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  • Letter

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

John D. Gibbon

  • Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom

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

DOI: https://doi.org/10.1103/PhysRevFluids.6.L082601

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·∇ρ is also discussed.

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