bluuebunny/crossref_metadata_2025 huggingface dataset:
Wave-induced plasma transport in the magnetic drift frequency range
Authors: Rosenberg M. , Krall N. A. , McBride J. B.
Published: July 2002

A calculation of the quasilinear transport and heating of plasma particles and diffusion of particle energy is presented, emphasizing the resonant interaction of plasma particles with waves in the magnetic drift frequency range. Substantial transport can occur for relatively small wave field amplitudes in a number of applications involving tandem mirrors and ELMO Bumpy Toruses (EBT), e.g., pumping of thermal barriers in tandems and profile control in EBT’s. The diffusion is selective and can cause preferential transport of a particular charge or energy component, and can even be inward in some cases.
Quasilinear saturation of the kinetic ion mixing mode
Authors: Migliuolo Stefano
Published: July 2002

The linear and quasilinear theories of the ion mixing mode are discussed in the electrostatic limit. The source of free energy for the instability is the ion temperature gradient. The parameter relevant to this calculation is ηi=(d ln Ti/dr)/(d ln n/dr). Generally, this mode has a phase velocity comparable to the ion thermal velocity and there exist values of ηi that yield maximum growth. By using a time-asymptotic formalism, we are able to discuss the quasilinear saturation of this mode. Short wavelength modes saturate at small amplitudes, ‖eφ1/Ti‖2 ≤(ηi−ηc)/ηc, where ηc is the value of ηi at marginal stability, and the saturated state is stable against further perturbations. Long wavelength modes also saturate, though the saturation is of the ‘‘hard’’ type: the saturated state itself is unstable. When saturation occurs, it is caused by reduced inverse ion Landau damping brought about both by the nonlinear frequency shift and by quasilinear modifications to the ion distribution function.
Generation of Alfvén waves caused by thermal modulation of the electrical conductivity
Authors: Shoucri Merit M. , Morales G. J. , Maggs J. E.
Published: July 2002

An analytic study is made of the effects produced by a localized modulation of the electrical conductivity of a magnetized plasma carrying a field-aligned current. The modulation is assumed to be caused by a heating source external to the plasma. The formulation used is applicable to modulation frequencies ω below the ion-cyclotron frequency ωci, and permits the calculation of the radiation pattern which contains shear as well as compressional Alfvén modes and near fields. For ω/ωci≪1, the radiation appears primarily in the form of a highly collimated shear mode traveling along the field lines passing through the spot where the modulation occurs.
Runaway tails in magnetized plasmas
Authors: Moghaddam-Taaheri E. , Vlahos L. , Rowland H. L. , Papadopoulos K.
Published: July 2002

The evolution of a runaway tail driven by a dc electric field in a magnetized plasma is analyzed. Depending on the strength of the electric field and the ratio of plasma to gyrofrequency, there are three different regimes in the evolution of the tail. The tail can be (a) stable with electrons accelerated to large parallel velocities, (b) unstable to Čerenkov resonance because of the depletion of the bulk and the formation of a positive slope, (c) unstable to the anomalous Doppler resonance instability driven by the large velocity anisotropy in the tail. Once an instability is triggered (Čerenkov or anomalous Doppler resonance) the tail relaxes into an isotropic distribution. The role of a convection type loss term is also discussed.
Dynamics of imploding neon gas-puff plasmas
Authors: Clark R. W. , Davis J. , Cochran F. L.
Published: July 2002

The implosion dynamics of a hollow cylindrical neon gas-puff plasma are investigated using a 1-D non-local thermodynamic equilibrium radiation hydrodynamic model. Two cases are considered: the implosion of the gas puff with and without a low-density central core plasma. It is shown that the implosion efficiently converts the kinetic energy of runin into radiation and that the radiation plays a significant role in the implosion energetics. For each case, the history of the implosion dynamics and emission spectra are presented as well as the distribution of radiative energy in the L and K shells. Finally, a comparison is made with purely hydrodynamic calculations.
Finite shift stabilization of ballooning modes in a high-beta tokamak
Authors: Choe W. H. , Freidberg J. P.
Published: July 2002

The widely used s vs α stability diagram for ballooning modes is based on the assumption of circular flux surfaces with small shifts. (Here s=rq′/q and α=−R0q2β′.) This analysis is extended to include finite shifts. There again results a universal stability diagram, although in this case it is parametrized by three quantities s, α, and σ′, the differential shift between flux surfaces. The analysis shows that the inclusion of a finite shift leads to a significant further stabilization of the ballooning modes over that from the standard case.
A kinetic analysis of thermal force on a spherical particle of high thermal conductivity in a monatomic gas
Authors: Soga Takeo
Published: July 2002

