Engineering topics
Publications and source records attributed to Zhou, YE.
Advancing the knowledge and understanding of turbulence theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.
The structure of a transport theory presented by Zhou and Matthaeus (1989), in which coupling of 'inward' and 'outward'-type fluctuations appears in the leading order, is studied. Allowance is made for the dynamic behavior of the 'fast' scale variables, which are averaged over to obtain slow-scale transport equations. The relationship of the two-scale transport models to transport models derived from the WKB approximation (Jeffreys and Jeffreys, 1980: Weinberg 1962; Dewar, 1970) as it has been applied to the solar wind MHD wave problem (Parker, 1965; Hollweg, 1973, 1974) is discussed.
A framework based on turbulence theory is presented to develop approximations for the local turbulence effects that are required in transport models. An approach based on Kolmogoroff-style dimensional analysis is presented as well as one based on a wave-number diffusion picture. Particular attention is given to the case of MHD turbulence with arbitrary cross helicity and with arbitrary ratios of the Alfven time scale and the nonlinear time scale.
A detailed derivation of a transport model for MHD fluctuations in the solar wind is presented. Dynamical equations based on a two-length scale expansion are derived from which the evolution of various wavenumber spectra may be computed, including magnetic and kinetic energies, cross helicity, induced electric field, and the corresponding helicities. Several simple analytic solutions of the equations are consistent with Helios and Voyager predictions.
A phenomenological treatment of the inertial range of isotropic statistically steady magnetohydrodynamic turbulence is presented, extending the theory of Kraichnan (1965). The role of Alfven wave propagation is treated on equal footing with nonlinear convection, leading to a simple generalization of the relations between the times characteristic of wave propagation, convection, energy transfer, and decay of triple correlations. The theory leads to a closed-form steady inertial range spectral law that reduces to the Kraichnan and Kolmogorov laws in appropriate limits. The Kraichnan constant is found to be related in a simple way to the Kolmogorov constant; for typical values of the latter constant, the former has values in the range 1.22-1.87. Estimates of the time scale associated with spectral transfer of energy also emerge from the new approach, generalizing previously presented 'golden rules' for relating the spectral transfer time scale to the Alfven and eddy-turnover time scales.
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.