Transition to three dimensional flow in thermal convection with spanwise rotation

TL;DR

This paper uses direct numerical simulations to study how thermal convection in a rotating rectangular cell transitions from two-dimensional to three-dimensional flow, revealing an elliptical instability mechanism affecting heat transport and energy scaling.

Contribution

It identifies the transition mechanism to three-dimensional flow as an elliptical instability and characterizes the scaling relationship between Reynolds and Rossby numbers at this transition.

Findings

Flow is two-dimensional near convection onset.

Flow becomes unstable to three-dimensional disturbances at high Rayleigh numbers.

Reynolds and Rossby numbers follow a Re ∝ Ro^{-2} scaling at the transition.

Abstract

We investigate by direct numerical simulation Rayleigh-B\'enard convection in a rotating rectangular cell with rotation vector and gravity perpendicular to each other. The flow is two dimensional near the onset of convection with convection rolls aligned parallel to the rotation axis of the boundaries. At a sufficiently large Rayleigh number, the flow becomes unstable to three dimensional disturbances which changes the scaling of heat transport and kinetic energy with Rayleigh number. The mechanism leading to the instability is identified as an elliptical instability. At the transition, the Reynolds and Rossby numbers $\mathrm{Re}$ and $\mathrm{Ro}$ based on the kinetic energy of the flow are related by $\mathrm{Re} \propto \mathrm{Ro}^{-2}$ at small $\mathrm{Ro}$ with a geometry dependent prefactor.