A linearized version of the hierarchy kinetic model equation was solved by applying a singular perturbation method and the half-range Hermite polynomials. The solution retains correct results up to O(Kn2) and suggests that, if the thermal conductivity of the spherical particle is infinite and the impinging molecules suffer complete energy accomodation at the surface, the thermal force of O(Kn2) disappears (or thermal force is very small) in the near continuum regime. The present results also indicate that the thermal force is sensitive to the variation in the energy accomodation coefficient for the accommodation coefficient of tangential momentum nearly equal to unity. With the effect of such accommodation coefficients, the present results are used to explain the existing experimental results from the viewpoint of kinetic theory as long as the Knudsen number is small.
Modification of lower-hybrid current ramp-up by runaways
Authors: Chan V. S. , Liu C. S. , Lee Y. C.
Published: July 2002

Runaway effects on lower-hybrid current ramp-up are studied numerically using a two-dimensional Fokker–Planck analysis and a nonlinear circuit equation. Runaway contribution to the inductance is shown to be important in limiting the magnitude of the induced electric field. This tends to reduce the current ramp-up efficiency. However, for a range of ωp/Ω, the anomalous Doppler instability can be excited and the runaway production rate as well as the associated inductance is significantly reduced when that happens. This allows the ramp-up efficiency to be further increased.
Reduced magnetohydrodynamic modeling of tearing mode interactions in tokamaks
Authors: Eastwood James W. , Arter Wayne
Published: July 2002

A series of three-dimensional reduced magnetohydrodynamic (MHD) simulations has been undertaken to investigate the nonlinear tearing mode interaction mechanism widely believed to explain hard disruptions in tokamaks. Validation of the computations has taken into account both linear and nonlinear numerical stability. Linear stability and energy conservation are shown to be necessary for convergence. Many features of ‘‘hard disruption’’ simulations bear out our theory of a spurious finite time singularity. Adjusting numerical and/or physical parameters suppresses the nonlinear instability as predicted, thus allowing calculations to be pursued indefinitely. The sensitivity of converged calculations to variations in the number of modes and to the initial and boundary conditions has been studied. Mode interactions are insensitive to parameter variations; large amplitude tearing modes lead to transient Alfvén wave bursts, with the persistence of the bursts being greater for fixed boundary voltage calculations.
The application of the generalized Bohm criterion to Emmert’s solution of the warm ion collisionless plasma equation
Authors: Bissell R. C.
Published: July 2002

Emmert et al. [Phys. Fluids 23, 803 (1980)] have modeled the flow of a one-dimensional collisionless plasma to a material wall by formulating and solving the warm-ion plasma equation. In contrast to the result of the cold-ion plasma equation it was found that the electric field at the plasma–sheath boundary was finite. It is first shown that Emmert’s solution satisfies the generalized Bohm criterion, and is thus a valid solution, before discussing the cause of the difference in the results of the two models in calculating the boundary electric field.
Stability of Alfvén ion-cyclotron modes with finite perpendicular wavenumber
Authors: Tsang K. T. , Smith Gary R.
Published: July 2002

The general dispersion relation for the Alfvén ion-cyclotron (AIC) modes with finite perpendicular wavelength k⊥ and a two-temperature Dory–Guest–Harris (DGH) [Phys. Rev. Lett. 14, 131 (1965)] ion distribution function is solved numerically. Conventional AIC instability is recovered in the limit k⊥ =0. It is shown that as k⊥ increases, the AIC instability smoothly goes over to the electrostatic loss cone instability. Instabilities at second and higher harmonics are excited at finite k⊥ .
Relaxation phenomena and on axis q limit in a reversed field pinch
Authors: Antoni V. , Ortolani S.
Published: July 2002

For sustained discharges at high values of the pinch parameter Θ large disturbances appear on the plasma current, loop voltage, and toroidal magnetic field signals. An increase of both plasma resistance and magnetohydrodynamic (MHD) activity measured at the edge is observed. The onset of such phenomena is found at values of Θ>1.5 and the amplitude of the disturbances increases with Θ. The oscillations are interpreted as the effect of major current redistributions occurring periodically in the central region of the plasma. Relating experimental field profiles and Θ values, the effect of the current redistribution is the recovery of the on axis q value when a lower limit is exceeded. From the experimental measurements such a lower limit has been found to be approximately q(0)≥2a/(3R).
Equilibrium and wave properties of two-dimensional ion plasmas
Authors: Prasad S. A. , Morales G. J.
Published: July 2002

Recent experiments [Phys. Rev. Lett. 49, 1708 (1982)] have demonstrated the existence of collective modes in a two-dimensional single-component ion layer residing just below the surface of liquid helium. A theory of the equilibrium and the wave properties of such a system is presented. The equilibrium is calculated by balancing the repulsive self-electric field pressure with the confining external electric field. In the limit of temperature T=0, the plasma is in the form of a constant density disk at the edge of which the density decreases to zero with a scale length set by the dimensions of the enclosing cylindrical box; increasing T increases the width of the transition region. Modeling the ions as a cold two-dimensional fluid, it is found that the plasma supports an infinite set of radial modes for each value of l, the azimuthal mode number. Imposition of a constant magnetic field perpendicular to the charge sheet increases the frequency of the l=0 modes and for l≠0, splits each mode into two; the lowest of these split modes is related to the diocotron mode.
Density fluctuations in a reversed-field pinch
Authors: Masamune Sadao
Published: July 2002

