Oblique and streamwise vortex paths in a plane Couette flow using a RNL system

Frédéric Alizard

doi:10.5802/crmeca.55

Abstract

This paper revisits oblique wave and streamwise vortex scenarios in a plane Couette flow using restricted nonlinear simulations, where only a single Fourier mode for perturbation is retained. It is shown that this restriction of full dynamics gives a good approximation of the two subcritical paths. In particular, critical energy thresholds and edge states compare favorably with results obtained using direct numerical simulations by Duguet et al. (Phys. Rev. E 82 (2010), 026316).

Highlights

Laminar/turbulent transition of wall-bounded shear flows is responsible for a dramatic increase in skin-friction drag for a wide variety of industrial applications
We introduce the Cartesian coordinate system (x, y, z) and consider the plane Couette flow (pCf) of an incompressible fluid with kinematic viscosity ν between two parallel plates located at y = ±h
The results of restricted nonlinear (RNL) simulations corresponding to the pure oblique wave (OW) and streamwise vortex (SV) scenarios are presented in parallel

Summary

Introduction

Laminar/turbulent transition of wall-bounded shear flows is responsible for a dramatic increase in skin-friction drag for a wide variety of industrial applications. In this regard, the determination of the initial perturbation that leads to transition is fundamental to designing efficient control strategies. The transition to turbulence often occurs even in the absence of an unstable linear mode associated with the laminar basic state In this subcritical scenario, both the initial amplitude and the spatial shape of the initial perturbation play prominent roles in triggering turbulence. The second route to turbulence begins with a pair of OWs that interact nonlinearly to create streamwise vortices This leads to the formation of streaks that break down to ISSN (electronic) : 1873-7234 https://comptes- rendus.academie- sciences.fr/mecanique/

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