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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1987

Density fluctuation spectra in magnetohydrodynamic turbulence

It is shown that within the framework of nearly incompressible magnetohydrodynamics, but not within that of neutral-fluid hydrodynamics, a k exp -5/3 inertial-range wave number density fluctuation spectrum is to be expected at the same times that k exp -5/3 kinetic energy and magnetic energy cascade spectra are present. A previous discrepancy between theory and observation in the local interstellar medium and solar wind is thereby resolved.

Montgomery, D.↗
NASA NTRS1993

Nearly incompressible fluids. II - Magnetohydrodynamics, turbulence, and waves

The theory of nearly incompressible (NI) fluid dynamics developed previously for hydrodynamics is extended to magnetohydrodynamics (MHD). Based on a singular expansion technique, modified systems of fluid equations are obtained for which the effects of compressibility are admitted only weakly in terms of the different possible incompressible solutions. NI MHD represents the interface between the compressible and incompressible magnetofluid descriptions in the subsonic regime. It is shown that three distinct NI descriptions exist corresponding to each of the three possible plasma beta regimes. The detailed theory of weakly compressible corrections to the various incompressible MHD descriptions is presented, and the implications for the solar wind are discussed.

Zank, G. P.↗
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 NTRS2014

Magnetohydrodynamic Turbulence and the Geodynamo

The ARES Directorate at JSC has researched the physical processes that create planetary magnetic fields through dynamo action since 2007. The "dynamo problem" has existed since 1600, when William Gilbert, physician to Queen Elizabeth I, recognized that the Earth was a giant magnet. In 1919, Joseph Larmor proposed that solar (and by implication, planetary) magnetism was due to magnetohydrodynamics (MHD), but full acceptance did not occur until Glatzmaier and Roberts solved the MHD equations numerically and simulated a geomagnetic reversal in 1995. JSC research produced a unique theoretical model in 2012 that provided a novel explanation of these physical observations and computational results as an essential manifestation of broken ergodicity in MHD turbulence. Research is ongoing, and future work is aimed at understanding quantitative details of magnetic dipole alignment in the Earth as well as in Mercury, Jupiter and its moon Ganymede, Saturn, Uranus, Neptune, and the Sun and other stars.

Shebalin, John V.↗
NASA NTRS1982

Two-and-a-half-dimensional magnetohydrodynamic turbulence

The homogeneous turbulence for which fluctuating magnetic fields and velocity fields are independent of one spatial coordinate but still possess all three components are studied to form a generalized two-and-half dimensional geometry. The integral of the z-vector potential and the magnetic helicity are shown to be ideal invariants, and the basic dynamical variables and the equations of uniform-density incompressible magnetohydrodynamics are defined. The possibility of simultaneous inverse cascades is considered, and Kolmogoroff dimensional analysis is employed to infer omnidirectional inverse cascade spectra. Implications of a selective decay hypothesis, where a tendency exists in the initial value problem for the ideal invariants directly cascaded to higher wavenumbers to be selectively dissipated, and the possibility of a dynamo action in the considered geometry, are examined.

Montgomery, D.↗
NASA NTRS1978

Three-dimensional magnetohydrodynamic turbulence in cylindrical geometry

A theory is developed in which a perfectly conducting cylindrical wall is used to describe incompressible MHD turbulence. Dynamic equations of incompressible MHD and its associated fields are expanded in a system of vector eigenfunctions of the curl. The total energy, magnetic helicity, and cross helicity have simple quadratic expressions in the expansion coefficients. The invariants are temporally constant for a truncation at a large, but finite, number of coefficients. The invariants are used to construct canonical distributions. It is noted that for all initial conditions, including quiescent ones, the mean-square velocity fields have finite values. The stability problem is transformed into a search for values of the integral variants which minimize the mean-square velocity fields. This leads to an extremal helicity principle.

Montgomery, D.↗
NASA NTRS1981

Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field

A strong external dc magnetic field introduces a basic anisotropy in incompressible MHD turbulence. The modifications that this is likely to produce in the properties of the turbulence are investigated for high Reynolds numbers. It is found that the turbulent spectrum splits into two parts: (1) an essentially two-dimensional spectrum with both the velocity field and the magnetic fluctuations perpendicular to the dc magnetic field, and (2) a generally weaker and more nearly isotropic spectrum of Alfven waves. These results are discussed in relation to measurements from the Culham-Harwell Zeta pinch device and the UCLA Macrorotor tokamak, as well as in relation to measurements of MHD turbulence in the solar wind.

