A Closed Stochastic Approximate Model for Time Dependent Turbulent Flows.
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF ENGINEERING SCIENCE AND MECHANICS
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Working along the lines of a procedure outlined by Keller, a technique is developed for deriving closed first- and second-order moment equations for a general class of stochastic nonlinear equations by performing a renormalization at the level of the second moment. The work of Weinstock, as reformulated recently by Balescu and Misguich, is extended in order to obtain two equivalent representations for the second moment using an exact, nonperturbative, statistical approach. These general results, when specialized to the weak-coupling limit, lead to a complete set of closed equations for the first two moments within the framework of an approximation corresponding to Kraichnans direct-interaction approximation. Additional restrictions result in a self-consistent set of equations for the first two moments in the stochastic quasi-linear approximation. Finally, the technique is illustrated by considering its application to two specific physical problems 1 Hydrodynamic turbulence and 2 Vlasov-plasma turbulence in the presence of an external stochastic electric field. Author
- Fluid Mechanics
- Nuclear Physics and Elementary Particle Physics