Engineering Papers⌕ Search

Engineering topics

Montgomery, D.

Publications and source records attributed to Montgomery, D..

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

A B-B-G-K-Y framework for fluid turbulence

A kinetic theory for fluid turbulence is developed from the Liouville equation and the associated BBGKY hierarchy. Real and imaginary parts of Fourier coefficients of fluid variables play the roles of particles. Closure is achieved by the assumption of negligible five-coefficient correlation functions and probability distributions of Fourier coefficients are the basic variables of the theory. An additional approximation leads to a closed-moment description similar to the so-called eddy-damped Markovian approximation. A kinetic equation is derived for which conservation laws and an H-theorem can be rigorously established, the H-theorem implying relaxation of the absolute equilibrium of Kraichnan. The equation can be cast in the Fokker-Planck form, and relaxation times estimated from its friction and diffusion coefficients. An undetermined parameter in the theory is the free decay time for triplet correlations. Some attention is given to the inclusion of viscous damping and external driving forces.

Montgomery, D.↗
NASA NTRS1975

Two-dimensional turbulence in inviscid fluids or guiding center plasmas

Numerical tests of the inviscid equilibrium theory of Kraichnan (1975) are described. The mathematical description applies equally well to the two-dimensional electrostatic guiding center plasma and to the two-dimensional inviscid Navier-Stokes fluid. The predictions of this analytic theory are discussed. A pair of coupled equations are derived for the two-time vorticity autocorrelation in Fourier space and the infinitesimal unit response function G of Kraichnan in the so-called Eulerian direct interaction approximation. Kraichnan's assertion that thermodynamic limits exist for the negative temperature states is questioned.

Seyler, C. E., Jr.↗
NASA NTRS1975

Two dimensional turbulence in inviscid fluids or guiding center plasmas

Analytic theory for two-dimensional turbulent equilibria for the inviscid Navier-Stokes equations is examined mathematically. Application of the technique to electrostatic guiding center plasma is discussed. A good fit is demonstrated for the approach to a predicted energy per Fourier mode obtained from a two-temperature canonical ensemble. Negative as well as positive temperature regimes are explored. Fluctuations about the mean energy per mode also compare well with theory. In the regime of alpha less than zero, beta greater than zero, with the minimum value of alpha plus beta times k squared near zero, contour plots of the stream function reveal macroscopic vortex structures similar to those seen previously in discrete vortex simulations. Eulerian direct interaction equations, which can be used to follow the approach to inviscid equilibrium, are derived.

Seyler, C. E., Jr.↗
NASA NTRS1974

Magnetic field dependence of plasma relaxation times

A previously derived Fokker-Planck collision integral for an electron plasma in a dc magnetic field is examined in the limit in which the Debye length is greater than the thermal gyroradius, which is in turn greater than the mean distance of closest approach. It is demonstrated that the collision integral can be satisfactorily approximated by the classical Landau value (which ignores the presence of a dc magnetic field) if the following replacement is made: In the Coulomb logarithm, the Debye length is replaced by the gyroradius. This induces a fundamental logarithmic dependence on magnetic field in the relaxation times. Numerical comparison of the asymptotic approximations with the previously derived exact results is made, and good agreement is found. The simplification this introduces into the description of collision processes in magnetized plasma is considerable.

Montgomery, D.↗
NASA NTRS1974

Thermal relaxation of a two-dimensional plasma in a d.c. magnetic field. I - Theory. II - Numerical simulation

Theoretical considerations relevant to the rate of thermal relaxation of a two-dimensional plasma in a strong uniform dc magnetic field are developed. The Vahala-Montgomery (1971) kinetic description is completed by providing a cut-off time for the time of interaction of two particles contributing to the collision term. The kinetic equation is shown to predict that thermal relaxation varies as a function of defined dimensionless time.

Hsu, J.-Y.↗
NASA NTRS1974

Statistical mechanics of 'negative temperature' states

Consideration of the dynamics of a two-dimensional guiding center plasma, recently shown by Taylor and McNamara (1971) to be identical to the dynamics of the discrete vortex model of Onsager (1949). A semirigorous application of the methods of equilibrium statistical mechanics to the guiding center plasma (or equivalently, the line vortex system) is presented. An adaptation of the apparatus of the theory of probability is attempted, in the form given by Khinchin (1949) to obtain ensemble-average predictions for the states of the guiding center plasma. Interest focuses primarily on the regime in which the interaction energy is high enough to be above the Onsager 'negative temperature' threshold.

