9600060 Turkington Recent progress with statistical equilibrium models of ideal fluid turbulence suggests that they have greater predictive power than previously believed. Unlike traditional homogeneous turbulence theory, these models capture the essential features of the long-lived, large-scale structures that form in the process of turbulent relaxation. Moreover, they furnish definite macroscopic equations for the coherent structures that persist amidst the microscopic disorder. The proposed investigations address the formulation, justification and solution of these statistical equilibrium models. The goal of the work is to answer fundamental questions about prototype models drawn from hydrodynamics and magnetohydrodynamics. Both analytical and numerical methods are employed. On the theoretical side, continuum and lattice models are constructed, and their properties are established using a synthesis of x-space and k-space methods. This approach is expected to yield new theories of turbulent relaxation for uniform and stratified fluids, and incompressible magnetofluids in two and three dimensions. On the computational side, optimization methods are designed to solve the constrained maximum entropy problems that govern the various models. These numerical methods are implemented to reveal the predictions of the models, especially in settings where experiments or simulations are available for comparison. %%% Turbulent fluid flow remains one of the unsolved puzzles of physical science. A satisfactory theoretical understanding of it would provide much more powerful means of computing the behavior of fluid motions than is presently available. Such computations are needed in numerous applied fields, from aerodynamic design to weather prediction. Similarly, the modeling of plasmas (hot, ionized gases), such as arise in fusion energy research, requires a theory of turbulence for electrically-conducting fluids in magnetic fields. The proposed work see ks to develop the mathematical tools necessary to calculate the persistent, predominant states of these fluid and magnetofluid systems without resolving the full complexity of their detailed behavior. Tools of this kind, which are built from basic concepts in statistical physics, are currently available only in some simplified systems. The motivation for the investigations is to extend the range of applications of these tools and to support them by complete theories and effective computational methods. ***
