes in spray densities and in local droplet size distributions across the shear layer. These effects are analyzed here via similarity solutions of the governing equations. A comparison between the behavior of the multisize sprays and their vapors in radially spreading versus unidirectional shear-layer flows is also presented and discussed here. The dynamics of the radially spreading spray is essentially different from that of the unidirectional spray. In the radial case, streamlines of the host-gas flow become more crowded with radial distance, and thus, it is shown here how lateral evolution in size histograms and lateral Sauter mean diameter (SMD) profiles are affected by this feature of the radially spreading flow. The effects of initial drop-size histograms on lateral distributions of: droplet SMD, overall spray densities, and vapor are also studied here for three basic initial drop-size distributions: monodisperse, bimodal, and polydisperse. It is shown how the behavior exhibited by polydisperse (and bimodal) sprays differs intrinsically from the behavior of monodisperse sprays. For example, for sprays which are initially monodisperse the lateral profile of the spray’s SMD across the shear layer always decreases, whereas for polydisperse or bimodal sprays it may increase or assume an ‘‘S’’ shaped curve.
Investigation of wetting hydrodynamics using numerical simulations
Authors: Finlow David E. , Kota Prakash R. , Bose Arijit
Published: July 2002

Meniscus shapes from a simulation of a plate immersing into an infinitely deep liquid bath, for a range of outer length scales, have been obtained numerically. These have been compared with the leading-order prediction from a three-region asymptotic analysis done in the double limit, Capillary number, Ca→0, LS/LC→0, with Ca ln(LC/LS) of O(1), where LS and LC represent the slip length and an outer macroscopic length, respectively. For Ca<0.01, the numerically computed and the perturbation solutions show excellent agreement. Within this range of Ca, the meniscus slope at a distance 10LS from the dynamic contact line is geometry independent, that is, does not vary with changes in the outer length LC. The interface slope at this point can serve as an appropriate material boundary condition for the outer problem. For 0.01<Ca<0.1, the intermediate region solution continues to closely fit the numerically generated solution, while the match in the outer region begins to degrade. By monitoring the pressure difference between the surrounding inviscid gas phase and arbitrarily chosen point in the liquid, we attribute this breakdown to infiltration of viscous effects into the outer region, so that static capillarity does not adequately describe meniscus shapes in this regime. For Ca≳0.1, there is no match between the numerical and perturbation solutions in both the intermediate and outer regions, indicating that higher-order contributions must be accounted for in the perturbation solutions.
On velocity-conditioned scalar mixing in homogeneous turbulence
Authors: Fox R. O.
Published: July 2002

Scalar mixing models are required to model turbulent molecular mixing in full probability density function (pdf) simulations of turbulent reacting flows. Despite the existence of direct numerical simulation (DNS) data suggesting the contrary, most scalar mixing models assume that molecular mixing is independent of the instantaneous velocity, i.e., 〈D∇2φ|V,ψ〉=〈D∇2φ|ψ〉. Since in a joint velocity, composition pdf calculation the velocity is known, this assumption is unnecessary and leads to a lack of local isotropy in the scalar field. Moreover, since velocity conditioning offers a numerically tractable approach for including the effects of local anisotropy and mean velocity gradients on scalar mixing, it should be of considerable interest for the numerical simulation of scalar mixing in inhomogeneous turbulent flows. An efficient numerical implementation of velocity-conditioned scalar mixing for full pdf simulations is proposed and verified against DNS data for homogeneous turbulence (isotropic and shear flow) with a uniform mean scalar gradient. A second-moment closure relating the velocity-conditioned scalar dissipation to the scalar fluxes and Reynolds stresses that is exact in the limit of a joint Gaussian pdf is also derived for use with moment closure models.
Magnetohydrodynamic wave-current system with constant vorticity
Authors: Brevik I. , Farsund O/. , Aarseth J. B.
Published: July 2002

