Index of content:
Volume 24, Issue 3, March 1981

Soret diffusion and convective stability in a closed vertical cylinder
View Description Hide DescriptionThe convective stability range of nonreactive binary gas mixtures (Xe:He,Xe:Ar) in a closed vertical cylinder with conducting walls heated from below was investigated. The xenon mole fraction was varied from X _{Xe} = 1 to 0.03 and from 1 to 0 for the helium and argon containing mixtures, respectively. Critical thermal Rayleigh numbers N _{Ra} ^{1} for the onset of convective flow were obtained from high resolution differential temperature measurements. Thermal diffusion ratios were calculated, based on Lennard–Jones potentials, over the whole composition range for both gas mixtures. Minima in N _{Ra} ^{1} occurred at the composition for which maximum relative mass separation of the components due to thermal diffusion is predicted. Specifically, the monocomponent value N _{Ra} ^{1}≊200 for a cylinder with height‐to‐radius ratio of 6 was reduced to 25 at X _{Xe}≊0.03, and 165 at X _{Xe}≊0.3 for the Xe:He and Xe:Ar systems, respectively. Comparison with Rayleigh–Bénard instability theory, including Soret and Dufour effects, shows that for (gas) mixtures, the lateral walls act convectively less stabilizing than for monocomponent systems. It is shown that Dufour contributions to convective stability in these gas mixtures are negligible.

Onset of convection in a permeable medium between vertical coaxial cylinders
View Description Hide DescriptionThe onset of natural convection is examined for a fluid‐saturated permeable medium contained between vertical coaxial cylinders of inner and outer radii r ^{*} _{ i } and r ^{*} _{0}. The annular space is of height h ^{*}. The horizontal boundaries are isothermal, with heating from below and cooling from above. Both permeable and impermeable upper boundaries are considered. Critical Rayleigh numbers Ra_{c} and the preferred convective modes are determined as functons of the geometric ratios h ^{*}/r ^{*} _{ i } and r ^{*} _{0}/r ^{*} _{ i }. The confining vertical walls of the annular space tend to increase Ra_{c} above the value for an infinite horizontal layer. The preferred modes are predominantly asymmetric.

Calculation of turbulent boundary layers on curved surfaces
View Description Hide DescriptionPublished data from boundary layers on convex surfaces are used to assess the performance of a calculation method based on the solution of modeled transport equations for the Reynolds’ stresses and the dissipation rate of turbulence energy. For flows with large curvature, the model closely reproduces the suppression of turbulence and the diminished growth rate and skin friction. The recovery of flow distorted by curvature is also predicted with results broadly in accord with the measurements.

Measurements of the growth of a turbulently mixed layer in a linearly stratified fluid
View Description Hide DescriptionMeasurements have been made of the growth of a turbulently mixed layer in a linearly stratified fluid for Brunt–Väisälä frequencies N in the range 0.099–0.386 Hz. Turbulent mixing was induced by a horizontal grid undergoing vertical oscillations at frequencies f in the range 5.3–20.5 Hz. The experimental results support a theory due to Long which predicts the size of the mixed layer D measured from a ’’virtual’’ source plane, as a function of time t, given by D∝f ^{1/2} N ^{−7/18} t ^{1/9}.

Rotational distribution of N_{2} in Ar free jet
View Description Hide DescriptionThe rotational distribution, temperature, and collision number of N_{2} in the Ar free jet are studied using the rotational transition cross sections of the exponential gap and power laws. The relaxation of the rotational distribution along the axis of the free jet is described by the master equation, where the velocity distribution is taken as the local Maxwell distribution. The effects of the stagnation density level n _{0} d and temperature T _{0} are investigated. The rotational distribution indicates a non‐Boltzmann distribution with overpopulation at the higher rotational levels. The degree of deviation from the Boltzmann distribution at the same axial distance increases with decreasing n _{0} d and decreases with increasing T _{0}. The rotational temperature ratio T _{ r }/T _{0} depends weakly on T _{0}, which is consistent with the experimental result of Poulsen and Miller in the N_{2}‐Ar system. The rotational collision number Z _{ r } is neither constant nor a monotonically increasing function of the translational temperature; still, the downstream Z _{ r } depends weakly on n _{0} d and T _{0} consistent with the experimental result of Poulsen and Miller and is in quantitative agreement with their N_{2}‐Ar value of 2±1.

