Compressible Fluids: the discontinuity of the vorticity vector on a shock wave in thermodynamical variables

TL;DR

This paper derives an expression for the discontinuity of vorticity across shock waves in compressible fluids, linking it to thermodynamic variables without relying on mass or momentum conservation equations.

Contribution

It introduces a novel formulation of vorticity discontinuity based solely on potential equations and thermodynamic variables, independent of traditional conservation laws.

Findings

Vorticity discontinuity expressed as a function of temperature and entropy gradients.

Derivation achieved without using mass conservation or momentum equations.

Provides a new perspective on vorticity behavior in shock waves.

Abstract

The discontinuity of the vorticity is written as a function of the vector T grad s, (where T is the temperature and s the specific entropy). The expression is obtained thanks to potential equations and independently of the mass conservation and the equation of momentum balance.