Density fluctuations have been studied using the multichord interferometer over a wide range of plasma parameters in the ZT-40M reversed-field pinch experiment [Nucl. Fusion 20, 1255 (1980)]. The total fluctuation power does not strongly depend upon the plasma current, and therefore, the relative fluctuation level decreases with increasing the current. Antisymmetric oscillations in the frequency region from 100–200 kHz are strongly excited in the outer region of the plasma column with increasing current. The maximum beta value attained seems to be inversely proportional to the magnitude of the fluctuations in this frequency region.
Heat transfer in rarefied gases: Critical assessments of thermal conductance and accommodation of argon in the transition regime
Authors: Thomas Lloyd B. , Krueger C. L. , Loyalka S. K.
Published: July 2002

Heat transfer measurements from thin filaments to argon gas in cells of cylindrical symmetry are made under extreme clean surface conditions so that known constant values of α, the thermal accommodation coefficient, on the filament pertain over the full range of pressures, 0.01–40 Torr. The results are used in an attempt to assess merit of principal theoretical treatments of heat transfer in the transition regime by extracting α according to each treatment and comparing results with the presumed known value. Before relative merit of the theories can be assigned with confidence, a wider differentiation in the α values obtained is needed. It is expected that this may result when similar experiments for the higher α gases, krypton and xenon, can be completed and critically examined.
Turbulence reduction in a boundary layer by a local spanwise oscillating surface
Authors: Laadhari F. , Skandaji L. , Morel R.
Published: July 2002

This Letter describes an experimental investigation of the response of a turbulent boundary layer on a flat plate to a local spanwise oscillation of the wall, with a nondimensional frequency f+ varying between 0.0033 and 0.0166. The investigation has been carried out for a wall motion amplitude Δz+=160. The three components of the turbulence intensities and the Reynolds stress prove to be a decreasing function of the frequency. This reduction affects almost the whole boundary layer in a cross section located at the middle of the oscillating wall. The mean streamwise velocity Ū is reduced throughout the region y+<30. The velocity profiles exhibit a well-defined log region when plotted against y, nondimensionalized with the friction velocity of the unperturbed boundary layer. The weighted probability density functions of u and v exhibit an increase in intensities of wallward motion related to changes in the structure of the oscillatory flow. The fine structure of the turbulence is also affected by the spanwise oscillation as shown by the reduction of Taylor’s microscale.
Diffusion in laminar Rayleigh–Bénard convection: Boundary layers versus boundary tubes
Authors: Dykhne A. M. , Isichenko M. B. , Horton W.
Published: July 2002

New results on the advection–diffusion of a passive tracer in a periodic system of hexagonal Rayleigh–Bénard convection cells at high Péclet number P=Lv/D0≫1 are presented, where L is the characteristic length scale of the flow, v is the velocity amplitude, and D0 is the molecular diffusivity. It is shown that the transport properties of this three-dimensional (3-D) laminar flow are drastically different from those of the well-studied two-dimensional convection rolls. The 3-D topology of the streamlines in the hexagonal convection leads to the formation of boundary tubes near the axes and the edges of the hexagons, in addition to the standard boundary layers found near the faces and the bases. A scaling theory is given and confirmed by test-particle simulations that show that the transport enhancement due to the hexagonal cells is controlled by the boundary tubes and scales only logarithmically with P. On the other hand, it is found that the subdiffusive regimes of transport in hexagons are similar to those found in other flows with constrained streamlines. The described effects can be used for the experimental investigation of structures in thermal convection.
The time dependent flow over V- and U-groove riblets of different sizes
Authors: Tullis S. , Pollard A.
Published: July 2002

The flow over V-groove and U-groove riblets is examined computationally using a time dependent model of the viscous wall region. The flow at the upper bound of the computational domain (y+≂40) is described using a streamwise eddy model. Both drag neutral and drag reducing riblets are considered. Results suggest that the riblets limit the lateral spread of inrushes towards the wall and retain low momentum fluid in the riblet valleys, thereby effectively isolating much of the wall from such inrushes. The generation of intermittent secondary vortices within the riblet valleys also occurs; however, these appear to be both quite weak and fairly short-lived.
On the characterization of the fine-scale intermittency of turbulence
Authors: Zubair Lareef
Published: July 2002

Some characterization of the fine-scale intermittency of turbulence is attempted utilizing the method of Kuo and Corrsin [J. Fluid Mech. 50, 285 (1971)] and the ‘‘envelope method’’ of Sreenivasan [J. Fluid Mech. 151, 81 (1985)]. It is found that the outcomes of these techniques are sensitively dependent on the details of the methods, and hence cannot be interpreted with complete confidence.
Inversion of acoustic waves reflection rules in near critical pure fluids
Authors: Zappoli B. , Carlès P. , Amiroudine S. , Ouazzani J.
Published: July 2002

