Invariant Solution underlying Oblique Stripe Patterns in Plane Couette Flow
Fluid Dynamics
2019-11-11 v1
Abstract
When subcritical shear flows transition to turbulence, laminar and turbulent flow often coexists in space, giving rise to turbulent-laminar patterns. Most prominent are regular stripe patterns with large-scale periodicity and oblique orientation. Oblique stripes are a robust phenomenon, observed in experiments and flow simulations, yet their origin remains unclear. We demonstrate the existence of an invariant equilibrium solution of the fully nonlinear 3D Navier-Stokes equations that resembles the oblique pattern of turbulent-laminar stripes in plane Couette flow. We uncover the origin of the stripe equilibrium and show how it emerges from the well-studied Nagata equilibrium via two successive symmetry-breaking bifurcations.
Cite
@article{arxiv.1809.02877,
title = {Invariant Solution underlying Oblique Stripe Patterns in Plane Couette Flow},
author = {Florian Reetz and Tobias Kreilos and Tobias M. Schneider},
journal= {arXiv preprint arXiv:1809.02877},
year = {2019}
}