Thermodynamically consistent semi-compressible fluids: a variational perspective

Abstract This paper presents (Lagrangian) variational formulations for single and multicomponent semi-compressible fluids with both reversible (entropy-conserving) irreversible (entropy-generating) processes. Semi-compressible are useful in describing low-Mach dynamics, since they soundproof . These models find wide use many areas of fluid including geophysical astrophysical dynamics. Specifically, the Boussinesq, anelastic pseudoincompressible equations developed through a unified treatment valid arbitrary Riemannian manifolds, thermodynamic potentials geopotentials. By design, these obey 1st 2nd laws thermodynamics, ensuring their consistency. general approach extends unifies existing work, helps clarify thermodynamics fluids. To further this goal, evolution presented range variables: entropy density s , specific η buoyancy b temperature T potential θ generic entropic variable χ ; along definition all three semicompressible Finally, elliptic equation pressure perturbation (the Lagrange multiplier that enforces semi-compressibility) is sets case Boussinesq/anelastic dynamics; some discussion given difficulty formulating it