The reflection of linear acoustic waves propagating in a very compressible, low heat diffusing, supercritical fluid (CO2) is studied by solving the nonlinear Navier–Stokes (NS) equations written for a near-critical van der Waals gas. It is shown that close enough to the critical point, the reflection rules of acoustic waves on thermostatted boundaries are inverted, compared to those usually observed in ideal gases. This phenomenon has been put in evidence by numerical simulations, and its mechanism is shown to be due to the strong contraction or expansion of a hypercompressible thermal adaptation boundary layer. The asymptotic analysis of the equations gives the order of magnitude of the distance to the critical point where the inversion occurs. This transition corresponds to the transition to the so-called Acoustically Saturated Regime, in which the characteristic time scale of heat transfer reaches its lower limit, which is the acoustic typical time.
Inertial manifolds, partially space-averaged equations, and the separation of scales in turbulent flows*
Authors: Manley Oscar , Temam Roger , Wang Shouhong
Published: July 2002

Recent theoretical results on the behavior of high-frequency modes in two-dimensional incompressible turbulent flows are reported. These results show that high-frequency modes in the dissipation range are slaved to the low-frequency modes. The physical significance of the results is discussed, as well as its utilization for the numerical simulation of turbulent flows.
A closure model for intermittency in three-dimensional incompressible turbulence
Authors: Olla Piero
Published: July 2002

A simplified Lagrangian closure for the Navier–Stokes equation is used to study the production of intermittency in the inertial range of three-dimensional turbulence. This is done using localized wave packets following the fluid rather than a standard Fourier basis. In this formulation, the equation for the energy transfer acquires a noise term coming from the fluctuations in the energy content of the different wave packets. Assuming smallness of the intermittency correction to scaling allows the adoption of a quasi-Gaussian approximation for the velocity field, provided a cutoff on small scales is imposed and a finite region of space is considered. In these approximations, the amplitude of the local energy transfer fluctuations can be calculated self-consistently in the model. Definite predictions on anomalous scaling are obtained in terms of the modified structure functions: 〈〈E(l,a)〉qR〉, where 〈E(l,a,r,t)〉R is the part of the turbulent energy coming from Fourier components in a band (a−1)k around k∼l−1, spatially averaged over a volume of size R∼l/(a−1) around r.
Stabilization of trapped vortices by alternating blowing suction
Authors: Chernyshenko S. I.
Published: July 2002

Motion of a free point vortex near a circular cylinder in a uniform oncoming flow is considered. There is a point at which the point vortex velocity is zero. This stationary position is unstable. Introducing two periodic point sources of zero mean flow rate modifies the point vortex velocity field so that instead of the stationary position there is a periodic trajectory. The corresponding periodic motion of the vortex is found to be stable over a certain range of characteristics of periodic blowing/suction modeled with periodic sources. In particular, for stabilization the amplitude of the source flow rate oscillations must not exceed a certain limit. The results are believed to bear on the problem of enhancing lift at high angle of attack with the use of trapped vortices.
Two counter-rotating diffusing vortices
Authors: van Dommelen Leon , Shankar Subramaniam
Published: July 2002

The problem of the diffusion of two counter-rotating vortices of equal strength is studied numerically and analytically. Asymptotic expansions are derived for the limiting behavior of the solution for small times, for small Reynolds numbers, and for large times. The results are used to more fully understand the drift and decay of the vortex system. Thus it is shown that different measures for the position of the vortex system used by previous authors may give significantly different values for the drift velocity of the vortices. The expansion for small Reynolds number shows that these differences remain even in the Stokes limit Re→0, in which the vorticity system becomes symmetric about the line connecting the vortex centers. But surprisingly, the large time expansion shows that for large times all drift velocities become identical. Moreover, this universal velocity is different from the average velocity in each half plane although it equals the velocity of the centers of vorticity of those planes. The small time expansion shows that increasing Reynolds number makes the vortices more symmetric. This tends to reduce the differences between the drift velocities. The small time expansion describes the numerical solution well as long as the vortices remain small compared to their spacing. The numerical results show that the Stokes solution describes various flow quantities fairly well for Reynolds numbers up to 600 based on the circulation; however, nonzero Reynolds number reduces the decay of the circulation of the vortices even on a diffusive time scale.
Anomalous sideband instabilities of thermal Rossby waves at low Prandtl numbers
Authors: Or A. C. , Herrmann J.
Published: July 2002

Convection in the form of thermal Rossby waves is studied in the low Prandtl number regime. An anomalous Eckhaus instability is found in the range between 10−3 and 10−2 for a moderately strong Coriolis parameter, where no supercritical stable solution can exist near the onset. Numerical results for higher Rayleigh numbers show detachment of the stability limit from the neutral curve, shrinkage and distortion of the stable region, and the onset of a second sideband mode of instability, which is characterized by a maximum growth rate at a finite modulation parameter. The new mode is more pronounced at higher Rayleigh numbers, and appears to destabilize all spatially periodic waves for the whole supercritical band for all Prandtl numbers below the anomalous range.
Analytic theory of Richtmyer–Meshkov instability for the case of reflected rarefaction wave
Authors: Velikovich Alexander L.
Published: July 2002

