Confinement suppresses the effect of rotation on convection

TL;DR

This study uses direct numerical simulations to investigate how bi-lateral confinement influences the onset of wall-mode convection in rotating Rayleigh-Bénard convection, revealing that strong confinement suppresses rotational effects.

Contribution

It demonstrates how aspect ratio and confinement alter the critical Rayleigh number for convection onset, showing that confinement can diminish rotation's influence in the system.

Findings

Ra_{wm} decreases with aspect ratio initially

Ra_{wm} approaches non-rotating critical Ra under strong confinement

Confinement suppresses horizontal velocity and rotation effects

Abstract

We perform direct numerical simulations (DNS) to study the effect of bi-lateral confinement, i.e., the effect of aspect ratio, on the Rayleigh number (Ra) for the onset of wall-mode convection ($Ra_{wm}$) in rotating Rayleigh-B\'enard convection (RBC) for various Ekman number E ($10^{-2}{\le}E{\le}10^{-5}$) and aspect ratio ${\Gamma}$ ($0.08{\le}{\Gamma}{\le}5$). For a given E, as the aspect ratio is lowered from a large value, $Ra_{wm}$ initially decreases slowly, reaching a minimum at ${\Gamma}={\Gamma}_{min}$ (${\Gamma}_{min}{\sim}E^{0.09}$). As ${\Gamma}$ is decreased further below ${\Gamma}_{min}$, $Ra_{wm}$ increases rapidly and for sufficiently strong confinement, i.e., ${\Gamma}<{\Gamma}_{\ast}$ (${\Gamma}_{\ast}{\sim}E^{\frac{1}{3}}$), becomes indistinguishable from $Ra_{c}$, the critical Rayleigh number for non-rotating RBC, at the same ${\Gamma}$. We designate the ranges ${\Gamma}_{min}<{\Gamma}<5$ as the 'confinement-affected' regime and ${\Gamma}<{\Gamma}_{\ast}$ as the 'spatially constrained' regime. For a given rotation rate, the spatially constrained regime extends to higher Ra as the aspect ratio is decreased. We propose that in this regime, strong lateral confinement suppresses the horizontal velocity, and hence the Coriolis force, rendering rotation ineffective over most of the domain.