Field Theory of the Eulerian Perfect Fluid

TL;DR

This paper reformulates the Eulerian perfect-fluid theory using a pure field-theoretic approach, emphasizing conservation of convective current and reducing degrees of freedom to clarify the dynamics of vorticity and charge exchange.

Contribution

It introduces a novel reformulation that reduces redundant variables and highlights the role of Clebsch fields in fluid dynamics and symmetry breaking.

Findings

Successfully reduces degrees of freedom in the fluid theory

Clarifies the role of Clebsch variables in vorticity and charge exchange

Provides a new field-theoretic perspective on fluid conservation laws

Abstract

The Eulerian perfect-fluid theory is reformulated from its action principle in a pure field-theoretic manner. Conservation of the convective current is no longer imposed by Lin's constraints, but rather adopted as the central idea of the theory. Our formulation, for the first time, successfully reduces redundant degrees of freedom promoting one half of the Clebsch variables as the true dynamical fields. Interactions on these fields allow for the exchange of the convective current of quantities such as mass and charge, which are uniformly understood as the breaking of the underlying symmetry of the force-free fluid. The Clebsch fields play the essential role in the exchange of angular momentum with the force field producing vorticity.