Mathematics – Logic
Scientific paper
Jan 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phdt........12o&link_type=abstract
PhD Dissertation, Delaware Univ. Wilmington, DE United States
Mathematics
Logic
4
Magnetohydrodynamic Turbulence, Homogeneous Turbulence, Isotropic Turbulence, Solar Wind, Chebyshev Approximation, Flow Distribution, Kinetic Energy, Magnetic Fields, Wave Propagation, Wentzel-Kramer-Brillouin Method, Astronomical Models
Scientific paper
Recently developed scale separated models for the transport of MHD scale turbulence in a weakly inhomogeneous background plasma, provide a basis for computing both radial and temporal dependence of solar wind fluctuations. Development of the new model was prompted by the inability of traditional approaches to explain the observed radial evolution properties of various quantities, and by the need for a formalism to provide information on the dynamical evolution of turbulence for use in models of solar wind acceleration and heating. When the solar wind fluctuations are considered to be MHD turbulence, two forms of the model can respectively be used to obtain the evolution of the inertial range spectra and the energy-containing range quantities. The model includes the effects of advection, wave propagation, expansion, non-WKB "mixing," as well as recently developed phenomenological models for non-linear decay of both the energy containing and the inertial range fluctuations in MHD turbulence. We derive the model and describe its numerical implementation, which is based upon a Chebyshev representation of the (large-scale) spatial dependence of the fluctuations. Solutions are obtained for the evolution of magnetic energy, kinetic energy, and cross helicity of the fluctuations, under the influence of linear transport effects and nonlinear effects appropriate to 2D or 3D isotropic turbulence, with specified large scale flow and magnetic field. The model accurately reproduces WKB and other well known solutions (such as steady inertial range spectra) in special cases. Comparison of the solutions with observational data shows that, for some conditions, the models have the potential to partially explain the observed evolutions of the cross helicity and the kinetic-to-magnetic energy ratio. Additionally, as an auxiliary problem, the general properties and forms of correlation functions and spectra for homogeneous MHD turbulence have been investigated in some detail. Several important and apparently new results have arisen from this work, which complete the theory of homogeneous second order correlation functions for MHD turbulence of arbitrary rotational symmetry.
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