Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields.

Monte Carlo methods for computing various statistical aspects of turbulent diffusion with long range correlated and even fractal random velocity fields are described here. A simple explicit exactly solvable model with complex regimes of scaling behavior including trapping, subdiffusion, and superdiffusion is utilized to compare and contrast the capabilities of conventional Monte Carlo procedures such as the Fourier method and the moving average method; explicit numerical examples are presented which demonstrate the poor convergence of these conventional methods in various regimes with long range velocity correlations. A new method for computing fractal random fields involving wavelets and random plane waves developed recently by two of the authors [J. Comput. Phys. 117, 146 (1995)] is applied to compute pair dispersion over many decades for systematic families of anisotropic fractal velocity fields with the Kolmogorov spectrum. The important associated preconstant for pair dispersion in the Richardson law in these anisotropic settings is compared with the one obtained over many decades recently by two of the authors [Phys. Fluids 8, 1052 (1996)] for an isotropic fractal field with the Kolmogorov spectrum. (c) 1997 American Institute of Physics.

The Seismic Structure of the Sun

Global Oscillation Network Group data reveal that the internal structure of the sun can be well represented by a calibrated standard model. However, immediately beneath the convection zone and at the edge of the energy-generating core, the sound-speed variation is somewhat smoother in the sun than it is in the model. This could be a consequence of chemical inhomogeneity that is too severe in the model, perhaps owing to inaccurate modeling of gravitational settling or to neglected macroscopic motion that may be present in the sun. Accurate knowledge of the sun's structure enables inferences to be made about the physics that controls the sun; for example, through the opacity, the equation of state, or wave motion. Those inferences can then be used elsewhere in astrophysics.