An analytic theory of the Richtmyer–Meshkov (RM) instability for the case of reflected rarefaction wave is presented. The exact solutions of the linearized equations of compressible fluid dynamics are obtained by the method used previously for the reflected shock wave case of the RM instability and for stability analysis of a ‘‘stand-alone’’ rarefaction wave. The time histories of perturbations and asymptotic growth rates given by the analytic theory are shown to be in good agreement with earlier linear and nonlinear numerical results. Applicability of the prescriptions based on the impulsive model is discussed. The theory is applied to analyze stability of solutions of the Riemann problem, for the case of two rarefaction waves emerging after interaction. The RM instability is demonstrated to develop with fully symmetrical initial conditions of the unperturbed Riemann problem, identically zero density difference across the contact interface both before and after interaction, and zero normal acceleration of the interface. This confirms that the RM instability is not caused by the instant normal acceleration of the interface, and hence, is not a type of Rayleigh–Taylor instability. The RM instability is related to the growth of initial transverse velocity perturbations at the interface, which may be either present initially as in symmetrical Riemann problem, or be induced by a shock passing a corrugated interface.
Collective behavior of wakes downstream a row of cylinders
Authors: Le Gal P. , Peschard I. , Chauve M. P. , Takeda Y.
Published: July 2002

This experimental study is devoted to visualisation and ultrasonic velocity measurement of the wakes formed behind a row of parallel cylinders placed side by side, perpendicular to an incoming flow at low Reynolds numbers. When the distance separating the cylinders is small compared to their diameter, two instability mechanisms, associated with different patterns and dynamics compete. A first spatial symmetry breaking appears when the stationary wakes behind each cylinder are deviated towards one side or the other and form large clusters containing from two to sometimes more than ten wakes. These clusters are separated by intense recirculating zones. When the Reynolds number is increased, the wakes belonging to the widest clusters experience a secondary temporal oscillatory bifurcation. Classical Bénard-Von Kármán vortex streets are thus shed in phase by these cylinders (acoustic mode), by contrast with the wakes outside these cells which stay stationary. Finally, the flow around far apart cylinders is also investigated. The primary instability does not occur in this case and a perfect optical mode of vortex shedding, with neighbours in phase opposition, takes place in the flow.
A model of wave dynamics in the far wake of a cylinder
Authors: Hooghe Muriel , Pumir Alain
Published: July 2002

Interesting interactions in the far wake behind a cylinder, leading in particular to the appearance of a strong secondary oblique wave, have recently been discovered experimentally by Williamson and Prasad [J. Fluid Mech. 256, 269, 315 (1993)]. They are induced from a very small amount of noise, added to the decaying primary wave. The problem is investigated theoretically with simple amplitude equations, based on temporal instability of the small amplitude waves. The symmetry of the wake flow requires that quadratic interactions arise only among triads of wave numbers involving one varicose and two sinuous waves, or three varicose waves. As the primary wave, corresponding to vortex shedding, is sinuous, the interacting secondary waves must be of opposite parities. In this case, it is found that the sinuous wave will always prevail downstream. The preferential appearance of the secondary oblique wave in the far wake can be reproduced by letting an initially very small varicose parallel wave interact with the primary wave. The secondary oblique wave results from a classical three-wave, quadratic nonlinear interaction between the waves. In addition, our model reproduces the observation that upon increasing the noise amplitude the oblique wave appears sooner (further upstream) in the wake. The occurrence of parallel waves very far downstream, which depends on the frequency relationship between the waves, can be understood by considering the interactions between parallel and oblique secondary waves of both parities. We propose a reasonable scenario explaining the experimental observations of Williamson and Prasad.
On the flux of fluctuation energy in a collisional grain flow at a flat, frictional wall
Authors: Jenkins James T. , Louge Michel Y.
Published: July 2002

We consider a flow of colliding spheres that interacts with a flat, frictional wall and calculate the flux of fluctuation energy in two limits. In the first limit, all spheres slide upon contact with the wall. Here, we refine the calculations of Jenkins [J. Appl. Mech. 59, 120 (1992)] and show that a correlation between two orthogonal components of the fluctuation velocity of the point of contact of the grains with the wall provides a substantial correction to the flux originally predicted. In the other limit, the granular material is agitated but the mean velocity of the contact points with respect to the wall is zero and Jenkins’ earlier calculation is improved by distinguishing between those contacts that slide in a collision and those that stick. The new expressions for the flux agree well with the computer simulations of Louge [Phys. Fluids 6, 2253 (1994)]. Finally, we extend the expression for zero mean sliding to incorporate small sliding and obtain an approximate expression for the flux between the two limits.
Convective effects on a propagating reaction front
Authors: Cliffe K. A. , Tavener S. J. , Wilke H.
Published: July 2002

Unstable concentration gradients inherent in traveling chemical waves can give rise to buoyancy-driven convection, altering the speed of the wave. When an excitable Belousov–Zhabotinsky reaction system is confined within a sufficiently narrow, vertical two-dimensional channel, convection arises at a symmetry-breaking bifurcation point. The observed linear rate of change of wave speed with the bifurcation parameter is a necessary consequence of the Z2 symmetry present.
Symmetry relations for nonlinear pressure interactions on oscillating cylinders
Authors: Williams David R.
Published: July 2002

