Index of content:
Volume 25, Issue 9, September 1982

Flute stabilization by a cold line‐tied blanket
View Description Hide DescriptionThe curvature‐driven flute instability in an axisymmetric mirror was stabilized by an annular line‐tied plasma blanket. A significant temperature difference was maintained between core and blanket. Theoretical calculations support the experimental observations.

Observation of the parametric decay instability during electron cyclotron resonance heating on the Versator II tokamak
View Description Hide DescriptionObservations are reported on a nonlinear, three‐wave interaction process occurring during high‐power electron cyclotron heating in the Versator II tokamak. The measured spectra and the threshold power are consistent with a model in which the incident power in the extraordinary mode of polarization decays at the upper‐hybrid resonance layer into a lower‐hybrid wave and an electron Bernstein wave.

Instabilities driven by the parallel variation of the electrostatic potential in tandem mirrors
View Description Hide DescriptionIt is demonstrated that the free energy associated with the sheared flow induced by the parallel variations of drift frequencies can provide a new destabilizing term. In particular, we show the existence of a magnetohydrodynamic‐like instability which may occur in the mirror end plugs or thermal barrier region of a tandem mirror fusion device.

Effect of finite aspect ratio on the neoclassical ion thermal conductivity in the banana regime
View Description Hide DescriptionBy considering the effect of finite aspect ratio, the neoclassical ion thermal conductivity has been found to be significantly larger than reported by Hazeltine, Hinton, and Rosenbluth. A simple correction to the expression of Hinton and Hazeltine is suggested.

Drag measurements for axisymmetric motion of a torus at low Reynolds number
View Description Hide DescriptionMeasurements are presented for the drag on a torus moving along its axis of rotational symmetry at low Reynolds number. If D is the outside diameter of the torus, and d is the thickness in the axial direction, then the measurements cover the range s _{0} = 1 (the closed torus) to s _{0} = 135, where s _{0}≡(D/d)−1. The effect of a coaxial cylindrical boundary (diameter H) is taken into account by an empirical correlation. The values of drag obtained by extrapolating to a fluid of infinite extent are in good agreement with the exact solution obtained by Majumdar and O’Neill. When πd(s _{0})^{1/2}≪H, the empirical boundary correlation is consistent with the result of Brenner for a particle of arbitrary shape. Measurements with outer boundaries of square and circular cross section indicate that the relative effect of the two boundary shapes on the drag is the same for the torus as that found by Happel and Bart for a sphere. Empirical results are presented for the case in which the torus is strongly influenced by a coaxial cylindrical boundary.

Accuracy of the mean field approximation and the physical effect of Prandtl number in Bénard convection
View Description Hide DescriptionThe mean field equations, which contain no explicit Prandtl number dependence, are shown to provide reasonably accurate predictions of average heat transport for Rayleigh numbers from 2000 to 18000 over a wide range of Prandtl numbers, provided physically observed wavenumbers are used in the calculations. It is concluded from this that the physical significance of Prandtl number in Bénard convection is principally in setting the ’’preferred’’ wavenumber, i.e., the size of the convection cell.

The nonaxisymmetric (buckling) flow regime of fast capillary jets
View Description Hide DescriptionThis paper reports an experimental study of the nonaxisymmetric flow of a fast liquid jet discharging into the atmosphere. The nonaxisymmetric shape of the jet was photographed and subjected to a wavelength analysis. The results of the wavelength analysis demonstrate that the jet shape is governed by a narrow band of wavelengths associated with a characteristic value λ_{max} which scales with the jet diameter D. It is shown that the experimental observations are in agreement with predictions based on hydrodynamic stability theory and buckling theory.

