bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear wave scattering and electron beam relaxation
Authors: Muschietti L. , Dum C. T.
Published: July 2002

The role played by nonlinear scattering during the relaxation of a warm electron beam is investigated with the help of a numerical code. The code is based on kinetic equations and includes the quasilinear wave–electron interaction as well as wave–wave scattering off ion clouds. Both mechanisms have been observed to play key roles in a recent particle simulation with a large number of modes. It is found that (1) ions with velocity 2vi (vi being the ion thermal velocity) are the most efficient to scatter the Langmuir waves off their polarization clouds. As a result, the transfer rate of the spectrum out of resonance with the beam is larger by a factor 3 compared to the usual estimates in the literature, which assume a static ion response. The predicted wave number k of the secondary spectrum differs also substantially. (2) If the beam density nb, drift Ub, and width vb satisfy the condition nb/n0>4.2(ve/Ub)2 ×(vb/Ub)3, the changes brought to the dispersion relation by the presence of the beam electrons dramatically alter the characteristics of the secondary spectrum.

Forward propagating waves may grow where the conventional picture expects backward propagating waves. Most strikingly, in a late phase the classic condensate about k∼0 is depleted with the formation of a new condensate in resonance with the flat-topped beam distribution. This contradicts the commonly assumed cascade in wave numbers, but follows simply from the fact that the mere presence of the beam electrons creates a minimum in the frequency–wave-number relation. There is no contradiction with a cascade toward lower frequencies driven by an isotropic ion distribution. For strong and slow beams (nb/n0∼10−2, Ub∼10ve) the predictions of this code can be compared with the results obtained in the particle simulation. The agreement is excellent if one uses a dispersion relation that includes the beam. Complete plateau formation by resonant diffusion and late formation of a secondary spectrum are observed. Time scales and spectral characteristics compare well. For faster and weaker beams, it is demonstrated that the nonlinear wave scattering may intervene before complete quasilinear relaxation. Once the beam top has been erased by diffusion, a wave condensate forms, which inhibits further relaxation toward lower velocities. Modes in resonance with the positive slope at the low-velocity front of the flat-topped beam are stabilized by a fast transfer of their energy into the condensate.
Chaotic dynamics of drift wave vortices in a bounded region
Authors: Shibahara Hideaki , Kono Mitsuo , Horton Wendell
Published: July 2002

The dynamical behavior of drift wave vortices in a bounded region is studied based on the modulated point vortex model associated with the Hasegawa–Mima equation. When a circle is taken as the boundary of the region, the potential for the vortices inside the circle can be constructed by the circle theorem which replaces the boundary by the image system of the vortices inside the circle and ensures that the potential for the vortices is zero on the boundary. The diamagnetic drift has a tendency to drive vortices into a chaotic motion.
Spectra and growth rates of resistive wall modes in a reversed-field pinch
Authors: Greene Philip , Robertson Scott
Published: July 2002

The Reversatron II [IEEE Trans. Plasma Sci. PS-16, 667 (1988)] reversed-field pinch has been operated with shells having magnetic penetration time comparable to and shorter than the discharge duration. The spectra and growth rates of the resistive wall modes have been measured and compared for the two cases. The growth rates of modes are typically in the expected range γτs=0.5–2 where γ is the growth rate and τs is the magnetic penetration time of the shell. The spectra, however, are broader than expected from linear theory and there are indications that both the growth rates and the mode spectra are affected by nonlinearities.
Magnetic surfaces in a steady-state tokamak
Authors: Kinney R. , Tajima T. , Irie H.
Published: July 2002

The effects of self-consistently interacting internal currents are modeled in a tokamak plasma with given external toroidal and poloidal magnetic fields. The unperturbed external magnetic surfaces are described through the well-known nonlinear ‘‘standard map.’’ When the magnetic field is allowed to carry an internal current, the self-interaction of these currents disturbs the integrity of the magnetic surfaces. A computational study of the effects of the interacting internal current filaments measures the diffusion of field lines from the unperturbed surfaces, and finds the self-interaction to be a significant effect that always serves to increase diffusion. Perfect surfaces are not maintained even when magnetic islands would not otherwise overlap. Diffusion from the current interaction dominates when current fluctuations reach a fraction of the applied field.
Electroacoustic radiation from a point source in a moving magnetoactive plasma
Authors: Dobrydnev B. V. , Rutkevich I. M.
Published: July 2002

The three-dimensional problem of the wave propagation from a point source in a moving magnetoactive plasma is considered for the case of monochromatic waves. The magnetic Reynolds number is assumed to be small, so that the potential approximation for the electric field perturbation can be accepted. The cases of subsonic and supersonic main flows are considered. The method of integral transformations is used for the solution of the problem. The high-frequency asymptotic expansion of the solution is obtained and analyzed. For a supersonic flow, the existence of the electric and gas-dynamic perturbations outside the classic Mach cone is established, and the properties of these perturbations are examined.
A kinetic theory analysis of evaporation and condensation of a diatomic gas
Authors: Soga Takeo
Published: July 2002

