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Montgomery, David

Publications and source records attributed to Montgomery, David.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Navier-Stokes relaxation to sinh-Poisson states at finite Reynolds numbers

A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier-Stokes fluid to a 'most probable', or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables.

Montgomery, David↗
NASA NTRS1992

Modifications of magnetohydrodynamics as applied to the solar wind

The effect of including the Braginskii viscous stress tensor in magnetohydrodynamics is remarked upon. It is shown that semiquantitative agreement with a recently observed anisotropy in the turbulent solar wind spectrum can be achieved in this way. The modifications of the dynamical equations are simple enough to permit their inclusion in numerical codes. The effects of large 'ion parallel viscosities' also may be significant for plasmas in quite different regimes than the solar wind.

Montgomery, David↗
NASA NTRS1992

'Reduced' magnetohydrodynamics and minimum dissipation rates

It is demonstrated that all solutions of the equations of 'reduced' magnetohydrodynamics approach a uniform-current, zero-flow state for long times, given a constant wall electric field, uniform scalar viscosity and resistivity, and uniform mass density. This state is the state of minimum energy dissipation rate for these boundary conditions. No steady-state turbulence is possible. The result contrasts sharply with results for full three-dimensional magnetohydrodynamics before the reduction occurs.

Montgomery, David↗
NASA NTRS1991

Nonlinear magnetohydrodynamics by Galerkin-method computation

A fully spectral numerical code is used to explore the properties of voltage-driven dissipative magnetofluids inside a periodic cylinder with circular cross section. The trial functions are orthonormal eigenfunctions of the curl (Chandrasekhar-Kendall functions). Transitions are observed from axisymmetric resistive equilibria without flow to helically deformed laminar states with flow, and between pairs of helical laminar states with different pairs of poloidal and toroidal m and n numbers. States of minimum energy dissipation rate seem to be preferred. At high values of the pinch ratio, fully developed magnetohydrodynamic turbulence is observed.

Shan, Xiaowen↗
NASA NTRS1991

Selective decay and coherent vortices in two-dimensional incompressible turbulence

Numerical solution of two-dimensional incompressible hydrodynamics shows that states of near minimal ratio of enstrophy to energy can be attained in times short compared with the flow decay time, confirming the simplest turbulent selective decay conjecture, and suggesting that coherent vortex structures do not terminate nonlinear processes. After all possible vortex mergers occur, the vorticity attains a particlelike character, suggested by the late-time similarity of the streamlines to Ewald potential contours.

Matthaeus, William H.↗
NASA NTRS1991

Statistical-mechanical selection of the shapes of disk galaxies

A new method is proposed for selecting steady state shapes of disk galaxies as 'most probable states' of a large number of stars, given only the total energy and total angular momentum. A partial differential equation is derived for the mean gravitational potential; it is closely related to the 'sinh-Poisson' equation for the mean-field description of a line vortex system or electrostatic guiding-center plasma. A 'water bag' approximation to the distribution function for bound stars renders the equation analytically tractable, but accurate solution of it may require numerical integration, in view of its general nonlinearity.

Montgomery, David↗
NASA NTRS1990

Galerkin approximations for dissipative magnetohydrodynamics

A Galerkin approximation scheme is proposed for voltage-driven, dissipative magnetohydrodynamics. The trial functions are exact eigenfunctions of the linearized continuum equations and represent helical deformations of the axisymmetric, zero-flow, driven steady state. The lowest nontrivial truncation is explored: one axisymmetric trial function and one helical trial function each for the magnetic and velocity fields. The system resembles the Lorenz approximation to Benard convection, but in the region of believed applicability, its dynamical behavior is rather different, including relaxation to a helically deformed state similar to those that have emerged in the much higher resolution computations of Dahlburg et al.

Chen, Hudong↗
NASA NTRS1990

A helically distorted MHD flux rope model

A flux rope model is proposed which has a variable degree of helical distortion from axisymmetry. The basis for this suggestion is a series of numerical and analytical investigations of magnetohydrodynamic states which result when an axial electric current is directed down on dc magnetic field. The helically distorted states involve a flow velocity and seem to be favored because of their lower rate of energy dissipation. Emphasis is on the magnetometer and particle energy analyzer traces that might be characteristic of such flux ropes. It is shown that even a fractionally small helical distortion may considerably alter the traces in minimum-variance coordinates. In short, what may be fairly common MHD processes can render a flux rope almost unrecognizable under standard diagnostics, even if the departures from axisymmetry are not great.

Theobald, Michael L.↗
NASA NTRS1990

Relaxed states of MHD turbulence - Minimum dissipation or minimum energy?

