The Consequences of the modulation instabilities - Kuklin, Volodimir M.; Куклін, Володимир Михайлович (My University, 2018)
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.
There are various cases of the development of the modulation instability of intense periodic structures in wave and non-wave media (see, for example [1]). The peculiarity of the modulation instability is the appearance of the perturbation spectrum, which is practically sym-metric with respect to large amplitude wave vector [2 - 6]. The modes of the perturbation spectrum are improper for a given medium, as a rule. The cases of different dis-sipation levels of large amplitude wave, in the presence of a source that supports it existence, are considered. 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 [7]. The line spectrum creates the conditions for the development of a more large-scale modulation [8]. Thus, the modulation instabilities near the threshold represent a cascade of processes with an increasing characteristic time of development and a larger characteristic scale [9, 10].