Combination modes appear in the spectrum of the surface pressure signals when a circular cylinder is forced to oscillate at a frequency different from the von Karman vortex shedding frequency. The spatial symmetry of the sum and difference modes depends on the direction of cylinder oscillation, and is predictable with a simple set of symmetry relations. As a result of the symmetry relations, cross-flow oscillations of the cylinder aimed at enhancing fluctuating lift also channel energy into the fluctuating drag component through the combination modes.
Numerical investigation of the stabilization of the no-motion state of a fluid layer heated from below and cooled from above
Authors: Tang Jie , Bau Haim H.
Published: July 2002

The feasibility of controlling flow patterns of Rayleigh–Bénard convection in a fluid layer confined in a circular cylinder heated from below and cooled from above (the Rayleigh–Bénard problem) is investigated numerically. It is demonstrated that, through the use of feedback control, it is possible to stabilize the no-motion (conductive) state, thereby postponing the transition from a no-motion state to cellular convection. The control system utilizes multiple sensors and actuators. The actuators consist of individually controlled heaters positioned on the bottom surface of the cylinder. The sensors are installed at the fluid’s midheight. The sensors monitor the deviation of the fluid’s temperatures from preset desired values and direct the actuators to act in such a way so as to eliminate these deviations. The numerical predictions are critically compared with experimental observations.
Symmetries and the approach to statistical equilibrium in isotropic turbulence
Authors: Clark Timothy T. , Zemach Charles
Published: July 2002

The relaxation in time of an arbitrary isotropic turbulent state to a state of statistical equilibrium is identified as a transition to a state which is invariant under a symmetry group. We deduce the allowed self-similar forms and time-decay laws for equilibrium states by applying Lie-group methods (a) to a family of scaling symmetries, for the limit of high Reynolds number, as well as (b) to a unique scaling symmetry, for nonzero viscosity or nonzero hyperviscosity. This explains why a diverse collection of turbulence models, going back half a century, arrived at the same time-decay laws, either through derivations embedded in the mechanics of a particular model, or through numerical computation. Because the models treat the same dynamical variables having the same physical dimensions, they are subject to the same scaling invariances and hence to the same time-decay laws, independent of the eccentricities of their different formulations. We show in turn, by physical argument, by an explicitly solvable analytical model, and by numerical computation in more sophisticated models, that the physical mechanism which drives (this is distinct from the mathematical circumstance which allows) the relaxation to equilibrium is the cascade of turbulence energy toward higher wave numbers, with the rate of cascade approaching zero in the low wave-number limit and approaching infinity in the high wave-number limit. Only the low-wave-number properties of the initial state can influence the equilibrium state. This supplies the physical basis, beyond simple dimensional analysis, for quantitative estimates of relaxation times. These relaxation times are estimated to be as large as hundreds or more times the initial dominant-eddy cycle times, and are determined by the large-eddy cycle times. This mode of analysis, applied to a viscous turbulent system in a wind tunnel with typical initial laboratory parameters, shows that the time necessary to reach the final stage of decay is astronomically large, and would require a wind tunnel of astronomical length.
The structure of energy conserving low-order models
Authors: Gluhovsky Alexander , Tong Christopher
Published: July 2002

General principles for developing physically sound low-order models in fluid dynamics are discussed. It is shown that low-order models with energy conserving properties of the original equations that arise in various important problems (Rayleigh–Bénard convection, rotating fluid, magnetohydrodynamic convection) may be presented in the form of coupled three-mode systems known in mechanics as Volterra gyrostats (plus terms describing forcing and friction). When these models are expanded by increasing the order of approximation or by adding new physical mechanisms, they still have the structure of coupled gyrostats. Conversely, when a low-order model cannot be transformed into coupled gyrostats, this may indicate that its conservation properties should be questioned. For instance, while the widely used (in convection studies) Howard–Krishnamurti model [J. Fluid Mech. 170, 385 (1986)] is not energy conserving and does not have a gyrostatic form, its simple extension to a system of coupled gyrostats possesses inviscid energy invariants. Integrals of motion in the fluid are shown to have their analogs in systems of coupled gyrostats. Thus, giving low-order models a gyrostatic structure ensures that certain important physics from the original fluid dynamical equations is retained. Finally, this approach is used to develop a coupled gyrostat model of turbulence that exhibits Kolmogorov spectral behavior.
Dry arches within flowing films
Authors: Podgorski T. , Flesselles J.-M. , Limat L.
Published: July 2002

