Exact coherent structures in a reduced model of parallel shear flow

TL;DR

This paper develops a reduced model for parallel shear flows that captures exact coherent structures, revealing differences between lower and upper branch states and providing a framework for studying subcritical patterns.

Contribution

A novel reduced model for shear flows is constructed, accurately capturing exact coherent structures and their characteristics, advancing understanding of flow dynamics.

Findings

Lower branch solutions have slowly varying fluctuations along the critical layer.

Upper branch solutions show bimodal structure focused on the critical layer.

The reduced model offers a framework for studying subcritical spatiotemporal patterns.

Abstract

A reduced description of shear flows consistent with the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow [J. Wang et al., Phys. Rev. Lett. 98, 204501 (2007)] is constructed. Exact time-independent nonlinear solutions of the reduced equations corresponding to both lower and upper branch states are found for Waleffe flow [F. Waleffe, Phys. Fluids 9, 883--900 (1997)]. The lower branch solution is characterized by fluctuations that vary slowly along the critical layer while the upper branch solutions display a bimodal structure and are more strongly focused on the critical layer. The reduced model provides a rational framework for investigations of subcritical spatiotemporal patterns in parallel shear flows.