Stochastic structure formation in random media
A M Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russian Federation
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.