When a liquid film flows down an inclined nonwettable surface, dewetting can be triggered at low flow rate. After a transient, stationary dry patches edged with a liquid rim form. From experimental investigations, we deduce that their shape arises in a large flow range from a balance between the rim weight and surface tension. A simple model based on this assumption provides an analytical expression for the arch shape, in excellent agreement with experiments. The patch size scales as lc2Uc/Γ (lc capillary length, Uc capillary velocity, Γ flow rate per unit length). Above a critical flow rate, of order lcUc, dry patches cannot be stationary and are swept away, leaving a fully wet surface. Both the typical size and the critical flow rate depend nontrivially on the contact angle and on the solid surface inclination.
A statistical model of particle transport and heat transfer in turbulent shear flows
Authors: Zaichik L. I.
Published: July 2002

The objective of the paper is to present a statistical model for predicting particle transport and heat transfer in two-phase quasi-homogeneous turbulent shear flows. This statistical model is based on a kinetic equation for the probability density function of the particle velocity and temperature distributions in nonuniform turbulent flows. The model developed is applied to predict the fluctuating particle motion in both homogeneous and near-wall turbulent shear flows.
Infrared pressure spectra in two- and three-dimensional isotropic incompressible turbulence
Authors: Lesieur Marcel , Ossia Sepand , Métais Olivier
Published: July 2002

We show, using a quasinormal or Eddy Damped Quasinormal Markovianised (EDQNM) approximation to evaluate fourth-order velocity correlations in Fourier space, that the pressure spectrum in three-dimensional isotropic incompressible turbulence is proportional to k2 in the limit k→0. This result is independent of both the infrared kinetic-energy spectrum and Reynolds number. Afterwards, direct numerical simulations and large-eddy simulations (LES) of decaying isotropic turbulence are performed: they agree with this prediction, and show a fast pressure-spectrum decay in this range. LES predict an asymptotic collapse of the infrared pressure spectrum as Epp(k,t)≈0.3∫0kC[E2(q,t)/q2]dqk2, where E(k,t) is the kinetic-energy spectrum. This permits us to predict theoretically that the pressure variance is exactly proportional to the squared kinetic energy, which we check numerically. The same QN/EDQNM analysis carried out in two dimensions predicts pressure spectra slopes of k, k−7/3, and k−5 in the infrared, inverse energy-cascade (in case of forcing), and enstrophy-cascade ranges, respectively.
Quadratic Markov modeling for intermittent turbulence
Authors: Pedrizzetti Gianni
Published: July 2002

A Markovian stochastic approach for the relative motion of particle pairs is here considered as a model for intermittency in inertial range turbulence. It is shown that a local acceleration term with quadratic velocity dependence permits a nonclassical scaling of the velocity differences between two points. A Lagrangian model is formulated such that Eulerian flow satisfies incompressibility, experimental second-order, and exact third-order statistics, and is consistent with nonclassical scale similarity. The equation for the Eulerian probability distribution is obtained and discussed.
The initial-value problem for a modeled boundary layer
Authors: Criminale W. O. , Drazin P. G.
Published: July 2002

The stability of a basic parallel flow of a viscous incompressible fluid has been traditionally investigated by linearizing the Navier–Stokes equations and using the method of normal modes in order to determine the temporal behavior. In this paper we adopt a method introduced by Lord Kelvin and used much in recent years, solving the equations instead as an initial-value problem and thereby the full dynamics, both the early transient and the long time asymptotic, can be determined directly. The basic flow investigated is a boundary-layer modeled by a piecewise linear profile. Various initial distributions of velocity and vorticity are used as a basis of fundamental solutions to represent more general initial disturbances of the basic flow. The simplicity of the model permits the problem to be solved by use of a moving-coordinate system and of matched asymptotics in the limit of small viscosity. The solutions are remarkably explicit, although complicated and substantiate the increasingly common view that linear disturbances, although decaying ultimately according to the linear theory, may grow so much transiently as to excite nonlinear growth and effective instability; in particular, streamwise vortices are found to be strongly amplified. Although not done here, the method can be applied to other parallel shear flows.
On the creation of stagnation points near straight and sloped walls
Authors: Mullin T. , Kobine J. J. , Tavener S. J. , Cliffe K. A.
Published: July 2002

We report the results of an experimental and numerical study of the creation of stagnation points in a rotating cylinder of fluid where one endwall is rotated. Good agreement is found with previous results where the stagnation points are formed on the free core of the primary columnar vortex. The effect of adding a small cylinder along the center of the flow is then investigated and the phenomena are found to be robust despite the qualitative change in the boundary conditions. Finally, we show that sloping the inner cylinder has a dramatic effect on the recirculation such that it can either be intensified or suppressed.
The double-helical branch structure of fixed contact line liquid bridge equilibria
Authors: Lowry Brian J.
Published: July 2002

