Boundary zonal flows in rapidly rotating turbulent thermal convection

TL;DR

This paper demonstrates that Boundary Zonal Flows (BZF) are a robust feature in rapidly rotating turbulent thermal convection across various container geometries and parameters, with specific scaling laws for their width and drift frequency.

Contribution

It extends previous findings by showing BZF's robustness and provides quantitative scaling laws for BZF characteristics across a broad parameter range.

Findings

BZF appears in various container geometries and parameter ranges.

BZF width scales with Ra and Ek as δ₀/H ∼ Ra^{1/4} Ek^{2/3}.

BZF drift frequency scales as ω/Ω ∼ Pr^{-4/3} Ra Ek^{5/3}.

Abstract

Recently, in Zhang et al. (2020), it was found that in rapidly rotating turbulent Rayleigh-B\'enard convection (RBC) in slender cylindrical containers (with diameter-to-height aspect ratio $\Gamma=1/2$) filled with a small-Prandtl-number fluid ($Pr \approx0.8$), the Large Scale Circulation (LSC) is suppressed and a Boundary Zonal Flow (BZF) develops near the sidewall, characterized by a bimodal PDF of the temperature, cyclonic fluid motion, and anticyclonic drift of the flow pattern (with respect to the rotating frame). This BZF carries a disproportionate amount ($>60\%$) of the total heat transport for $Pr < 1$ but decreases rather abruptly for larger $Pr$ to about $35\%$. In this work, we show that the BZF is robust and appears in rapidly rotating turbulent RBC in containers of different $\Gamma$ and in a broad range of $Pr$ and $Ra$. Direct numerical simulations for $0.1 \leq Pr \leq 12.3$, $10^7 \leq Ra \leq 5\times10^{9}$, $10^{5} \leq 1/Ek \leq 10^{7}$ and $\Gamma$ = 1/3, 1/2, 3/4, 1 and 2 show that the BZF width $\delta_0$ scales with the Rayleigh number $Ra$ and Ekman number $Ek$ as $\delta_0/H \sim \Gamma^{0} \Pr^{\{-1/4, 0\}} Ra^{1/4} Ek^{2/3}$ (${Pr<1, Pr>1}$) and the drift frequency as $\omega/\Omega \sim \Gamma^{0} Pr^{-4/3} Ra Ek^{5/3}$, where $H$ is the cell height and $\Omega$ the angular rotation rate. The mode number of the BZF is 1 for $\Gamma \lesssim 1$ and $2 \Gamma$ for $\Gamma$ = {1,2} independent of $Ra$ and $Pr$. The BZF is quite reminiscent of wall mode states in rotating convection.