Montgomery, D.↗
NASA NTRS1974

Thermal relaxation of a two dimensional plasma in a dc magnetic field. Part 2: Numerical simulation

The thermal relaxation process for a spatially uniform two dimensional plasma in a uniform dc magnetic field is simulated numerically. Thermal relaxation times are defined in terms of the time necessary for the numerically computer Boltzman H-function to decrease through a given part of the distance to its minimum value. Dependence of relaxation time on two parameters is studied: number of particles per Debye square and ratio of gyrofrequency to plasma frequency.

Hsu, J. Y.↗
NASA NTRS1974

Electric field correlations in the guiding-center plasma

Electric field autocorrelations for the two-dimensional electrostatic guiding-center plasma are calculated numerically. It is concluded that the autocorrelation, averaged over a thermal equilibrium ensemble, is damped in an approximately exponential fashion, as predicted by Taylor and McNamara. Oscillatory behavior of the type predicted by Taylor and Thompson is not observed.

Joyce, G.↗
NASA NTRS1974

Strongly magnetized classical plasma models

Discrete particle processes in the presence of a strong external magnetic field were investigated. These processes include equations of state and other equilibrium thermodynamic relations, thermal relaxation phenomena, transport properties, and microscopic statistical fluctuations in such quantities as the electric field and the charge density. Results from the equilibrium statistical mechanics of two-dimensional plasmas are discussed, along with nonequilibrium statistical mechanics of the electrostatic guiding-center plasma (a two-dimensional plasma model).

Montgomery, D.↗
NASA NTRS1972

Multiple soliton production and the Korteweg-de Vries equation.

Compressive square-wave pulses are launched in a double-plasma device. Their evolution is interpreted according to the Korteweg-de Vries description of Washimi and Taniuti. Square-wave pulses are an excitation for which an explicit solution of the Schrodinger equation permits an analytical prediction of the number and amplitude of emergent solitons. Bursts of energetic particles (pseudowaves) appear above excitation voltages greater than an electron thermal energy, and may be mistaken for solitons.

Hershkowitz, N.↗
NASA NTRS1972

Simulation of the 'negative temperature' instability for line vortices.

In previous numerical solution to the continuum Navier-Stokes equations, a 'negative temperature' instability for the two-dimensional motions of interacting line vortices was observed. The experiment is repeated for a discrete vortex model, thus obtaining a numerical simulation of the 'negative temperature' instability for a large number of discrete line vortices. Typical results which are shown, are thought to lie above and below the energy threshold for negative temperature instability.

Joyce, G.↗
NASA NTRS1972

Three-dimensional plasma diffusion in a very strong magnetic field.

The thermal equilibrium coefficient of spatial diffusion transverse to a strong uniform dc magnetic field is calculated for a fully ionized plasma. The particles are assumed to move transverse to the field only as a consequence of the E x B drift, but to move freely parallel to it. The particles interact only electrostatically. The calculation is done at large, but fixed and finite, plasma volume. It is shown that, as magnetic field density approaches infinity, the leading term of the coefficient of transverse spatial diffusion falls off in a prescribed manner, but contains a multiplicative factor which goes to zero as the plasma volume becomes infinite. The method of calculation fails for unbounded plasmas.

Montgomery, D.↗
NASA NTRS1972

Two-dimensional vortex motion and 'negative temperatures.'

Explanation of the novel phenomenon, tentatively identified as the 'ergodic boundary' in a space of initial conditions for turbulent flow, suggested by the recent numerical integration of the two-dimensional Navier-Stokes equations at high Reynolds numbers reported by Deem and Zabusky (1971). The proposed explanation is presented in terms of negative temperatures for a point vortex model.

Montgomery, D.↗
NASA NTRS1972

Conductivity of a two-dimensional guiding center plasma.

The Kubo method is used to calculate the electrical conductivity of a two-dimensional, strongly magnetized plasma. The particles interact through (logarithmic) electrostatic potentials and move with their guiding center drift velocities (Taylor-McNamara model). The thermal equilibrium dc conductivity can be evaluated analytically, but the ac conductivity involves numerical solution of a differential equation. Both conductivities fall off as the inverse first power of the magnetic field strength.

Montgomery, D.↗