Second order Galilean fluids & Stokes' law

TL;DR

This paper investigates second derivative effects in Galilean fluids using null fluid formalism, deriving higher-order constitutive relations and analyzing their impact on Stokes' law and drag force invariance.

Contribution

It introduces a generic algorithm for obtaining high-order constitutive relations in Galilean fluids via null fluid formalism, with a focus on second order effects.

Findings

Derived second order constitutive relations for Galilean fluids.

Identified second order transport coefficients that do not affect drag force.

Extended understanding of fluid dynamics beyond first order approximations.

Abstract

We study the second derivative effects on the constitutive relations of an uncharged parity-even Galilean fluid using the null fluid framework. Null fluids are an equivalent representation of Galilean fluids in terms of a higher dimensional relativistic fluid, which makes the Galilean symmetries manifest and tractable. The analysis is based on the offshell formalism of hydrodynamics. We use this formalism to work out a generic algorithm to obtain the constitutive relations of a Galilean fluid up to arbitrarily high derivative orders, and later specialise to second order. Finally, we study the Stokes' law which determines the drag force on an object moving through a fluid, in presence of certain second order terms. We identify the second order transport coefficients which leave the drag force invariant.