Spatially evolving vortex-gas turbulent free shear layers: Part 1. Effect of velocity ratio, and upstream and downstream conditions on spread-rate

TL;DR

This study uses vortex-gas simulations to analyze how velocity ratio and boundary conditions influence the growth rate of turbulent free shear layers, showing universal behavior and agreement with experimental data.

Contribution

It introduces an improved vortex-gas model that conserves circulation and explores the effects of velocity ratio and boundary conditions on shear layer growth.

Findings

Flow conditions at inlet and exit influence evolution, especially as velocity ratio approaches 1.

A universal self-preserving growth rate function of velocity ratio is identified.

Computed growth rates align with experimental and high Reynolds number simulation data.

Abstract

The relevance of the vortex-gas model to the large scale dynamics of temporally evolving turbulent free shear layers in an inviscid incompressible fluid has recently been established by extensive numerical simulations (Suryanarayanan et al, Phys. Rev. E 89, 013009, 2014). Here, the effects of the velocity ratio across a spatially evolving 2D free shear layer are investigated by vortex-gas simulations, using a computational model based on Basu et al (1992, 1995), but with a crucial improvement that ensures conservation of global circulation. These are carried out for a range of values of the velocity ratio parameter $\lambda= (U_1-U_2)/(U_1+U_2)$, where $U_1$ and $U_2$ ($< U_1$) are respective velocities across the layer. The simulations show that the conditions imposed at the beginning of the free shear layer and at the exit to the domain can affect the flow evolution in their respective neighborhoods, the latter being particularly strong as $\lambda \rightarrow 1$. In between the two neighborhoods is a regime of universal self-preserving growth rate given by a universal function of $\lambda$ The computed growth rates are located within the scatter of experimental data on plane mixing layers, and in close agreement with recent high Reynolds number experiments and 3D LES studies, past the mixing transition, and support the view that free shear layer growth can be largely explained by the 2D vortex dynamics of the quasi-two-dimensional large scale structures.