Hydrodynamic Impulse in a Compressible Fluid

TL;DR

This paper derives a new expression for hydrodynamic impulse in compressible fluids, confirming its validity and exploring implications for vortex dynamics and variational principles in such fluids.

Contribution

It introduces a novel formulation of hydrodynamic impulse for compressible fluids and discusses its application to vortex rings and axisymmetric vortex systems.

Findings

Validated the new impulse expression for compressible Euler equations

Applied the formulation to analyze vortex rings in compressible fluids

Discussed variational principles for steady vortex systems

Abstract

A suitable expression for hydrodynamic impulse in a compressible fluid is deduced. The development of appropriate impulse formulation for compressible Euler equations confirms the propriety of the hydrodynamic impulse expression for a compressible fluid given here. Implications of the application of this formulation to a compressible vortex ring are pointed out. A variational characterization for an axisymmetric vortex system moving steadily in an ideal, compressible fluid is discussed.