Variable density model for the Rayleigh-Taylor instability and its transformation to the diffusive, inhomogeneous, incompressible Navier-Stokes equations

Letter

Variable density model for the Rayleigh-Taylor instability and its transformation to the diffusive, inhomogeneous, incompressible Navier-Stokes equations

John D. Gibbon

Phys. Rev. Fluids 6, L082601 – Published 5 August 2021

Abstract

It is shown how the variable density model that governs the Rayleigh-Taylor instability for the miscible mixing of two incompressible fluids can be transformed into a diffusive version of the inhomogeneous, incompressible Navier-Stokes equations forced by gradients of the composition density $ρ$ of the mixing layer. This demonstrates how buoyancy-driven flows drive and enhance Navier-Stokes turbulence. The role of the potential vorticity $q = ω \cdot \nabla ρ$ is also discussed.