Montgomery, D.↗
NASA NTRS1982

Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind

Measurements of the total energy, cross helicity, and magnetic helicity of the solar wind at 1, 2.8, and 5 AU are presented. These quantities are the three rugged invariants of three-dimensional ideal incompressible MHD turbulence theory. The theoretical technique for measuring the magnetic helicity from the matrix of two-point correlations is shown. The length scales characterizing the magnetic helicity are found to be equal to or greater than those which characterize the magnetic energy. The magnetic helicity typically lies at scales larger than the magnetic correlation length, consistent with the expectations of the inverse cascade and selective decay hypotheses of three-dimensional MHD turbulence. At smaller scales, the magnetic helicity oscillates in sign. Measurements of the cross helicity are not fully consistent with the usual interpretation in terms of outward propagating Alfvenic functions. Especially during the interval at 5 AU the cross helicity is found to oscillate in sign indicating fluctuations propagating both outward and inward.

Matthaeus, W. H.↗
NASA NTRS1983

Determining the alpha dynamo parameter in incompressible homogeneous magnetohydrodynamic turbulence

Alpha, an important parameter in dynamo theory, is proportional to either the kinetic, current, magnetic, or velocity helicity of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first order smoothed equations that describe the alpha effect. In two cases, when alpha is proportional to either the magnetic helicity or velocity helicity, alpha is determined experimentally from two point measurements of the fluctuating fields in incompressible, homogeneous turbulence having arbitrary symmetry. For the other two possibilities, alpha is determined if the turbulence is isotropic.

Matthaeus, W. H.↗
NASA NTRS1983

Magnetohydrodynamic turbulence in the solar wind

Recent work in describing the solar wind as an MHD turbulent fluid has shown that the magnetic fluctuations are adequately described as time stationary and to some extent as spatially homogeneous. Spectra of the three rugged invariants of incompressible MHD are the principal quantities used to characterize the velocity and magnetic field fluctuations. Unresolved issues concerning the existence of actively developing turbulence are discussed.

Matthaeus, W. H.↗
NASA NTRS1985

Forced magnetohydrodynamic turbulence in a uniform external magnetic field

Two-dimensional dissipative MHD turbulence is randomly driven at small spatial scales and is studied by numerical simulation in the presence of a strong uniform external magnetic field. A behavior is observed which is apparently distinct from the inverse cascade which prevails in the absence of an external magnetic field. The magnetic spectrum becomes dominated by the three longest wavelength Alfven waves in the system allowed by the boundary conditions: those which, in a box size of edge 2 pi, have wave numbers (kx, ky) = (1, 1), and (1, -1), where the external magnetic field is in the x direction. At any given instant, one of these three modes dominates the vector potential spectrum, but they do not constitute a resonantly coupled triad. Rather, they are apparently coupled by the smaller-scale turbulence.

Hossain, M.↗
NASA NTRS1986

The alpha dynamo parameter and measurability of helicities in magnetohydrodynamic turbulence

Alpha, an important parameter in dynamo theory, is shown to be proportional to either the kinetic, current, magnetic, or velocity helicities of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first-order smoothed equations that describe the alpha effect. In two cases, viz., when alpha is proportional to either the magnetic helicity or velocity helicity, alpha can be determined experimentally from two-point measurements of the fluctuating fields in incompressible, homogeneous turbulence with arbitrary rotational symmetry. For the other two possibilities, alpha can be determined if the turbulence is isotropic.

Matthaeus, W. H.↗
NASA NTRS1988

Helical magnetohydrodynamic turbulence and the coronal heating problem

Numerical simulations are used to investigate the relaxation of an unconfined, helically turbulent, fully three-dimensional magnetofluid, with conditions similar to those which are thought to result in the heating of the solar corona. In these simulations, the system evolves through a succession of force free states. After a relatively quiescent period of Ohmic decay, a phase of accelerated magnetic energy dissipation occurs. Some magnetic energy is transformed into kinetic energy, and the magnitude of entrophy created is a nontrival fraction of the mean square electric current. Concentrated vorticity structures are seen to play almost as important a role as electric current sheets in the heating process. Coincident with this accelerated dissipation process, a reorganization of the magnetic fields occurs, with transfer of magnetic energy to both shorter and longer wavelength modes than are initially present. The ratio of the magnetic field to the electric current density, alpha does not in general tend to assume a constant value in the force free regions during the evolution of the magnetofluid.

Dahlburg, R. B.↗