The clebsch potential approach to fluid lagrangians

TL;DR

This paper develops the clebsch potential approach to fluid Lagrangians, exploring three variants to connect with other fluid models and extend the theoretical framework.

Contribution

It introduces three new variants of fluid Lagrangians using clebsch potentials, including fixed, higher power, and dual vector field formulations.

Findings

Explicit linear Lagrangian with fixed equation of state

Generalized Lagrangians from higher powers of the comoving vector

Lagrangians with two vector fields representing density and entropy flows

Abstract

The clebsch potential approach to fluid lagrangians is developed in order to establish contact with other approaches to fluids. Three variants of the perfect fluid approach are looked at. The first is an explicit linear lagrangian constructed directly from the clebsch potentials, this has fixed equation of state and explicit expression for the pressure but is less general than a perfect fluid. The second is lagrangians more general than that of a perfect fluid which are constructed from higher powers of the comoving vector. The third is lagrangians depending on two vector fields which can represent both density flow and entropy flow.