Localized layers of turbulence in stratified horizontally sheared Poiseuille flow

TL;DR

This paper investigates the nonlinear development of stratified, horizontally sheared Poiseuille flow, revealing localized turbulence layers, symmetry-breaking bifurcations, and intermittent disordered motions through numerical simulations.

Contribution

It extends previous linear instability analysis to nonlinear regimes, identifying localized turbulence layers and symmetry-breaking mechanisms in stratified shear flows.

Findings

Flow develops localized turbulence layers

Secondary bifurcation causes symmetry breaking

Intermittent disordered motions emerge away from threshold

Abstract

This article presents a numerical analysis of the instability developing in horizontally sheared Poiseuille flow, when stratification extends along the vertical direction. Our study builds up on the previous work that originally detected the linear instability of such configuration, by means of experiments, theoretical analysis and numerical simulations \citep{G21}. We extend hereafter this former investigation beyond linear theory, investigating nonlinear regimes with direct numerical simulations. We notice that the flow loses its vertical homogeneity through a secondary bifurcation, due to harmonic resonances, and further describe this symmetry-breaking mechanism in the vicinity of the instability threshold. When departing away from this limit, we observe a series of bursting events that break down the flow into disordered motions driven by localized shear instabilities. This intermittent dynamics leads to the coexistence of horizontal localized layers of stratified turbulence surrounded by quiescent regions of meandering waves.