Transition from shear-dominated to Rayleigh-Taylor turbulence

TL;DR

This paper develops a phenomenological theory identifying a cross-over time-scale that marks the transition from shear-dominated to buoyancy-driven turbulence in mixing layers, validated by DNS simulations.

Contribution

The paper introduces a new theoretical framework for predicting the transition time between shear and buoyancy turbulence regimes in mixing layers.

Findings

The cross-over time depends on buoyancy difference, velocity difference, and gravity.

DNS simulations confirm the predicted transition timing.

Energy spectra and mixing layer growth match theoretical predictions.

Abstract

Turbulent mixing layers in nature are often characterized by the presence of a mean shear and an unstable buoyancy gradient between two streams of different velocity. Depending on the relative strength of shear versus buoyancy, either the former or the latter may dominate the turbulence and mixing between the two streams. In this paper, we present a phenomenological theory that leads to the identification of two distinct turbulent regimes: an early regime, dominated by the mean shear, and a later regime dominated by the buoyancy. The main theoretical result consists of the identification of a cross-over time-scale that discerns between the shear- and the buoyancy-dominated turbulence. This cross-over time depends on three large-scale constants of the flow, namely the buoyancy difference, the velocity difference between the two streams, and the gravitational acceleration. We validate our theory against direct numerical simulations (DNSs) of a temporal turbulent mixing layer compounded with an unstable stratification. We observe that the cross-over time correctly predicts the transition from shear to buoyancy driven turbulence, in terms of turbulent kinetic energy production, energy spectra scaling and mixing layer thickness.