Large-scale instability in a sheared nonhelical turbulence: formation of vortical structures

TL;DR

This paper investigates large-scale vorticity instabilities in sheared nonhelical turbulence, revealing the formation of vortical structures and turbulent Tollmien-Schlichting waves driven by small-scale turbulence and shear effects.

Contribution

It demonstrates the instability of certain large-scale flows in turbulence and introduces a turbulent analogue of Tollmien-Schlichting waves caused by shear and Reynolds stresses.

Findings

Large-scale vortical structures form due to instability in sheared turbulence.

The growth rate of the instability is higher for

A turbulent analogue of Tollmien-Schlichting waves exists in sheared turbulence.

Abstract

We study a large-scale instability in a sheared nonhelical turbulence that causes generation of large-scale vorticity. Three types of the background large-scale flows are considered, i.e., the Couette and Poiseuille flows in a small-scale homogeneous turbulence, and the "log-linear" velocity shear in an inhomogeneous turbulence. It is known that laminar plane Couette flow and antisymmetric mode of laminar plane Poiseuille flow are stable with respect to small perturbations for any Reynolds numbers. We demonstrate that in a small-scale turbulence under certain conditions the large-scale Couette and Poiseuille flows are unstable due to the large-scale instability. This instability causes formation of large-scale vortical structures stretched along the mean sheared velocity. The growth rate of the large-scale instability for the "log-linear" velocity shear is much larger than that for the Couette and Poiseuille background flows. We have found a turbulent analogue of the Tollmien-Schlichting waves in a small-scale sheared turbulence. A mechanism of excitation of turbulent Tollmien-Schlichting waves is associated with a combined effect of the turbulent Reynolds stress-induced generation of perturbations of the mean vorticity and the background sheared motions. These waves can be excited even in a plane Couette flow imposed on a small-scale turbulence when perturbations of mean velocity depend on three spatial coordinates. The energy of these waves is supplied by the small-scale sheared turbulence.