The evaporation and condensation problem of diatomic gas was studied based on the BGK–Morse kinetic model equation. The results showed that (1) the macroscopic jump coefficients were insensitive to the variation in the relaxation time of internal energy, (2) the pressure jump caused by evaporation (condensation) or by heat transfer was almost the same as the value of a monatomic gas, and (3) the temperature jumps of a diatomic gas were smaller than those of a monatomic gas in accordance with the quantities of specific heats. Approximate expressions of macroscopic jump coefficients of a diatomic gas for arbitrary values of the internal degrees of freedom and those of accommodation coefficients of mass, translational energy, and internal energy are obtained using the jump coefficients of a monatomic gas.
Instability of natural convection in a tall vertical annulus
Authors: Weidman P. D. , Mehrdadtehranfar G.
Published: July 2002

An experimental study has been made of the hydrodynamic stability of viscous fluid flow contained between the differentially heated walls of a tall vertical annulus. Tests were conducted using different glycerol solutions spanning a range of Rayleigh numbers (104–106) and moderately high Prandtl numbers (15–150) for a height/gap ratio of 64 and a radius ratio equal to 0.62. Visualization studies show that the unstable flow consists of two separate progressive wave systems, one ascending the hot inner wall and the other descending the cold outer wall. The approximate Rayleigh number, phase speed, and wavelength at the onset of instability for each wave system were determined for several Prandtl numbers. The regular wave patterns observed near the stability boundary persist over only a very limited range of supercritical Rayleigh numbers above which flow dislocations set in. At higher Rayleigh numbers these random dislocations appear in increasing numbers and ultimately render the flow turbulent.
Semicollisional drift-tearing modes in toroidal plasmas
Authors: Hahm T. S. , Chen Liu
Published: July 2002

Semicollisional drift-tearing modes are studied analytically in toroidal plasmas. Corresponding differential equations for the eigenmodes are derived via the ballooning mode representation and flux-surface averaging. A dispersion relation is then obtained using asymptotic matching. It is found that the stabilizing effects of good average curvature and finite plasma compression lead to a tearing instability threshold Δc, which is independent of the resistivity.
Buoyancy-driven convection in a horizontal fluid layer extending over a porous substrate
Authors: Poulikakos D.
Published: July 2002

In this study a series of numerical simulations is reported that aims to document the phenomenon of buoyancy-driven flow instability in a fluid layer extending over a porous substrate. The numerical simulations focus primarily on the parametric domain in which the flow in the system is well established, i.e., the value of the Rayleigh number is larger than critical. A general flow model is used to describe the flow inside the porous bed. This flow model accounts for friction caused by macroscopic shear [Brinkman extension of the Darcy model; Appl. Sci. Res. Sect. A 1, 27 (1947)], as well as for the phenomenon of flow inertia [Forchheimer’s extension of the Darcy model; Dtsch. Ingenieure 45, 1782 (1901)]. Several important characteristics of the flow and temperature fields inside the composite layer (porous/fluid) are reported and the dependence of these characteristics on the problem dimensionless groups is documented.
Wave interactions in swept-wing flows
Authors: Reed Helen L.
Published: July 2002

The leading-edge region of swept wings is dominated by the crossflow instability, resulting in vortices that all rotate in the same sense. The effect of these vortices on the behavior of other disturbances is examined and an interaction between these and disturbances of half the dominating crossflow wavelength is predicted. According to theory, the interaction is of crossflow–crossflow type. The effect explains the anomalies found in the experimental observations of Saric and Yeates [Laminar-Turbulent Transition (Springer, Berlin, 1985), p. 429]. Visually Saric and Yeates observe vortices at the wavelength predicted by linear theory; however, in their hot-wire measurements they find that the second harmonic dominates disturbance growth, with eventually three times the amplitude of the primary wave. In this case, the usual transition–prediction methods would fail, clearly indicating the importance of studying interactions of this sort.
Theory of trapped-ion-temperature-gradient-driven turbulence and transport in low-collisionality plasmas
Authors: Biglari H. , Diamond P. H. , Terry P. W.
Published: July 2002