The basic linear theory is given for a perfectly conducting stratified wave-current system in which there is an upper layer of incompressible fluid of constant vorticity propagating on a slightly heavier lower layer of stagnant fluid. An extraneous homogeneous horizontal magnetic field B0 is present, directed either longitudinally or transversely. Because of the magnetic field the basic governing equations for the system form a set of differential equations, in marked contrast to the single algebraic dispersion equation that would result were the magnetic field absent. The differential equations are solved, and the solutions are shown graphically for various cases of the magnetic field strength.
A stability study of the developing mixing layer formed by two supersonic laminar streams
Authors: Liang Fang-Pei , Reshotko Eli , Demetriades Anthony
Published: July 2002

An inviscid, parallel, spatial linear stability analysis is performed on both bounded and semibounded developing mixing layers formed between a laminar Mach 8 stream and another at Mach 3. Three unstable modes have been found in the initial mixing zone of the unbounded flow. In the downstream region of this flow the slowest of these modes becomes stable, and the remaining two correspond to the fast and slow modes of the self-similar mixing layer. For the semibounded flow, a wall in the slow stream introduces a series of acoustic modes which replace the fast mode of the unbounded flow. For both the unbounded and the semibounded flows the largest growth rates belong to the slowest mode which resides in the developing region and is insensitive to the presence of the wall. The existence of this mode has been detected in a wind-tunnel experiment, at frequency ranges suggested by, and with maximum growth rates in agreement with, the theory.
Boundary layer separation due to gas thermal expansion
Authors: Higuera F. J.
Published: July 2002

An analysis is carried out of the viscous-inviscid interaction due to the thermal expansion of the gas in the laminar boundary layer over a flat plate whose temperature presents a step elevation above the ambient temperature at a finite distance of its leading edge. Numerical solution of the triple-deck problem for infinitely large Reynolds numbers shows that the boundary layer separates for a critical value of the ratio of plate-to-gas temperature, dependent on the Prandtl number and the temperature sensitivity of the gas viscosity (which is assumed to increase as a power of the temperature). As the temperature ratio increases above this value, the separation point continuously shifts upstream of the temperature step whereas reattachment occurs shortly downstream of the step, leading to a triangle shaped recirculation bubble. An asymptotic description is given of the flow with incipient separation. For very large values of the temperature ratio a neatly defined interface develops between the cold and hot parts of the flow and the closure of the bubble becomes very abrupt, with the fluid recirculating near its rear section in a characteristic manner that depends on the combined effects of the large decrease of density and increase of viscosity due to the strong heating.
Transport coefficients in weakly compressible turbulence
Authors: Rubinstein Robert , Erlebacher Gordon
Published: July 2002

A theory of transport coefficients in weakly compressible turbulence is derived by applying Yoshizawa’s two-scale direct interaction approximation to the compressible equations of motion linearized about a state of incompressible turbulence. The result is a generalization of the eddy viscosity representation of incompressible turbulence. In addition to the usual incompressible eddy viscosity, the calculation generates eddy diffusivities for entropy and pressure, and an effective bulk viscosity acting on the mean flow. The compressible fluctuations also generate an effective turbulent mean pressure and corrections to the speed of sound. Finally, Yoshizawa’s two-scale approximation generates terms in the mean flow equations which contain gradients of incompressible turbulence quantities. A preliminary description of these terms is given.
Fluorescence visualization of a convective instability which modulates the spreading of volatile surface films
Authors: Dussaud Anne D. , Troian Sandra M. , Harris Scott R.
Published: July 2002

The spontaneous spreading of a thin liquid film along the surface of a deep liquid layer of higher surface tension is a ubiquitous process which provides rapid and efficient surface transport of organic or biological material. For a source of constant concentration, the leading edge of a nonvolatile, immiscible film driven to spread by gradients in surface tension is known to advance as t3/4 in time. Recent experiments using laser shadowgraphy to detect the advancing front of spreading films indicate, however, that immiscible but volatile sources of constant concentration spread with a reduced exponent according to t1/2. Using a novel technique whereby fluorescent lines are inscribed in water, we have detected the evolution of a thermal instability beneath the leading edge of volatile films which strongly resembles a Rayleigh-Bénard roll. We propose that the increased dissipation from this rotational flow structure is likely responsible for the reduction in spreading exponent. This observation suggests a conceptual framework for coupling the effects of evaporation to the dynamics of spreading.
Parametrizing the growth rate influence of the velocity ratio in compressible reacting mixing layers
Authors: Day M. J. , Reynolds W. C. , Mansour N. N.
Published: July 2002

