Direct-Interaction Approximation for a System of Several Interacting Simple Shear Waves

The direct-interaction approximation is applied to the evolution in time of systems of several interacting, inviscid, simple, shear waves whose initial amplitudes have a Gaussian statistical distribution. The results are compared numerically with exact statistical solutions obtained by numerical integration of the equations of motion of the wave amplitudes for a large Gaussian sample of initial conditions. It is found that the direct-interaction results can provide an adequate approximation in cases where both perturbation theory and the quasinormality approximation give physically unacceptable results.