Length scales of turbulence in stably stratified mixing layers

TLDR

The study aims to provide a comprehensive description of turbulence evolution using conceptual shear–buoyancy interaction pictures based on uniform stratification and shear assumptions. Direct numerical simulations of Kelvin–Helmholtz instability in localized stratified shear layers were performed, and the evolution of key turbulence length scales was examined to characterize the flow. The analysis revealed evolving layer thicknesses, overturning, Ozmidov, Corrsin, and Kolmogorov scales, clarified the link between uniform‑gradient and localized‑gradient models, and showed that the Ozmidov‑to‑Thorpe scale ratio indicates the age of a Kelvin–Helmholtz turbulent event.

Abstract

Turbulence resulting from Kelvin–Helmholtz instability in layers of localized stratification and shear is studied by means of direct numerical simulation. Our objective is to present a comprehensive description of the turbulence evolution in terms of simple, conceptual pictures of shear–buoyancy interaction that have been developed previously based on assumptions of spatially uniform stratification and shear. To this end, we examine the evolution of various length scales that are commonly used to characterize the physical state of a turbulent flow. Evolving layer thicknesses and overturning scales are described, as are the Ozmidov, Corrsin, and Kolmogorov scales. These considerations enable us to provide an enhanced understanding of the relationships between uniform-gradient and localized-gradient models for sheared, stratified turbulence. We show that the ratio of the Ozmidov scale to the Thorpe scale provides a useful indicator of the age of a turbulent event resulting from Kelvin–Helmholtz instability.