A novel theory for the nonlinear evolution of the trapped-ion-temperature-gradient-driven mode, based on the turbulent trapping of resonant ions in the electrostatic potential of the waves, is proposed. A statistical description is adopted whereby the self-consistent evolution of the two-point correlation function of the trapped-particle distribution function is followed in phase space. Threshold-dependent, non-steady-state turbulence (nonlinear instability) is shown to develop when the decay of the correlation function is overcome by a source term that derives its free energy from the relaxation of the average distribution function. This nonlinear instability leads to anomalous thermal and particle transport that in turn reconfigure the equilibrium temperature and density profiles in such a way as to return the system toward its marginal point. Expressions for the nonlinear dispersion relation and threshold, as well as estimates of the thermal and particle transport level, are derived. The estimated flux levels are sufficiently high as to make any significant departure away from marginality unlikely. The scenario outlined serves to underscore the desirability for pellet injection in experimental devices such as the Compact Ignition Tokamak [Bull. Am. Phys. Soc. 32, 1921 (1987)] that operate in the very low ion collisionality regime where this mode would be expected to become relevant. As with a number of recent theories, the present work further reinforces the notion that unfavorably drifting trapped particles pose a serious menace to confinement and suggests inboard, off-axis radio-frequency heating as one means of reducing the size of this population, at least for the case of those energetic trapped particles created during auxiliary heating.
Stability of Bernstein–Greene–Kruskal plasma equilibria. Numerical experiments over a long time
Authors: Ghizzo A. , Izrar B. , Bertrand P. , Fijalkow E. , Feix M. R. , Shoucri M.
Published: July 2002

Bernstein–Greene–Kruskal (BGK) equilibria for a Vlasov plasma consisting of a periodic structure exhibiting depressions or ‘‘holes’’ in phase space are under consideration. Marginal stability analysis indicates that such structures are unstable when the system contains at least two holes. An Eulerian numerical code is developed allowing noiseless information on the long time phase space behavior (about 103ω−1p) to be obtained. Starting with equilibria with up to six holes, it is shown that the final state is given by a structure with only one large hole, the initial instability inducing coalescences of the different holes. On the other hand, starting with a homogeneous two-stream plasma it is shown that, in a first step, a BGK periodic structure appears with a number of holes proportional to the length of the system, followed, in a second step, by a coalescence of the holes to always end up with the above mentioned one large hole structure.
Temporal evolution of ion energy in a plasma focus
Authors: Rhee M. J. , Weidman D. J.
Published: July 2002

For the first time, the temporal structure of ion energy in a plasma focus is revealed using a time-resolving Thomson spectrometer. The velocities and arrival times of ions are determined from the spectrogram. The resulting distribution of ions in velocity–time space at the source is found to be a line distribution, as if the ions were accelerated in a diode by a pulsed voltage.
Nonlinear particle diffusion in a time-dependent host medium
Authors: Zanette D. H. , Barrachina R. O.
Published: July 2002

The dynamics of a gas in a time-dependent host medium is studied by means of a generalized Boltzmann equation. Removal and regeneration events, as well as linear external sources, are taken into account. The corresponding continuity equation is solved, and the time evolution of the system is investigated, with particular attention paid to its asymptotic regime.
Ion distribution functions during ion cyclotron resonance heating at the fundamental frequency
Authors: Hassan Mohamed H. A.
Published: July 2002

The distribution function of ions during ion cyclotron resonance heating (ICRH) is studied analytically using a simplified one-dimensional Fokker–Planck equation incorporating ion–ion and ion–electron collisions and rf quasilinear diffusion. By including source and loss terms in the equation, steady-state and time-dependent solutions, which are regular near the origin and vanish at high energies, are found. It is shown that an initially Maxwellian distribution function is transformed by the ICRH into a non-Maxwellian distribution with a tail of energetic ions. The tail is more pronounced when quasilinear diffusion dominates over collisions and losses.
Transition to chaos in converging–diverging channel flows: Ruelle–Takens–Newhouse scenario
Authors: Guzmán A. M. , Amon C. H.
Published: July 2002

Direct numerical simulations of the transition process from laminar to chaotic flow in converging–diverging channels are presented. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic self-sustained flow regimes. The numerical experiments reveal three distinct bifurcations as the Reynolds number is increased, each adding a new fundamental frequency to the velocity spectrum. In addition, frequency-locked periodic solutions with independent but synchronized periodic functions are obtained. A scenario similar to the Ruelle–Takens–Newhouse scenario of the onset of chaos is verified in this forced convective open system flow. The results are illustrated for different Reynolds numbers using time-velocity histories, Fourier power spectra, and phase space trajectories. The global structure of the self-sustained oscillatory flow for a periodic regime is also discussed.
Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis
Authors: Perry A. E. , Marušić I. , Li J. D.
Published: July 2002

A new look at the closure problem of turbulent boundary layers is taken here using recently derived analytical expressions for the shear stress distributions. These expressions are based on the logarithmic law of the wall and law of the wake formulation of Coles [J. Fluid Mech. 1, 191 (1956)] with the mean continuity and the mean momentum differential and integral equations. The concept of equilibrium layers of Clauser [Adv. Mech. 4, 1 (1956)] is extended and using similar ideas as Rotta [Prog. Aeronaut. Sci. 2, 1 (1962)] for self-similarity, a closure scheme is proposed for layers developing in arbitrary pressure gradients for the case where the streamwise derivative of the Coles wake factor is not too large. For a given flow case, this Coles wake condition can be tested with internal consistency checks. The mathematical framework is most suitable for incorporating Townsend’s attached eddy hypothesis as recently developed by Perry, Li, and Marušić [Philos. Trans. R. Soc. London Ser. A 336, 67 (1991)] for closure. This gives an opportunity to incorporate coherent structure concepts into closure schemes. Possible ways of handling the difficult case where the streamwise derivative of the Coles wake factor is significant are discussed.
The fractal aspect of an isovelocity set and its relationship to bursting phenomena in the turbulent boundary layer
Authors: Tsuji Yoshiyuki , Nakamura Ikuo
Published: July 2002

