HRT

Abstract

Plane Couette flow near transition displays steady periodic oblique bands of alternating turbulent and laminar flow. Numerical simulations of the Navier-Stokes equations in a tilted domain show a rich variety of such patterns, including spatio-temporal intermittency, branching and travelling states, and localized states analogous to spots. Quantitative analysis of the Reynolds-averaged equations reveals that both the mean flow and the turbulent force are centrosymmetric and can be described by only three trigonometric functions, leading to a model of 6 ODEs. The transition is best described as a bifurcation in the probability distribution function of the first Fourier component.