Large-scale mean flow and inclination of isolated turbulent band in channel flow

TL;DR

This paper investigates the large-scale mean flow and inclination of isolated turbulent bands in channel flow, revealing the vortex structures and velocity mechanisms that maintain their characteristic inclination angle.

Contribution

It introduces a numerical and theoretical analysis of vortex structures and flow velocities that explain the inclination stability of turbulent bands in channel flow.

Findings

Identification of a $ u$-shape vortex at the head of turbulent bands.

Convection velocities reflect self-induced vortex velocities.

A self-adjustment process maintains the inclination angle.

Abstract

Isolated turbulent bands observed in transitional channel flows have downstream heads and inclined bulks at a characteristic angle. In the large-scale mean flow, a $\nu$-shape vortex found at the head elongates into the bulk part, forming a pair of counter-rotating vortex tube structures. It is revealed numerically and theoretically that the head and the bulk convection velocities reflect the obliquely forward and the backward self-induced velocities of the $\nu$-shape vortex and the vortex tube pair, respectively, and the difference between these convection velocities provides a restoring angular momentum to retain the characteristic inclination angle through a self-adjustment process.