Impact of transverse strain on linear, transitional and self-similar turbulent mixing layers

TL;DR

This paper investigates how transverse strain affects the development of turbulent mixing layers, proposing a new framework and validating it through simulations, revealing opposite effects in linear and turbulent regimes.

Contribution

It introduces a novel framework based on mean strain rates for analyzing mixing layer evolution and derives a model validated by simulations, highlighting the impact of transverse strain.

Findings

Transverse compression amplifies instability growth in the linear regime.

Transverse compression reduces mixing layer growth in the turbulent regime.

Shear production under transverse compression enhances mixing and transverse kinetic energy.

Abstract

The growth of interfacial instabilities such as the Rayleigh-Taylor (RTI) and Richtmyer-Meshkov instability (RMI) are modified when developing in convergent geometries. Whilst these modifications are usually quantified by the compression rate and convergence rate of the mixing layer, an alternative framework is proposed, describing the evolution of the mixing layer through the effects of the mean strain rates experienced by the mixing layer. An investigation into the effect of the transverse strain rate on the mixing layer development is conducted through application of transverse strain rates in planar geometry. A model for the linear regime in planar geometry with transverse strain rate is derived, with equivalent solutions to convergent geometry, and validated with two-dimensional simulations demonstrating the amplification of the instability growth under transverse compression. The effect of the transverse strain rate on the transitional-to-turbulent mixing layer is investigated with implicit large eddy simulation based on the multi-mode quarter-scale $\theta$-group case by Thornber et al. (Phys. Fluids, vol. 29, 2017, 105107). The mixing layer's growth exhibits the opposite trend to the linear regime model, with reduced growth under transverse compression. The effect of shear-production under transverse compression causes the mixing layer to become more mixed and the turbulent kinetic energy is increasingly dominated by the transverse directions, deviating from the unstrained self-similar state. The mixing layer width is able to be predicted by adjusting the buoyancy-drag model by Youngs & Thornber (Physica D, vol. 410, 2020, 132517) to utilise a drag length scale that scales with the transverse expansion.