The results of driven, steady-state MHD computations are described by adapting the principle of minimum energy dissipation rate to MHD. It is argued that there is a variational principle that is as useful for the driven, steady-state problem as the minimum energy principle is for isolated mechanical systems, particularly for fluids and magnetofluids. Driven, dissipative MHD is reexamined from the standpoint of minimum-dissipation-rate principles.

Montgomery, David↗
NASA NTRS1989

Helical, dissipative, magnetohydrodynamic states with flow

It is shown that for an axially periodic column of magnetofluid driven by an applied axial electric field, the total rate of energy dissipation (Ohmic plus viscous) can be lowered by permitting a helical component with vortical flow in the solution. The principle of minimum energy-dissipation rate suggests that this partially helical state will be preferred to the axisymmetric one that exists for the same parameters. The result is consistent with the repeated appearance of such partially-helical states in several fully three-dimensional numerical computations and is not inconsistent with the data from some confinement experiments.

Montgomery, David↗
NASA NTRS1989

Magnetic dynamo activity in mechanically driven compressible magnetohydrodynamic turbulence

Magnetic dynamo activity in a homogeneous, dissipative, polytropic, two-dimensional, turbulent magneto-fluid is simulated numerically. The magneto-fluid is simulated numerically. The magneto-fluid is, in a number of cases, mechanically forced so that energy input balances dissipation, thereby maintaining constant energy. In the presence of a mean magnetic field, a magneto-fluid whose initial turbulent magnetic energy is zero quickly arrives at a state of non-zero turbulent magnetic energy. If the mean magnetic field energy density is small, the turbulent magnetic field can achieve a local energy density more than four hundred times larger; if the mean magnetic field energy density is large, then equipartition between the turbulent magnetic and kinetic energy is achieved. Compared to the presence of a mean magnetic field, compressibility appears to have only a marginal effect in mediating the transfer of turbulent kinetic energy into magnetic energy.

Shebalin, John V.↗
NASA NTRS1989

Sawtooth oscillations about helical current channels

An existing pseudospectral code for solving the three-dimensional equations of reduced magnetohydrodynamics is extended by adding a temperature equation. Resistivities and thermal conductivities are given their (isotropic) Braginskii temperature dependences, and are advanced self-consistently. Realistic-looking sawtooth oscillations are observed at modest Lundquist and Reynolds numbers. However, the oscillations are excited upon, and relax back to, a helical (rather than an axisymmetric) current channel.

Theobald, M. L.↗
NASA NTRS1988

Minimum dissipation rates in magnetohydrodynamics

Minimum dissipation rate states are explored for a current-carrying channel of magnetofluid, supported by a dc magnetic field and driven by an applied electric field. The minimization is carried out subject to the constraints of constant axial (toroidal) magnetic flux and constant time-averaged rate of supply of magnetic helicity. The solutions of the resulting Euler-Lagrange equations are sensitive to boundary conditions on the current density j. One set of boundary conditions on j leads to the same consequences as Taylor's 'minimum-energy' theory. A different set leads to significantly different consequences, including a departure from the 'force-free' magnetic profile and a toroidal component of current density that does not reverse at the wall when the toroidal magnetic field reverses.

Montgomery, David↗
NASA NTRS1988

Turbulent magnetohydrodynamic density fluctuations

A spectral-method numerical code is used to compute mass-density fluctuation spectra in turbulent magnetofluids. The computations are used to test and extend the analytical theory of density variations in slightly compressible magnetofluids given by Montgomery, et al. (1987) and used to infer inertial-range density-fluctuation spectra for the nearby interstellar medium and solar wind. A local equation of state is assumed, relating density to pressure. Constant, scalar resistivities and viscosities are used. In the limit of low Mach numbers and high mechanical-to-magnetic pressure ratios, the fit of the computations to the analytical theory is seen to be close.

Shebalin, John V.↗
NASA NTRS1988

MHD turbulent processes

Three areas of study in MHD turbulence are considered. These are the turbulent relaxation of the toroidal Z pinch, density fluctuations in MHD fluids, and MHD cellular automata. A Boolean computer game that updates a cellular representation in parallel and that has macroscopic averages converging to solutions of the two-dimensional MHD equations is discussed.

Montgomery, David↗
NASA NTRS1987

Noise and compressibility in lattice-gas fluids

Computations are reported in which the hexagonal lattice gas is used to simulate two-dimensional Navier-Stokes shear flows. Limitations associated with noise in the initial loading and compressible effects associated with a velocity-dependent equation of state arise and interact with each other. A relatively narrow window in density and flow speed exhibits physical behavior.

Dahlburg, Jill P.↗
NASA NTRS1987

Magnetohydrodynamic cellular automata

A generalization of the hexagonal lattice gas model of Frisch, Hasslacher and Pomeau is shown to lead to two-dimensional magnetohydrodynamics. The method relies on the ideal point-wise conservation law for vector potential.

Montgomery, David↗