In this paper, the fractal property of an isovelocity set which is defined by the instantaneous streamwise velocity signal obtained in a turbulent boundary layer is reported. In the present study, the aim is to provide further evidence for the fractal property of the set and to investigate which physical and dynamical quantities significantly affect the fractal property of an isovelocity set. The instantaneous Reynolds stress is found to be a key factor of this fractal property. Using the variable interval time average (VITA) method and the quadrant analysis technique, the bursting events in the turbulent boundary layer are conditionally sampled and investigated in relation to the isovelocity set. The quadrant analysis technique is used to demonstrate that the fractal property appears only in the bursting period and that there is a close connection between the Reynolds stress producing structure and the fractality. Also considerations are given on the bursting distribution itself by means of fractals. In the near wall region, the bursting distribution has a self-affine fractal property as detected by the quadrant analysis technique. The VITA method, however, does not yield the fractal bursting distribution.
Dynamic behavior of variable-density, turbulent jets in their near development fields
Authors: Sautet J. C. , Stepowski D.
Published: July 2002

Four round turbulent jets of hydrogen–nitrogen mixtures (initial density ratio ranging from 0.07 to 1) discharging into a slow air coflow are experimentally and analytically studied. The investigation is restricted to the near development field over which both buoyancy and coflow effects have negligible influence on the jet expansion. Two-color laser Doppler anemometry provides the mean and fluctuation of the velocity components, while a laser Mie scattering technique with conditional seeding provides the radial profiles of mean density. Self-similar behavior is investigated by using a local effective jet diameter that accounts for the strong density variations in the near development field. This scaling based on momentum flux conservation appears to be efficient for collapsing the centerline velocity data (mean and RMS) along a unique self-similar curve for all jets.
Forced nonlinear disturbances in incompressible boundary layers
Authors: Bogdanova-Ryzhova E. V. , Ryzhov O. S.
Published: July 2002

In this paper we explore essentially nonlinear disturbances produced in an incompressible boundary layer by a roughness on the wall. The scale of the stationary roughness is supposed to be large enough so that generated waves are governed by the forced Benjamin–Davis–Acrivos (fBDA) equation. The disturbance patterns for a wide range of roughness sizes are analyzed revealing the remarkable phenomenon of bifurcations. A very specific oscillation motion over the obstacle is found. It appears to be the basic mechanism causing the periodic generation of solitary waves upstream and downstream. The general structure of disturbances in space at different values of time is discussed. The asymptotic analysis of the solution, when the intensity of the external agency Q becomes a small parameter, is given. The quadratic term of an expansion based on this parameter is responsible for the redistribution of solution mass between regions located ahead and behind the obstacle, inevitably leading to the gradual growth of nonlinear effects. According to the asymptotic consideration, the time Tc* determining the onset of the nonlinear stage of disturbance development is O(Q−3), this estimation correlates well with numerical results.
A threshold line dissociation model for the direct simulation Monte Carlo method
Authors: Boyd Iain D.
Published: July 2002

A new dissociation model for the direct simulation Monte Carlo (DSMC) method is formulated using the threshold line concept. This model considers in some detail the coupling between the vibrational energy distribution of molecules in a gas and the rate of dissociation. For a particular reaction, the new threshold line model only requires determination of a leading multiplicative constant and is therefore significantly less deterministic than existing DSMC chemistry models. The new model is evaluated in a heat bath under equilibrium and nonequilibrium conditions. It is also employed to calculate hypersonic shock waves of nitrogen and air. Comparison of the results generated with the new model is made with existing experimental data and with previous computational results. The more detailed DSMC implementation reveals properties of the threshold line dissociation model not apparent in the previous continuum implementation.
Turbulent traveling-wave convection in a two-layer system
Authors: Stamp Andrew P. , Griffiths Ross W.
Published: July 2002

When layers of salt and sugar solution are separated by a “diffusive” interface, interfacial waves are spontaneously generated by the turbulent convection once the system evolves to a critical value of the density–anomaly ratio Rρ≡βΔS/αΔT (Stamp et al., to appear in J. Fluid Mech). The waves modulate the interfacial fluxes by modifying the interface thickness and thereby organize the otherwise random convective motions into coherent large-scale circulations. In narrow rectangular channels a wide range of conditions give rise to a single wave which propagates back-and-forth, resulting in quasi-periodic reversals of tank-scale circulations. Here it is shown that in annular and equant rectangular cavities this same coupling phenomenon produces turbulent convection cells of a traveling-wave nature, coupled to large-amplitude solitary waves on the interface.
Mixing mechanisms in turbulent pipe flow
Authors: Guilkey J. E. , Kerstein A. R. , McMurtry P. A. , Klewicki J. C.
Published: July 2002