The application of kinematic wave theory to wave trains and packets with small dissipation
View Description Hide DescriptionThe validity of kinematic wave theory for linear waves with small dissipation propagating through a homogeneous medium is examined with the aid of the higher‐order theory of Chin. It is shown that both for nondissipative and weakly‐dissipative waves the kinematic theory holds with errors of order ε^{2} for times of order ε^{−1} times the wave period, where ε is a measure of the nonuniformity of the wave train. For longer times, of order ε^{−2} times the period, secular terms arise, which makes the theory invalid when wave dispersion becomes vanishingly small. By selecting a complex wavenumber chosen such as to make the group velocity real, it is possible to remove the first‐order secular terms and thus produce a modified theory uniformly valid within the longer time period. This modification is also applied to wave trains propagating in a nonhomogeneous medium. General solutions are presented for wave trains or packets of arbitrary initial conditions.

On the linear inviscid stability of rotating Poiseuille flow
View Description Hide DescriptionThis paper continues an earlier study by S. A. Maslowe of inviscid asymmetric disturbances to flow with rotation along a pipe. It is shown that there is a class of neutral modes with a critical layer near the wall of the pipe when the azimuthal wavenumber is large and negative. Analytic and numerical properties of these modes are studied and found to lead to consistent results, notable among which is the severe singularity in the disturbance velocity at the critial level. Some of the properties of the most unstable modes are also examined.

Nonlinear wave interactions in supersonic wind‐generated waves
View Description Hide DescriptionA nonlinear analysis is presented for the case of second‐harmonic resonant interactions on the interface of a liquid film and a supersonic gas stream. The analysis takes into account the effects of the gas viscosity and mean profiles. Moreover, the extent of the gas disturbance layer is not restricted to the region in which the mean profiles are linear. Self‐sustained oscillations are calculated for low and intermediate liquid Reynolds numbers. The present solution is compared with available experimental data. The predicted and observed wave amplitudes, wavenumbers, and frequencies are in good agreement for intermediate liquid Reynolds numbers. The calculated amplitudes overpredict the observed values by about a factor of three for low liquid Reynolds numbers.

A statistically‐derived subgrid model for the large‐eddy simulation of turbulence
View Description Hide DescriptionA subgrid model in the large‐eddy simulation of turbulent flows is derived from the statistical viewpoint. The subgrid‐scale (SGS) Reynolds stress playing a central role in the derivation is estimated from a shear‐turbulence theory which is based on the direct‐interaction formalism incorporated with the separation of scales of mean and fluctuating fields. A resulting subgrid model is written in terms of the grid‐scale (GS) velocity, the GS pressure, and the SGS turbulent energy. The Smagorinsky model used frequently in the large‐eddy simulation is derived under the special situation that production and dissipation terms are dominant in the transport equation for the SGS turbulent energy.

Turbulence structure in unstably‐stratified open‐channel flow
View Description Hide DescriptionThe buoyancy effects on the turbulence structure in unstably‐stratified shear flow generated by cooling the top of the layer in an open channel were investigated. Measurements were made of the characteristics of the turbulent fluctuations; turbulence intensities, correlation coefficients, joint probability density functions, and coherence‐phase relationships. The results show that the buoyancy‐driven motions cause substantial changes in the turbulence structure. Of the buoyancy‐driven motions, the intermittent downward motion contributes mainly to the turbulent transport of heat in the vertical direction. A parameter which characterizes the stability dependence of the turbulence structure is the local gradient Richardson number Ri, and the turbulence quantities are well correlated with Ri. A theoretical spectral equation model is applied to the stratified flow and well compared with the experimental results.

A nonstationary solution to Liouville’s equation for a randomly forced two‐dimensional flow
View Description Hide DescriptionLiouville’s equation for randomly forced two‐dimensional flow with Rayleigh friction is examined. An exact nonstationary solution is presented for a special form of the forcing and zero energy initial condition. This solution is such that the fluctuation‐dissipation relation is valid at all times.

