Stability Criteria and Turbulence Paradox Problem For Type II 3D Shears

TL;DR

This paper investigates the stability criteria of type II 3D shears in channel flows and supports the turbulence paradox resolution by analyzing a sequence of these shears.

Contribution

It introduces stability criteria for type II 3D shears and extends the turbulence paradox discussion with new analysis of shear sequences.

Findings

Stability criteria for type II 3D shears established

Support for turbulence paradox resolution provided

Sequence analysis of shears enhances understanding of flow stability

Abstract

There are two types of 3D shears in channel flows: ($U(y,z),0,0$) and ($U(y),0,W(y)$). Both are important in organizing the phase space structures of the channel flows. Stability criteria of the type I 3D shears were studied in [Li, 2010]. Here we study the stability criteria of the type II 3D shears. We also provide more support to the idea of resolution of a turbulence paradox, introduced in [Li and Lin, 2010], by studying a sequence of type II 3D shears.