The ability of the velocity ratio parameter λ=(U1−U2)/(U1+U2) to scale linear stability amplification rates for a compressible reacting and compressible variable-density mixing layer is reported. Extensions to the definition of λ to reflect the dominance of outer modes in the flow structure at significant levels of heat release and compressibility are proposed and their performance is evaluated.
Experiments on homogeneous turbulence in an unstably stratified fluid
Authors: Thoroddsen S. T. , Van Atta C. W. , Yampolsky J. S.
Published: July 2002

We have studied experimentally the effects of an unstable linear density profile on the evolution of homogeneous grid-generated turbulence. The experiments were performed in a thermally stratified wind tunnel employing hot- and cold-wire anemometry. The unstably stratified air stream was passed through a biplanar grid and the down-stream evolution of the turbulence statistics were studied. Contrary to the stably stratified case, where vertical velocity fluctuations are inhibited, here the buoyancy forces feed energy into the vertical motions. This injection at the actively turbulent length scales continues up to a critical time at which large-scale overturning of the entire fluid volume occurs. This overturn is due to the Rayleigh–Benard-type instability, which is manifest in the mean temperature field by a large plume rising up from the tunnel floor at the centerline. During the viscous decay, downstream of the grid, the r.m.s. vertical velocity fluctuations are relatively enhanced becoming 1.45 times the stream-wise fluctuations, before this overturn. The normalized buoyancy flux is also enhanced by the destabilizing buoyancy forces, reaching values as large as 0.88, significantly larger than those observed in the passively stratified case. Spectral ratios identify the length scales most affected. Results for different grid mesh-sizes show that the statistics are Reynolds number independent over the range of values studied here, i.e., Reλ between 21 and 66. The probability density functions of temperature and velocity remain Gaussian in the homogeneous region. As the large-scale overturn takes over the flow, the scalar and velocity fluctuations are enhanced dramatically and qualitative changes are observed in the pdf of the temperature fluctuations.
The decay of bubble oscillations
Authors: Roberts P. H. , Wu C. C.
Published: July 2002

We study the initial value problem posed by the small amplitude free oscillations of a bubble in a viscous fluid. The solution consists of a linear combination of discrete normal modes and an integral over a continuous spectrum. The continuous spectrum dominates the solution for large times. As a result, the surface deformation ultimately decays algebraically and not as a modulated damped wave, as has sometimes been suggested.
Comment on “Particle collision rate in fluid flows” [Phys. Fluids 10, 1028 (1998)]
Authors: Collins Lance R. , Sundaram Shivshankar
Published: July 2002

In the publication by Hu and Mei [Phys. Fluids 10, 1028 (1998)] a correction to the collision formula is described for like particles within a given size category. Here we show that the formula derived by Sundaram and Collins (1997) is already consistent with Hu and Mei (1998) and so their correction does not apply.
Ensemble-average versus suspension-scale Cauchy continuum-mechanical definitions of stress in polarized suspensions: Global homogenization of a dilute suspension of dipolar spherical particles
Authors: Almog Y. , Brenner H.
Published: July 2002

