Second order Galilean fluids and Stokes’ law

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 off-shell 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 specialize 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.