An experimental investigation of passive scalar mixing in turbulent pipe flow is carried out using a new non-intrusive scalar initialization technique. The measurements support a recently predicted similarity scaling of concentration spectra in flows that are unbounded in one direction. Reflecting this scaling, the scalar variance exhibits a power-law rather than exponential decay, indicating that the traditional plug-flow reactor picture of turbulent pipe-flow mixing omits key physical mechanisms.
On the unsteady low-Rossby number flow of a rotating fluid past a circular cylinder
Authors: Stocker Jennifer R. , Duck Peter W. , Page Michael A.
Published: July 2002

The unsteady flow of a homogeneous viscous fluid past a straight circular cylinder (radius l*) confined between two infinite parallel plates (a distance d* apart) relative to a rapidly rotating frame is considered. The cylinder is impulsively started from rest to a uniform velocity. The unsteady form of the boundary-layer equations for a rotating fluid is used to examine the flow Rossby number Ro∼O(E1/2), where E≪1 is the Ekman number. A range of values of the non-dimensional parameter N=lE1/2/Ro (where l=l*/d*) is considered. For 0⩽N<1, the flow pattern resembles that of the non-rotating case (N=0). Initially, the wall shear around the cylinder is positive everywhere. After a time, flow reversal begins at the rear stagnation point and then the position of zero wall shear moves upstream, towards the front stagnation point. The boundary-layer thickness in the region of reversed flow grows with time until a singularity/eruption at a point in the flow occurs. The boundary-layer equations are written in terms of Lagrangian coordinates in order to numerically investigate the finite-time singularity for 0⩽N<1. The flow close to the rear stagnation point is also examined in detail for a range of values of N and results are compared with the large-time asymptotic forms for the growth of the displacement thickness. The analysis suggests the displacement thickness in this region grows exponentially with time, for certain ranges of N. For 0<N<1, the displacement thickness grows exponentially with time in a manner similar to the non-rotating case. For N>1, the wall shear remains positive for all time. However, for 1⩽N<2, the displacement thickness of the boundary layer close to the rear stagnation point again grows exponentially with time. For 2<N<3 the flow close to the rear stagnation point also grows exponentially with time, although the form of solution differs from that for 0⩽N<2. For N>3, the solution tends to a truly steady limit, consistent with previous studies on the steady problem.
Coherent vortex model for surface pressure fluctuations induced by the wall region of a turbulent boundary layer
Authors: Dhanak Manhar R. , Dowling Ann P. , Si Chao
Published: July 2002

Exact solutions of the Navier–Stokes equations describing the interaction of streamwise vortices with a rigid surface are utilized to develop a conceptual model for the surface pressure spectrum associated with the wall region of a turbulent boundary layer. The evolution of single as well as pairs of coherent streamwise vortices, which principally govern the production of turbulence in the wall region, is considered in the presence of local straining flow induced by larger, outer-layer eddies. The surface pressure signatures of the coherent vortex motion and the associated power spectrum of the pressure are examined. Based on the results of the exact solutions, the surface pressure spectrum of an ensemble of independent coherent structures is modeled using the assumption of ergodicity in the manner described by Townsend and Lundgren for homogeneous turbulence. The free parameters in the model are estimated through comparison with available results from experiments and numerical simulations. The model, especially the one involving pairs of streamwise vortices, predicts the high frequency and high spanwise wave number range of the surface pressure spectrum quite well. Further, the probability density function of surface pressure associated with the model compares well with experimental results. Interestingly, the model also suggests that the contribution of the viscous interaction to low wave number spectral elements accounts for the discrepancy between experimental observations at such wave numbers and the prediction of the Kraichnan–Phillips theorem.
Hydrodynamic interactions between a particle and two rigid walls: Effect of surface roughness and many-body hydrodynamic interactions
Authors: Grasselli Y. , Lobry L.
Published: July 2002

The sedimentation of a particle trapped between two rigid walls allow us to demonstrate the effect of many-body hydrodynamic effects arising in a confined geometry. A theoretical treatment of this problem is presented together with an experimental investigation of the sedimentation of a macroscopic particle by image analysis which allows us to directly obtain the trajectory of the particle. Theoretical drag force in the presence of the two planes is shown to be in good agreement with the experimental results. The determination of the sedimentation of a particle, initially applied on the upper plate by a magnetic field gradient, is shown to provide a relevant information on the average surface roughness.
Time-dependent equations governing the shape of a two-dimensional liquid curtain, Part 2: Experiment
Authors: Clarke Andrew , Weinstein Steven J. , Moon Alice G. , Simister Elizabeth A.
Published: July 2002

