Diffusion spreading of localized hydrodynamic disturbances under the action of random forces

Abstract

The effect of a time-dependent random force on fluid flow may be found by changing to a non-inertial coordinate system. It is shown that, under the action of a Gaussian random force, initially localized disturbances undergo spreading of a diffusion type. Explicit analytic solutions are given for the interior wave soliton under the action of a random force. It is shown that, in the presence of a soliton, the growth of velocity pulsing may either increase or moderate.