Motion of a sphere in a rarefied gas
View Description Hide DescriptionThe problem of the motion of a single spherical particle in a rarefied gas is considered, and results for the velocity profiles and the drag forces for all rarefactions are obtained using the Bhatanagar–Gross–Krook model and diffuse reflection at the surface of the sphere. Results for the drag forces are in good agreement with previously available results of Cercignani, Pagani, and Bassanini. The velocity profile results are also in good agreement with the results of Sone and Aoki who had considered the slip limit.

Propagation of hydromagnetic waves in a rotating nonisothermal compressible atmosphere: WKB approximation
View Description Hide DescriptionThe propagation of internal Alfvén‐inertio‐acoustic‐gravity waves in a rotating, stratified, inviscid, perfectly conducting nonisothermal atmosphere in the presence of a nonuniform magnetic field is investigated near the critical levels using the group velocity method based on the WKB approximation. It was found that these waves (approaching the critical level from one side) are neither transmitted nor reflected, but are completely captured in the neighborhood of the critical levels and are constrained thereafter to propagate in the horizontal directions. The same wave, if it approaches the critical level from the other side, is transmitted across the critical level without any absorption or reflection, thus establishing the valve effect, as in the case of Rudraiah and Venkatachalappa, even in the absence of the components of rotation in the plane normal to the direction in which the medium varies.

Enforced gyroresonance of electrons in large‐amplitude whistler waves
View Description Hide DescriptionPhase trapping of ’’cold’’ electrons in a finite amplitude whistler wave is possible.

Ion acoustic double layers in the presence of plasma source
View Description Hide DescriptionSteady‐state plasma turbulence and the formation of negative potential spikes and double layers in the presence of ion acoustic instabilities have been studied by means of one‐dimensional particle simulations in which the velocities of a small fraction of electrons are replaced by the initial drifting Maxwellian at a constant rate. A steady state is found where negative potential spikes appear randomly in space and time giving rise to an anomalous resistivity much greater than previously found. Comparisons of the simulation results with laboratory and space plasmas are discussed.

Numerical simulation of tokamak electron dynamics
View Description Hide DescriptionIn a tokamak, the electron distribution deviates from a Maxwellian because magnetically untrapped electrons run away parallel to the applied electric field. A new method for calculating the dynamics of the electron distribution is presented. This method is novel because it can treat systems with comparable numbers of trapped and untrapped electrons, and an electric field comparable with (but smaller than) the Dreicer field. The electron distribution function and the plasma resistivity are presented for representative values.

Shear‐ballooning stability analysis of low‐β plasmas
View Description Hide DescriptionA model of magnetic configurations that has both shear and variation of the field curvature along the magnetic field is constructed. The stability analysis of this system is performed by expanding the perturbation function in φ_{0} which is constant along the field and φ_{1} which varies sinusoidally along the field line. The shear term is retained in the form of differential operations in ξ, the coordinate parallel to the pressure gradient. After several simplifications, the equation reduces to a fourth‐order differential equation. The eigenvalue of this equation is obtained numerically. The calculated critical β plotted versus the well depth parameter, h, makes a smooth transition betweeen h<0 (maximum average B) and h≳0 (minimum average B). Using the same technique, the nondivergent solution to the localized shear mode (Suydam mode) is also obtained by retaining the inertia term.

Kinetic theory of electrostatic ballooning instabilities
View Description Hide DescriptionThe numerical solution of a high‐n electrostatic ballooning mode is obtained. Correct forms of electron and ion responses to the wave are retained. Instabilities which arise because of toroidal effects are found. Dependence on the aspect ratio, magnetic shear, wavelength, electron–ion–temperature ratio, and the electron temperature gradient is also studied. The growth rate γ is large and satisfies the relation ω<γ∼ω_{*}. Depending on the parameters, the real frequency ω changes sign. The drift mode, which has been found to be stable in a slab plasma, persists in the toroidal plasma, almost always remaining stable. The density fluctuations in tokamaks, which have been observed when the microwave scattering method is used, can be qualitatively explained by the theory of the electrostatic ballooning mode.