In Part I of this paper, two governing equations have been derived that describe the shape of a falling liquid sheet (a curtain) subjected to ambient pressure disturbances. These equations are termed varicose and sinuous. The varicose equation governs thickness variations in the curtain, for which the two air–liquid interfaces move exactly out of phase. The sinuous equation governs the deflection of the curtain centreline, i.e., the two air–liquid interfaces move in phase such that the local thickness of the liquid is preserved. To the order of the approximations used, the theory presented in Part 1 indicates that pressure disturbances invoke a sinuous curtain deflection with no varicose contribution. In Part 2 of this paper, the sinuous equation is verified by means of a localised pressure disturbance induced by an electrostatic field. After initiation, the propagation of this disturbance is followed and the shape of the air liquid interface is measured using a laser reflection technique. Both the generation and detection of the disturbance are non-contacting and therefore allow a precise verification of the equation.
Disturbances produced by motion of an actuator
Authors: Hofmann Lorenz M. , Herbert Thorwald
Published: July 2002

Laminar flow control methods employ some device to act on the flow. These devices, termed actuators, vary from blowing-suction holes, to heating strips, to wall-deflected membranes. We use computer simulations to optimize membrane actuators to generate single-mode disturbances which develop in an unstable laminar boundary layer. We compare how varied actuator dimensions and motions reproduce the disturbance velocity profiles of naturally occurring disturbances. Finally, we use an analytical technique to support numerical simulations which determine actuator dimensions that generate the largest streamwise velocity disturbances downstream of the actuator.
Development and application of a hierarchical system for digital particle image velocimetry to free-surface turbulence
Authors: Kumar S. , Banerjee S.
Published: July 2002

A method for particle image velocimetry (PIV) is presented which improves upon the accuracy, computational efficiency and dynamic range (i.e., the difference between the largest and smallest resolvable particle displacement vectors) of conventional PIV techniques. The technique is applied to free-surface turbulence to resolve energy spectra for motions with a wide dynamic range. The methodology—based on multi-grid image processing algorithms for rigid body motion analysis, estimates the displacement vectors at discrete particle locations. The essence of this technique is to estimate large scale motions from image intensity patterns of low spatial frequencies and small scale motions from intensity patterns of high spatial frequencies. Cross-correlation between a pair of time separated particle images is implemented by the hierarchical computational scheme of Burt [“Fast filter transforms for image processing,” Int. J. Comput. Vision 16, 20 (1981)]. Each image is convolved with a series of band-pass filters and subsampled to obtain a set of images progressively decreasing in resolution and size. A coarse estimate of the displacement field obtained from pairs of lower resolution images are used to obtain more accurate estimates at the next (finer) level. Processing starts at the level of lowest resolution and stops at the highest resolution level, which contains the original image pair. Due to subsampling of low resolution images, the match template size can be kept constant for all stages of computation, thus eliminating the dependence of the largest resolvable displacement on the size of match template. In the present work, the search area at each level is kept constant at 3×3 pixels and the match template size at 5×5 pixels for all levels of computation. The algorithm has been implemented using simple thresholding based on the confidence level of an estimated displacement vector, as suggested by Anandan [“A computational framework and an algorithm for measurement of visual motion,” Int. J. Comput. Vision, 2, 283, (1987)]. However, the confidence-level-based smoothing technique for rigid body motions (continuous velocity fields) could not be applied to displacement estimates obtained at discrete points i.e., the particle locations. Instead, smoothing was performed over the area covered by each particle. The algorithm has been tested against direct numerical simulations of turbulent flows when the flow field is known and particle images have been generated from these with the addition of noise. Both the accuracy of motion estimation and the computation time are seen to improve as compared to conventional PIV methods. Finally, video images taken of particle motion on the free-surface of a channel flow have been used to determine the capabilities of the technique in an experimental study. The resulting spectra show a quasi-two-dimensional character of the free-surface turbulent flow field, which corresponds well with the direct numerical simulations.
Instabilities and singularities in Hele–Shaw flow
Authors: Goldstein Raymond E. , Pesci Adriana I. , Shelley Michael J.
Published: July 2002

A mechanism by which smooth initial conditions evolve towards a topological reconfiguration of fluid interfaces is studied in the context of Darcy’s law. In the case of thin fluid layers, nonlinear PDEs for the local thickness are derived from an asymptotic limit of the vortex sheet representation. A particular example considered is the Rayleigh–Taylor instability of stratified fluid layers, where the instability of the system is controlled by a Bond number B. It is proved that, for a range of B and initial data “subharmonic” to it, interface pinching must occur in at least infinite time. Numerical simulations suggest that “pinching” singularities occur generically when the system is unstable, and in particular immediately above a bifurcation point to instability. Near this bifurcation point an approximate analytical method describing the approach to a finite-time singularity is developed. The method exploits the separation of time scales that exists close to the first instability in a system of finite extent, with a discrete spectrum of modes. In this limit, slowly growing long-wavelength modes entrain faster short-wavelength modes, and thereby, allow the derivation of a nonlinear evolution equation for the amplitudes of the slow modes. The initial-value problem is solved in this slaved dynamics, yielding the time and analytical structure of a singularity that is associated with the motion of zeros in the complex plane, suggesting a general mechanism of singularity formation in this system. The discussion emphasizes the significance of several variational principles, and comparisons are made between the numerical simulations and the approximate theory.
Experiments on the stability of streamwise streaks in plane Poiseuille flow
Authors: Elofsson Per A. , Kawakami Mitsuyoshi , Alfredsson P. Henrik
Published: July 2002

