Random changes of flow topology in two dimensional and geophysical turbulence

TL;DR

This paper investigates how flow topologies in 2D and geophysical turbulence change randomly due to bifurcations influenced by domain shape, nonlinearity, or energy, with implications for experiments and models.

Contribution

It proves bifurcation phenomena in 2D stochastic Navier-Stokes equations and links them to observable bistable flow behaviors in geophysical turbulence.

Findings

Flow topology bifurcations depend on domain shape, nonlinearity, and energy.

SNS exhibits bistability with random transitions between flow states.

Phenomena are applicable to experiments and geophysical flow models.

Abstract

We study the two dimensional (2D) stochastic Navier Stokes (SNS) equations in the inertial limit of weak forcing and dissipation. The stationary measure is concentrated close to steady solutions of the 2D Euler equation. For such inertial flows, we prove that bifurcations in the flow topology occur either by changing the domain shape, the nonlinearity of the vorticity-stream function relation, or the energy. Associated to this, we observe in SNS bistable behavior with random changes from dipoles to unidirectional flows. The theoretical explanation being very general, we infer the existence of similar phenomena in experiments and in models of geophysical flows.