Attempts to stabilize the fixed contact line cylindrical liquid bridge have generally implicitly assumed that it was related to stable equilibria in a continuous manner. An examination of the branch structure of equilibria demonstrates that for longer liquid bridges, the cylinder becomes separate from normally stable equilibria and hence likely cannot be stabilized by a continuous perturbation. All axisymmetric equilibria for a fixed contact line liquid bridge of fixed moderate length in the absence of applied forces (zero gravity, no spin) are found to lie on a single semi-infinite bridged double helix. This helix breaks repeatedly as the length of the liquid bridge is increased, separating the stable truncated sphere state from the generally desirable cylindrical state. This structural change appears to explain why several approaches to stabilization of long cylindrical liquid bridges beyond the classical Plateau–Rayleigh limit have been largely unsuccessful over the past few decades. The first breakage of the helix, when liquid bridge length equals 9.0973 times radius, corresponds roughly to the maximum length of cylindrical liquid bridge achieved experimentally via a perturbative applied force (using acoustic radiation pressure). An examination of the deformations of the helix under gravity reveals that for moderate length liquid bridges at small Bond number, all axisymmetric equilibria lie on a single unbroken branch which forms a single (unbridged) semi-infinite double helix. Combined effects of gravity and length are investigated as well, resulting in multiple disconnected loops of equilibria.
The nonlinear development of three-dimensional disturbances at hyperbolic stagnation points: A model of the braid region in mixing layers
Authors: Caulfield C. P. , Kerswell R. R.
Published: July 2002

The properties of steady, two-dimensional flows with spatially uniform strain rates ε and rotation rates γ where ε2⩾γ2, and hence open, hyperbolic, streamlines are investigated. By comparison with a high resolution numerical simulation of a free shear layer, such a quadratic flow is an idealized local model of the “braid” region which develops between neighboring saturated Kelvin–Helmholtz billows in an unstable free shear layer. A class of exact three-dimensional nonlinear solutions for spatially periodic perturbations is derived. These solutions satisfy the condition that the amplitude of the time-varying wave number of the perturbation remains bounded in time, and hence that pressure plays an asymptotically small role in their dynamics. In the limit of long time, the energy of such perturbations in an inviscid flow grows exponentially, with growth rate 2ε2−γ2, and the perturbation pressure plays no significant role in the dynamic evolution. This asymptotic growth rate is not the maximal growth rate accessible to general perturbations, which may grow transiently at rate 2ε, independently of γ. However, almost all initial conditions lead to, at most, transient growth and hence finite asymptotic perturbation energy in an inviscid flow as time increases, due to the finite amplitude effects of pressure perturbations. Perturbations which do undergo significant transient growth take the form of streamwise-aligned perturbation vorticity which varies periodically in the spanwise direction. By comparison of this local model with a numerically simulated mixing layer, appropriately initialized “hyperbolic instabilities” appear to have significantly larger transient growth rates than an “elliptical instability” of the primary billow core. These hyperbolic instabilities appear to be a simple model for the spanwise periodic perturbations which are known to lead to the nucleation of secondary rib vortices in the braid region between adjacent billow cores.
Generalized Chapman–Enskog method in the kinetic theory of reacting ionized gases
Authors: Alexeev B. V. , Chikhaoui A. , Méolans J. G. , Grushin J. T. , Grushina L. P.
Published: July 2002

In this paper the problem of kinetic coefficient calculations for a nonequilibrium mixture of chemically reacting ionized gases is investigated. The study is based on the generalized Chapman–Enskog method (GCEM) proposed by Alexeev [Theor. Exp. Chem. 5, 541 (1969)]. This work should be considered as a direct continuation of the paper [Phys. Rev. E 49, 2809 (1994)]. An effective method for the solution of the basic equation with non-self-adjoint operator (A equation) of the GCEM is developed for the case of reacting ionized gases and the calculation of the bracket expressions for elastic collisions of charged particles is given. Several concrete results of the kinetic coefficient calculations are discussed.
On current sheets in two-dimensional ideal magnetohydrodynamics caused by pressure perturbations
Authors: Rastätter L. , Voge A. , Schindler K.
Published: July 2002

In this paper it is shown that in ideal magnetohydrodynamics (IMHD) a two-dimensional equilibrium with an X-shaped neutral point (X-point) configuration reacts to small and smooth perturbations of the plasma pressure by the development of sheets with singular current density while the X-point structure is replaced by a different kind of configuration containing either cusp-like or T-shaped singularities. This behavior is demonstrated by computing the time dependent response to a suitable initial perturbation using a relaxation method within ideal MHD. The two-dimensional configurations considered in this paper are motivated by models of space plasma systems like, e.g. the Earth’s magnetotail containing a distant X-point where perturbations caused by the solar wind may force the formation of current sheets and the subsequent occurrence of magnetic reconnection.
Finite beta effects in quasihelical stellarators
Authors: Garren David A. , Boozer Allen H.
Published: July 2002

An analytic expansion about a magnetic axis is applied to investigate finite beta effects such as bootstrap current on toroidal plasma equilibria which approximate quasihelical symmetry (QHS). It is found that quasihelically symmetric configurations can be found through the second order in terms of a helical inverse aspect ratio ε, even with the inclusion of a bootstrap current on the magnetic axis. Permitting the on-axis rotational transform to decrease as the on-axis bootstrap current is increased has little effect on the shape of the QHS flux surfaces. However, shifting the position of the magnetic axis in order to maintain the on-axis transform causes a stronger change in the QHS flux surface shape, especially axis shifts in the major radial direction.