Stochastic structure formation in random media is considered using examples of elementary dynamical systems related to the two-dimensional geophysical fluid dynamics (Gaussian random fields) and to stochastically excited dynamical systems described by partial differential equations (lognormal random fields). In the latter case spatial structures (clusters) may form with probability one in almost every system realization due to rare events happening with vanishing probability. The problems involving stochastic parametric excitation occur in fluid dynamics, magnetohydrodynamics, physics of plasma, astrophysics and radiophysics. A more complicated stochastic problem dealing with anomalous structures on the sea surface (the rogue waves) is also considered, where random Gaussian generation of sea surface roughness is accompanied by the parametric excitation.

Keywords: stochastic equations, intermittency, Lyapunov characteristic parameter, typical realization curve, dynamical localization, statistical topography, clustering PACS: 05.40.−a, 05.45.−a, 46.65.+g, 47.27.−i (all) DOI: 10.3367/UFNe.0186.201601e.0075 URL: https://ufn.ru/en/articles/2016/1/d/ 000374119000003 2-s2.0-84962844410 2016PhyU...59...67K Citation: Klyatskin V I "Stochastic structure formation in random media" Phys. Usp. 59 67–95 (2016) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 29th, June 2015, revised: 19th, November 2015, accepted: 24th, November 2015 Оригинал: Кляцкин В И «Стохастическое структурообразование в случайных средах» УФН 186 75–104 (2016); DOI: 10.3367/UFNr.0186.201601e.0075