Generalized potentiality of inhomogeneous media flows

Abstract

A method for specifying a class of potential flows of inhomogeneous continuous media is developed. The general approach is based on expanding a medium material symmetry group to a special volume-preserving group, allowing us to obtain a law for the conservation of vorticity and, when there is no vorticity, to derive the unsteady Bernoulli equation. As illustrations, plane steady stationary flows of an inhomogeneous incompressible fluid and variable-entropy gas are considered. The problem of an inhomogeneous gas flow around a wedge yielding the formation of a shock wave is solved.