Non-equilibrium Thermodynamics of Rayleigh–Taylor Instability

Abstract

Here, the fundamental problem of Rayleigh–Taylor instability (RTI) is studied by direct numerical simulation (DNS), where the two air masses at different temperatures, kept apart initially by a non-conducting horizontal interface in a 2D box, are allowed to mix. Upon removal of the partition, mixing is controlled by RTI, apart from mutual mass, momentum, and energy transfer. To accentuate the instability, the top chamber is filled with the heavier (lower temperature) air, which rests atop the chamber containing lighter air. The partition is positioned initially at mid-height of the box. As the fluid dynamical system considered is completely isolated from outside, the DNS results obtained without using Boussinesq approximation will enable one to study non-equilibrium thermodynamics of a finite reservoir undergoing strong irreversible processes. The barrier is removed impulsively, triggering baroclinic instability by non-alignment of density, and pressure gradient by ambient disturbances via the sharp discontinuity at the interface. Adopted DNS method has dispersion relation preservation properties with neutral stability and does not require any external initial perturbations. The complete inhomogeneous problem with non-periodic, no-slip boundary conditions is studied by solving compressible Navier–Stokes equation, without the Boussinesq approximation. This is important as the temperature difference between the two air masses considered is high enough ( $$\Delta T = 70$$ K) to invalidate Boussinesq approximation. We discuss non-equilibrium thermodynamical aspects of RTI with the help of numerical results for density, vorticity, entropy, energy, and enstrophy.