Bifurcation and multiple states in plane Couette flow with spanwise rotation

TL;DR

This paper derives a theoretical framework explaining the existence of multiple stable turbulent states in spanwise rotating plane Couette flow, influenced by domain size and initial conditions, with specific predictions about rotation speed effects.

Contribution

It provides a derivation from Navier-Stokes equations predicting exactly two stable states in large-scale spanwise rotating Couette flow, explaining turbulence multistability.

Findings

Multiple statistically stable states are predicted in rotating Couette flow.

The number of stable states depends on domain size and initial conditions.

Limit cycles are observed near stable states.

Abstract

We present a derivation that begins with the Navier--Stokes equation and ends with a prediction of multiple statistically stable states identical to those observed in a spanwise rotating plane Couette flow. This derivation is able to explain the presence of multiple states in fully developed turbulence and the selection of one state over the other by differently sized computational domains and different initial conditions. According to the present derivation, two and only two statistically stable states are possible in an infinitely large plane Couette flow with spanwise rotation, and that multiple states are not possible at very slow or very rapid rotation speeds. We also show the existence of limit cycles near statistically stable states.