The development and stability of streamwise streaks are studied in an air-flow channel experiment at subcritical Reynolds numbers. The streaks were generated by continuous suction through small slots at the wall. The streak amplitude first grows algebraically, and if the amplitude exceeds a certain threshold secondary instability in the form of travelling waves is observed. These waves give rise to high urms values in the region of large spanwise mean flow gradient. Measurements with two hot-wire probes indicate that velocity fluctuations are 180° out of phase at two neighboring peaks at each side of a low velocity region and implies the existence of a sinuous type instability. Measurements were also made with controlled disturbances where earphones were used to force the secondary instability. Phase averaged data clearly show the oscillation of the low velocity region and also provides the growth rate, phase speed as well as amplitude and phase distributions of the secondary instability. Several of these features suggest that the instability is of inflectional origin. Finally the disturbance breaks down and the flow undergoes transition to turbulence.
On the shape of granular fronts down rough inclined planes
Authors: Pouliquen O.
Published: July 2002

The shape of fronts obtained when releasing a cohesionless granular material at the top of a rough inclined plane is experimentally investigated. The measurements are compared with theoretical predictions given by a model based on a depth averaged momentum equation. Good agreement is found when the empirical friction law proposed in a previous study [O. Pouliquen, Phys. Fluids 11, 542 (1999)] is introduced in the model.
Propagation of sound generated by weak shock–vortex interaction
Authors: Inoue Osamu
Published: July 2002

The basic nature of sound generated by the interaction between a single vortex and a shock wave is studied numerically. Special attention is paid to the propagation process of the sound from near to far fields. The results show that the generation of sound is closely related to the generation of reflected shock waves, and that the sound waves are generated three times, basically. A stronger vortex produces a stronger reflected shock wave, resulting in the generation of additional pressure waves.
The effect of asymmetries on non-neutral plasma confinement time
Authors: Notte J. , Fajans J.
Published: July 2002

Theory predicts that perfectly azimuthally symmetric non-neutral plasma traps should confine plasma forever. Unintentional trap asymmetries are believed to limit plasma confinement times to less than <105 s. Deliberately applied electrostatic fields break the azimuthal symmetry and affect the plasma confinement time. While small, deliberate asymmetries do not significantly reduce the trap’s confinement properties, large asymmetries significantly degrade the plasma confinement. The scaling laws of this degradation are studied herein. The mechanism of plasma loss appears to change when deliberate asymmetries are applied.
Nonlinear dynamics of kink-tearing modes and their interaction with the current profiles in a reversed-field pinch
Authors: Nordlund P. , Mazur S.
Published: July 2002

New insight in the nonlinear and quasilinear dynamics of kink-tearing modes in reversed-field pinches (RFP’s) is obtained by simultaneous measurements of the evolution of current profiles and associated m=1 helical mode spectra in the Extrap T1 RFP [Nucl. Fusion 34, 427 (1994)]. Results concerning near single helicity states, m=0 mediated m=1 spectral broadening and cascade, together with the associated relaxation dynamics, are reported. The role of phase locking, between the nonlinearly interacting modes, in the pinch dynamics is also discussed.
Stability of current-driven modes in reversed field pinches with resistive walls and plasma rotation
Authors: Jiang Z. X. , Bondeson A. , Paccagnella R.
Published: July 2002

The linear stability of reversed field pinches (RFP’s) to current driven modes is investigated including the effects of resistive walls at a finite distance from the plasma and mode rotation. A comprehensive study is made of the stability to ideal and resistive modes and the implications for long-pulse operation of RFP’s are discussed. Stability to resistive modes of poloidal mode number m=1 requires conducting walls at a distance b/a<1.11 (a is the plasma and b the wall radius) for optimally peaked current profiles. Stability to m=0 requires very close-fitting conductors, b/a<1.03. The requirements on wall times and mode rotation frequencies posed by these modes are discussed. Nonresonant m=1 modes cannot be stabilized by resistive walls and require active feedback.
Space charge effects in the Paul trap
Authors: Avinash K. , Agarwal A. K. , Jana M. R. , Sen A. , Kaw P. K.
Published: July 2002

