Robust wall states in rapidly rotating Rayleigh-B\'enard convection

TL;DR

This study demonstrates that wall modes in rapidly rotating Rayleigh-Bénard convection persist far from their linear onset, survive turbulence, and are robust to boundary shape changes, resembling topologically protected states.

Contribution

It reveals the robustness and persistence of nonlinear wall states in turbulent rotating convection, linking them to topological protection concepts.

Findings

Wall modes persist far from linear onset.

Wall states survive turbulence in the bulk.

Modes are robust to boundary shape changes.

Abstract

We show, using direct numerical simulations with experimentally realizable boundary conditions, that wall modes in Rayleigh-B\'enard convection in a rapidly rotating cylinder persist even very far from their linear onset. These nonlinear wall states survive in the presence of turbulence in the bulk and are robust with respect to changes in the shape of the boundary of the container. In this sense these modes behave much like the topologically protected states present in two-dimensional chiral systems even though rotating convection is a three-dimensional nonlinear driven dissipative system. We suggest that the robustness of this nonlinear mode may provide an explanation for the strong zonal flows observed recently in simulations and experiments on rapidly rotating convection at high Rayleigh number.