The macroscale rheological properties of a dilute suspension exposed to a uniform external field and composed of identical, rigid, inhomogeneous, dipolar, spherical particles dispersed in an incompressible Newtonian fluid and possessing the same mean density as the latter fluid are derived from knowledge of its microscale properties by applying a global ensemble-averaging technique. Each dipole, which is permanently embedded in the particle, is assumed to be generated by the presence of an inhomogeneous external body-force field in the particle interior resulting from the action of the uniform external field on an inhomogeneous distribution of interior matter. It is shown that although the ensemble-average stress tensor is symmetric, the suspension nevertheless behaves macroscopically as if it possessed an asymmetric stress tensor. This seeming contradiction can be traced to the fact that the average body force acting on the contents of any arbitrarily drawn volume lying in the interior of the suspension does not vanish despite the fact that each particle is “neutrally buoyant.” That this force is not zero stems from the fact that some particles necessarily straddle the closed surface bounding that volume, and that the distribution of external body forces over the interiors of these particles is nonuniform. As such, that portion of the spherical particle lying outside of the surface enclosing the domain exerts a force on the remaining portion of the sphere lying within that domain. We then demonstrate that the natural macroscopic model, which is derived by equating the divergence of the suspension-scale stress appearing in that model to the ensemble-average external body-force field, and which predicts a symmetric stress tensor, is macroscopically deficient with respect to the more intuitive asymmetric stress model usually proposed by continuum mechanicians for such a suspension. It is shown that the latter, continuum-mechanical model recovers all the physically interesting properties of the suspension.
Isotropic prestress theory for fully developed channel flows
Authors: Weispfennig K. , Parks S. M. , Petty C. A.
Published: July 2002

The anisotropic distribution of turbulent kinetic energy in fully developed channel flows is examined by using an algebraic preclosure which relates the Reynolds stress to the mean field gradient and to a prestress correlation, (I̳+τR∇〈u_〉)T⋅〈u_′u_′〉⋅(I̳+τR∇〈u_〉)=τR2〈f_′f_′〉. Local fluctuations in the pressure field and in the instantaneous Reynolds stress are responsible for the prestress correlation τR2〈f_′f_′〉. Closure requires a phenomenological model for the anisotropic prestress 2kH̳, defined by 2kH̳≡τR2〈f_′f_′〉−2αI̳/3. The prestress coefficient α(=τR2〈f_′⋅f_′〉/2) depends algebraically on the components of the Reynolds stress, the mean velocity gradient, the relaxation time τR, and the turbulent kinetic energy k. Previously reported direct numerical simulations (DNS) results for fully developed channel flows (δ+=395) are used to evaluate the behavior of the Reynolds stress for an isotropic prestress (IPS) correlation (i.e., H̳=O̳). The IPS theory predicts the existence of a nonzero primary normal stress difference and shows that a significant transfer of kinetic energy occurs from the transverse and normal components of the Reynolds stress to the longitudinal component for τR‖∇〈u_〉‖≫1. The spatial distributions of the two nontrivial invariants of the anisotropic stress predicted by the IPS theory are consistent with DNS results for 10⩽y+⩽395. The practical utility of the isotropic prestress theory is further demonstrated by predicting the low-order statistical properties of the turbulence in the outer region of fully developed channel flows. Transport equations for the turbulent kinetic energy and the turbulent dissipation are used to estimate the spatial distributions of the turbulent time scales k/ε and τR.
Axial instability of a free-surface front in a partially filled horizontal rotating cylinder
Authors: Hosoi A. E. , Mahadevan L.
Published: July 2002

We investigate the axial instability of the free-surface front of a viscous fluid in a horizontal cylinder rotating about its longitudinal axis. A simplified model equation for the evolution of the free surface is derived and includes the effects of gravity, capillarity, inertia, and viscosity. This equation is solved numerically to determine the base state with no axial variation, and a numerical linear stability analysis is carried out to examine the onset of unstable axial modes. Various computational results are presented for the wavelength of the axial instability. Inertia is found to play an important role in the onset of the instability and the wavelength of the instability λ satisfies the power law λ∼γ1/3, where γ is surface tension. Finally some numerical simulations of the simplified evolution equation are presented to show that they can capture the steady shark-teeth patterns observed in recent experiments [R. E. Johnson, in Engineering Science, Fluid Dynamics: A Symposium to Honor T. Y. Wu (World Scientific, Singapore, 1990), pp. 435–449; S. T. Thoroddsen and L. Mahadevan, “Experimental studies of the instabilities in a partially filled horizontal rotating cylinder,” Exp. Fluids 23, 1 (1997)].
Variational methods and nonlinear quasigeostrophic waves
Authors: Duan Jinqiao , Holm Darryl D. , Li Kaitai
Published: July 2002

