Doubly localized states in plane Couette flow

Abstract

AbstractMuch of our understanding of the transition to turbulence in flows without a linear instability came with the discovery and characterization of fully three-dimensional solutions to the Navier–Stokes equation. The first examples in plane Couette flow were periodic in both spanwise and streamwise directions, and could explain the transitions in small domains only. The presence of localized turbulent spots in larger domains, the spatiotemporal decoherence on larger scales and the ability to trigger turbulence with pointwise perturbations require solutions that are localized in both directions, like the one presented by Brand & Gibson (J. Fluid Mech., vol. 750, 2014, R3). They describe a steady solution of the Navier–Stokes equations and characterize in unprecedented detail, including an analytic computation of its localization properties. The study opens up new ways to describe localized turbulent patches.