The Consequences of the modulation instabilities

Abstract

The paper demonstrates the consequences of modulation instability of intense periodic structures in wave and non-wave media. In the case of a large dissipation level, near and above the threshold, the instability leads to the excitation of spectra whose width narrows, forming narrow spectral lines and self-similar structure of the big spatial clearness. At an insignificant level of dissipation, far from the threshold of modulation instability, the wave motion (initiated by the source) forms anomalous amplitude waves and envelopes exceeding the average amplitude by at three times. The shape of the envelope or wave packet is similar to the shape of Peregrine breather, and the dynam-ics over time is also similar. The formation of self-similar spatial structures in the developed convection of a thin liquid or gas layer due to the development of modulation instability is presented. In this case, toroidal convection vortices generate poloidal vortices of large scale − the effect of a hydrodynamic dynamo. Experimental results of the investigation of emerging self-similar structures on the graphite surface are presented. The features of the develop-ment of parametric instabilities are discussed.