Magnetohydrodynamic Taylor vortex flow under a transverse pressure gradient
View Description Hide DescriptionElectromagnetically driven flows between infinite conducting cylinders subjected to a constant axial magnetic field B_{0} are considered. The linear stability problem for axisymmetric stationary disturbances is treated. In contrast with Chandrasekhar’s conjecture, the present numerical results indicate that the critical wave‐number tends to infinity with the magnetic field. The nonlinear state of the flow, slighly above transition, is investigated by means of Stuart’s energy approach. Further theoretical results are compared with experiment. At criticality, excellent agreement is found between linear stability theory and experiment. Above transition, only the shape of the experimental curves is correctly predicted by Stuart’s energy method.

Quasi‐linear theory without the random phase approximation
View Description Hide DescriptionThe system of quasi‐linear equations is derived without making use of the random phase approximation. The fluctuation quantities are described by the autocorrelation function of the electric field using the techniques of Fourier analysis. The resulting equations possess the necessary conservation properties, but comprise new terms which hitherto have been lost in the conventional derivations.

A steady‐state fluid model of a rotating plasma
View Description Hide DescriptionA steady‐state, three‐fluid model of the boundary layer in a rotating plasma is presented. Predictions of the model are compared with discharge voltage measurements from rotating plasma experiments. These measurements have previously been interpreted in terms of Alfvén’s critical velocity interaction. The model here, which takes centrifuging in the rotating plasma into account, offers an alternative description.

Nonlinear ion‐acoustic waves and solitons in a magnetized plasma
View Description Hide DescriptionA unified formulation is presented to study the nonlinear low‐frequency electrostatic waves in a magnetized low‐b plasma. It is found that there exist three types of nonlinear waves; (i) nonlinear ion‐cyclotron periodic waves with a wave speed V _{ p }≳C _{ s } (ion‐acoustic velocity); (ii) nonlinear ion‐acoustic periodic waves with V _{ p }<C _{ s } cosq; and (iii) ion‐acoustic solitons with C _{ s } cosq<V _{ p }<C _{ s }, where q is the angle between the wave vector and the magnetic field.

Initial damping of large amplitude waves
View Description Hide DescriptionNonlinear damping rates of finite amplitude electrostatic waves are obtained by using an invariant perturbation method. The result is valid in an initial phase defined by 0<t≲t _{ b }≡r/w_{ b } (w_{ b } is the bounce frequency). As e‖f‖/T (f is the wave potential, and T is the temperature) increases, the nonlinear initial damping becomes significant and it dominates the linear damping rate g_{ l } when, for example, e‖f‖/T≳0.3 for k = 0. 2k _{D} (k _{D} the Debye shielding constant) and e‖f‖/T≳0.7 for k = 0.3k _{D}. The theory does not assume a constant slope of the velocity distribution function f _{0} at the phase velocity v _{ p } since higher order derivatives of f _{0} at v _{ p }, ∂^{ n } f _{0}/∂v_{ p } ^{ n } (n = 3,5) play an essential role in enhanced damping. First, a dispersion relation is obtained, is solved for the Langmuir wave, and the theory is applied to an ion‐acoustic wave. A simulation study is carried out on the latter wave. The result confirms the validity of the theory.

Modulational instability in a plasma with suprathermal electrons
View Description Hide DescriptionThe consequences of the presence of suprathermal electrons on the linear stage of modulational instabilities are investigated for a range of parameters appropriate to both laboratory and astrophysical plasmas. Substantial modifications to the growth rate and secondary spectrum are found to occur for instabilities driven by large amplitude Langmuir waves in the dipole limit due to the kinetic effects of the suprathermal electrons. In particular, for reasonable choices of pump amplitude and suprathermal energy density, additional modes become unstable.

Saturation of stimulated Brillouin scattering by ion wave decay in a dissipative plasma
View Description Hide DescriptionSecondary decay of an ion‐acoustic wave is shown to provide an efficient saturation mechanism for stimulated Brillouin scattering in underdense plasma (n<0.5n _{ c r }). Phase effects and linear damping of ion waves are included in the analysis. In the weak damping regime, secondary decay dominates linear damping providing efficient saturation of Brillouin scattering. Heavy linear damping of ion waves increases the threshold for secondary decay considerably and very small densities are required to obtain saturation.