The effects of finite space charge on the equilibrium characteristics of charges confined in a Paul trap are investigated. It is found that space charge introduces two effects that have opposing influences on the confining pseudopotential well. The effect of electrostatic repulsion between like charges is to make the potential well shallower, but the plasma collective response can lead to a deepening of the well. Illustrative numerical solutions of thermal equilibria as well as an approximate analytical equilibrium are discussed.
Conditional analysis of floating potential fluctuations at the edge of the Texas Experimental Tokamak Upgrade (TEXT-U)
Authors: Filippas A. V. , Bengston Roger D. , Li G.-X. , Meier Mark , Ritz Ch. P. , Powers E. J.
Published: July 2002

Fluctuations in floating potential in the scrape-off layer and plasma edge were analyzed using a conditional statistical analysis technique. The floating potential fluctuations had a nearly Gaussian probability density function with the largest deviation from a Gaussian at the shear layer. The conditional averaging technique followed the statistical evolution of selected conditions in the floating potential signal. The decay rate of a conditional feature in time or space showed a small systematic variation with the amplitude of condition chosen. Either long-lived coherent structures are not present in statistically significant numbers, or the fluctuations are dominated by a large number of coherent structures with a nearly Gaussian distribution of fluctuation amplitudes, or conditional analysis using the amplitude of the floating potential as a condition is not a sensitive technique for identifying coherent structures.
Current–voltage response of anodic plasma contactors with external ionization
Authors: Ahedo E.
Published: July 2002

A spherical, steady-state model that considers the combined influence of plasma emission and external ionization of neutral gas on the operation of electron-collecting contactors is presented. Ionization by both Maxwellian and streaming electrons is investigated. A core (or quasineutral cloud) and a no-core mode are considered and the transition conditions from one to another are derived. The collected current is determined in terms of the main plasma and contactor parameters. The current-voltage response reproduces the ignited regime observed in experiments. The transition to the ignited regime and the transition to the core mode are not equivalent. It is shown that ionization by the electron beam is the main driver of ignition. The Langmuir law for the double layer causes a self-regulation of the core that affects the collection of current and leads to a multiplicity of solutions. Different neutral gas profiles are analyzed. It is uncertain whether ignition is reached when the neutral gas is provided by the contactor exclusively. The appearance of nonmonotonic potential profiles for low plasma emissions is noted.
Temperature and anisotropic-temperature relaxation measurements in cold, pure-electron plasmas
Authors: Beck B. R. , Fajans J. , Malmberg J. H.
Published: July 2002

Plasma temperatures in the range 25 to 2×106 K have been measured using a cryogenic, ultra-high vacuum, pure-electron plasma trap. The rate ν at which the temperatures parallel and perpendicular to the applied magnetic field relax to a common value has been measured over the temperature range 28 to 3.8×105 K and the magnetic field range 20 to 60 kG. This rate ν is closely related to the plasma collision frequency. When the cyclotron radius rc is large compared to the classical distance of closest approach b (rc/b≫1), the measured values of ν are in agreement with conventional collision theory. When the cyclotron radius is small compared to the classical distance of closest approach (rc/b≪1), ν drops precipitously as rc/b is decreased, in agreement with the many-electron adiabatic invariant theory of O’Neil and Hjorth.
Coalescence of two parallel current loops in a nonrelativistic electron–positron plasma
Authors: Zhao J. , Sakai J. I. , Nishikawa K.-I.
Published: July 2002

The coalescence of two parallel current loops in an electron–positron plasma is investigated by a three-dimensional electromagnetic relativistic particle code. Instead of mixing uniformly in the dissipation region as observed for current coalescence in an electron–ion plasma, electrons and positrons initially in the loops are driven to move separately by the magnetic gradient drift. Redistribution of the current-carrying electrons and positrons creates new current loops, which coalesce again, if the initial drift velocities remain greater than a critical value after coalescence. It was found that the energy stored in the current loops dissipates gradually through several coalescences. Consequently, the electrons and positrons near the current loops are heated through the coalescence. This process is qualitatively different from the explosive energy release during coalescence in an electron–ion plasma.
Nonlinear tearing mode interactions and mode locking in reversed-field pinches
Authors: Hegna C. C.
Published: July 2002

The nonlinear interaction of a set of tearing instabilities and plasma flow is studied in a cylindrical plasma. An analytic theory of mode locking is developed, which includes the effects of the localized electromagnetic torques, plasma inertia, and cross-field viscosity. The calculation is specialized for the case of mode locking on the Madison Symmetric Torus (MST) reversed-field pinch [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. In MST plasmas, a set of m=1 tearing instabilities become phase locked and form a toroidally localized, rotating magnetic disturbance. An evolution equation for the phase velocity of this magnetic disturbance is derived that accounts for two types of electromagnetic torques. The external torques describe the interaction of the tearing modes with static magnetic perturbations located outside the plasma region. The interior torques describe the nonlinear interaction of three tearing modes that satisfy a wave number resonance condition. For conditions typical of MST, the internal torques dominate the external torques, which suggest the nonlinear interaction of tearing instabilities play a prominent role in the momentum degradation and mode locking.