The realizable Markovian closure and realizable test-field model. II. Application to anisotropic drift-wave dynamics

The test-field model is shown to be potentially nonrealizable in the presence of linear waves such as those frequently encountered in models of plasma and geophysical turbulence. A new statistical closure, the realizable test-field model (RTFM), is proposed as a remedy. Both the damping rate and frequency are renormalized to account for nonlinear damping and frequency shifts. Like the realizable Markovian closure (RMC), the RTFM is based on a modified fluctuation-dissipation ansatz. Numerical solutions of the RTFM, RMC, and direct-interaction approximation for the Hasegawa–Mima equation are presented; rough agreement with direct numerical solution is found. The number of retained Fourier modes is dramatically reduced with an anisotropic generalization of a recently developed wave-number partitioning scheme.