Boundary zonal flows in rapidly rotating turbulent thermal convection

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.