Point-Vortex Simulations Reveal Universality Class in Growth of 2D Turbulent Mixing Layers

TL;DR

This study uses high-precision point-vortex simulations to demonstrate that the growth rate of 2D turbulent mixing layers is universal, independent of initial conditions, confirming a specific asymptotic growth rate.

Contribution

It provides the first extensive numerical evidence for the universality of growth rates in 2D turbulent mixing layers using a novel ensemble-averaging approach.

Findings

Growth rate of 0.0167 ± 0.00017 times velocity differential

Universality holds across various initial conditions

Long transient phases before reaching asymptotic behavior

Abstract

A central but controversial issue in free turbulent shear flows has been the universality (or otherwise) of their growth rates. We resolve this issue here in the special case of a temporal 2D mixing layer in a point vortex gas by extensive high-precision numerical simulations, utilizing for the first time a powerful ensemble-averaging strategy. The simulations show that the momentum thickness of such a mixing layer grows at the universal asymptotic rate of 0.0167 +/- 0.00017 times the velocity differential across the layer over a wide range of initial conditions, often after very long transients.