The Variable Density Model for the Rayleigh-Taylor Instability and its transformation to the diffusive, inhomogeneous, incompressible Navier-Stokes equations

TL;DR

This paper demonstrates how the variable density model for Rayleigh-Taylor instability can be transformed into a diffusive inhomogeneous Navier-Stokes framework, highlighting the role of buoyancy and potential vorticity in turbulence.

Contribution

It introduces a transformation of the variable density model into a diffusive Navier-Stokes form, linking buoyancy-driven flows with turbulence dynamics.

Findings

Transformation of VDM to Navier-Stokes equations

Role of buoyancy in turbulence enhancement

Discussion of potential vorticity effects

Abstract

It is shown how the variable density model (VDM) that governs the Rayleigh-Taylor instability (RTI) 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 $\rho$ of the mixing layer. This demonstrates how buoyancy-driven flows drive and enhance Navier-Stokes turbulence. The role of the potential vorticity $q = \omega\cdot\nabla\rho$ is also discussed.