Self-Consistent-Field Approach to Nonstationary Turbulence

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Abstract
The self‐consistent‐field method proposed earlier [J. R. Herring, Phys. Fluids 8, 2219 (1965)] to treat stationary turbulence is generalized to include the case of time dependent turbulence. The predictions of the method are compared to exact and direct‐interaction solutions for simple model systems consisting of several interacting shear waves. The main features of the system's approach to equilibrium are correctly predicted by the method. The predicted single‐mode‐energy spectrum has small spurious oscillations, which result from truncating the perturbation series at second order. These oscillations are somewhat larger in amplitude than those that would result from using the direct‐interaction approximation for the same system.