In this paper, we discuss zonally periodic steady quasigeostrophic waves in a β-plane channel, by using variational methods. A class of steady quasigeostrophic waves are determined by the potential vorticity field profile, g(⋅), which is a function of the stream function. We show that zonally periodic steady quasigeostrophic waves exist when the bottom topography and the potential vorticity field are bounded. We also show that these waves are unique if, in addition, the potential vorticity field profile is increasing and passes through the origin. Finally, we demonstrate that the zonal periodic wave in the case with g(ψ)=arctan(ψ) is nonlinearly stable in the sense of Liapunov, under a boundedness condition for the potential vorticity field, or equivalently, under suitable conditions on the bottom topography, β parameter, and zonal period T.
Magnetohydrodynamic flow in a rectangular duct in a cusped magnetic field
Authors: Molokov S. , Emmrich D. M. , Kutev V. A.
Published: July 2002

Liquid metal flow in a rectangular duct in a plane cusped magnetic field is considered with the main objective being to investigate the effect of the sidewalls on the flow. At high values of the Hartmann number Ha the velocity profile is characterized by the presence of three jets. One jet is at the symmetry plane, where the transverse component of the magnetic field changes sign, and the magnetic field is parallel to the flow. The other two are at the sidewalls parallel to the field. The overall flow balance is determined by the wall conductance ratios of the sidewalls and the Hartmann walls (these are the walls with a nonzero normal component of the field). If the sidewalls are conducting, the jet at the symmetry plane dominates. If the sidewalls are electrically insulating, the sidewall jets dominate. In the latter case the flow pattern exhibits only a small resemblance to the analogous flow between two parallel plates (no sidewalls), which was investigated before. The pressure drop is O(Ha1/2) higher than in the corresponding flow in a uniform, transverse magnetic field. This means that braking the flow by a cusped field is more effective, and this feature can be used in some applications of magnetohydrodynamics, such as electromagnetic brakes and semiconductor crystal growth from melts.
Determination of particle size distributions from acoustic wave propagation measurements
Authors: Spelt Peter D. M. , Norato Michael A. , Sangani Ashok S. , Tavlarides Lawrence L.
Published: July 2002

The wave equations for the interior and exterior of the particles are ensemble averaged and combined with an analysis by Allegra and Hawley [J. Acoust. Soc. Am. 51, 1545 (1972)] for the interaction of a single particle with the incident wave to determine the phase speed and attenuation of sound waves propagating through dilute slurries. The theory is shown to compare very well with the measured attenuation. The inverse problem, i.e., the problem of determining the particle size distribution given the attenuation as a function of frequency, is examined using regularization techniques that have been successful for bubbly liquids. It is shown that, unlike the bubbly liquids, the success of solving the inverse problem is limited since it depends strongly on the nature of particles and the frequency range used in inverse calculations.
Pulsed gradient spin echo nuclear magnetic resonance measurements of hydrodynamic instabilities with coherent structure: Taylor vortices
Authors: Seymour Joseph D. , Manz Bertram , Callaghan Paul T.
Published: July 2002

Pulsed gradient spin echo (PGSE) nuclear magnetic resonance (NMR) is applied to the characterization of hydrodynamic instabilities. It is demonstrated theoretically and experimentally that for Taylor vortex flow in a Couette cell the PGSE NMR data is coherently modulated in an interference pattern dependent upon the vortex size, or wavelength, and velocity intensity. Spatially resolved NMR velocity images of all three velocity components for water in supercritical Taylor number flow and NMR velocity image data of the axial disturbance velocity for pentane at three supercritical values of the Taylor number are presented. For the short column used the NMR velocity data clearly show axial asymmetry with maximum velocities and the center (eye) of the vortex drawn toward the radial outflow boundary.