Secondary and correlation instabilities in distributed systems

Secondary instabilities and cascade processes in certain hydrodynamic plasma and fluid models ar considered. The energy-transfer mechanism and spectrum are analyzed for drift turbulence arising in the ionospheric electrojet due to gradient instability. As an example of correlation instability, attention is given to instability in a second-order correlator for a system of surface waves propagating in shallow water over a bottom with random topography. An analysis is also made of the effect of finite-amplitude waves on the stability of the shear flows of an ideal stratified fluid. A type of explosive instability described by second-order truncated equations is found for wave modes close to the stability boundary determined in the linear approximation.