Directed Burgers waves interacting with mean field the modified Burgers equation and its stationary solutions

Abstract

Projecting technique is used for a system of coupled nonlinear equations for interacting modes derivation. Three independent modes of the viscous flow: leftwards, rightwards propagating (acoustic) and the stationary one (heat) are specified by a set of orthogonal projectors. The final system of coupled equations is equivalent to the basic one with the accuracy up to the third-order nonlinear terms and its form allows to apply nonsingular perturbations method for an approximate solution in the case when one mode is dominant compared with other iterated modes. Caloric and thermal equations of state are taken in the general form. Thermoviscous media are treated, that leads to a system of coupled equations of the Burgers type. The modified Burgers equation for rightwards mode affected by other ones is obtained as well as its stationary solutions.