Nonlinear evolution of Buneman instability
View Description Hide DescriptionThe nonlinear evolution of one‐dimensional electron‐ion two‐stream instability in a field‐free plasma is studied both analytically and numerically (computer simulation). The instability is dominated by the fastest growing mode and its harmonics, provided that the initial fluctuation level is sufficiently small. A nonlinear dispersion relation is derived and solved numerically, taking into account; (a) the frequency and growth rate modulation, (b) the electric field up to ‖E _{ k }‖^{4}, and (c) the ’’renormalized’’ particle distribution functions. The model can successfully explain the results of a computer simulation, particularly the presence of an algebraic growth stage following the breakdown of the exponential linear growth, the appearance of harmonics, and the final saturation level. The minimum conductivity found scales as (M/m)^{0.61}w_{ p e }, where M/m is the ion/electron mass ratio.

Theory of m = l modes in collisionless plasmas
View Description Hide DescriptionModes with azimuthal or poloidal wavenumber m = 1 can appear in the form of internal kinks that are described by the ideal magnetohydrodynamic approximation, or in the form of ’’reconnecting’’ modes that lead to the formation of magnetic islands. An analysis of these modes is developed for collisionless regimes, where the collisional electrical resistivity is negligible and the effects of finite ion inertia and mode‐particle resonance play the most important role.

Nonlinear theory of high‐m tearing modes
View Description Hide DescriptionA simplified nonlinear theory of short wavelength (high‐m) electron temperature‐gradient‐driven tearing modes is presented. Saturation of the linear instability results from nonlinear mode coupling in which energy may cascade to both short and long wavelength modes. The resulting electron thermal conductivity exhibits the density scaling and absolute magnitude observed experimentally.

Low‐frequency modes with high toroidal mode numbers: A general formulation
View Description Hide DescriptionLow‐frequency waves with high toroidal mode numbers in an axisymmetric toroidal configuration are studied. In particular, the relationship between the periodicity constraints imposed by the geometry, magnetic shear, and the spatial structure of eigenmodes is investigated. By exploiting the radial translational invariance and the poloidal periodicity of the gyro‐kinetic and Maxwell equations, the two‐dimensional problem can be converted into a one‐dimensional one, and the mode structure can be expressed in terms of a single extended poloidal variable. This representation is used in the description of electromagnetic modes with phase velocities larger than the ion thermal velocity and with frequencies below the ion gyro‐frequency. Trapped particle, curvature, and compressional effects are retained. The dispersion equations for drift modes and Alfvén‐type modes are given in general geometry and simplified solutions are presented in the configuration of a double periodic plane slab.

Nonlinear effects of ion cyclotron heating of bounded plasmas
View Description Hide DescriptionAn investigation of space charge effects associated with moving ions across dc magnetic field lines due to ion cyclotron heating is investigated. Within an electrostatic approximation, an inductive electric field is imposed across a highly inhomogeneous plasma. Two and one‐half dimensional particle simulations examine this problem when electron motion is allowed along but not across the magnetic field. Finite k _{∥} driving structures which allow electron flow, appear to greatly minimize both surface and volume ion space charge effects. Left‐hand electric fields are observed in the plasma which are comparable to the vacuum left‐hand field. Substantial ion heating occurs to the point where ion Larmor radii can be compared to a scale length.

Effect of resonance broadening on the evolution of the edge of a turbulent spectrum
View Description Hide DescriptionThe extent to which nonlinear wave‐particle resonance broadening results in a narrowing of an incident lower‐hybrid wave spectrum is investigated. This narrowing is of concern because it could make control of lower‐hybrid heating difficult. It is shown numerically, however, that relatively uniform spatial power deposition occurs if resonance broadening effects are treated consistently on both the wave spectrum and the particle distribution.

Structure in the ion‐acoustic spectrum
View Description Hide DescriptionA mode simulation study using the renormalized turbulence theory for the current‐driven ion‐acoustic problem shows the presence of time‐dependent structure in the wavenumber and frequency spectrum.

Toroidal plasma equilibrium with gravity
View Description Hide DescriptionA toroidal magnetic field configuration in a gravitational field is calculated both from a simple force‐balance and by using magnetic surfaces. The configuration is found to be positionally stable in a star. The vibrational frequency near the equilibrium point is proportional to the hydrostatic frequency of a star multiplied by the ratio (W _{ B }/W _{ m })^{1/2}, where W _{ B } is the magnetic field energy density, and W _{ m } is the material pressure at the equilibrium point. It is proposed that this frequency may account for the observed solar spot cycles.