Inertial nonlinearity and chaotic motion of particle fluxes.

Abstract

A brief review is given of the nonlinear phenomena arising in the evolution of random perturbations in particle fluxes of the hydrodynamical type, the velocity field of which is described by equations similar to the Riemann and Burgers equations. It is shown that a nonlinearity of the inertial type deforming the fluxes owing to the inertia of the motion of their constituent particles leads to the formation of singularities in the realizations of the velocity and density fields, and, consequently, to the appearance of universal asymptotes in their spectra and probability distributions. Methods are presented for the statistical description of waves in dispersionless media. A brief discussion is given of the laws of evolution of the statistical characteristics of the velocity and density fields of particle fluxes, both without interactions and with a contact interaction. In particular, the analogy between the solution of the Burgers equation and a particle flux with adhesion is studied. Diverse physical applications are discussed: to the dynamics of particles and mixtures, intensity fluctuations of an optical wave which has passed through a phase screen and in a randomly nonuniform medium, gravitational instability, and acoustical turbulence.