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arXiv · 2009.03401

Boundary zonal flows in rapidly rotating turbulent thermal convection

Xuan Zhang·Robert E. Ecke·Olga Shishkina
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Abstract

Recently, in Zhang et al. (2020), it was found that in rapidly rotating turbulent Rayleigh-Bénard convection (RBC) in slender cylindrical containers (with diameter-to-height aspect ratio $Γ=1/2$) 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 $Γ$ 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 $Γ$ = 1/3, 1/2, 3/4, 1 and 2 show that the BZF width $δ_0$ scales with the Rayleigh number $Ra$ and Ekman number $Ek$ as $δ_0/H \sim Γ^{0} \Pr^{\{-1/4, 0\}} Ra^{1/4} Ek^{2/3}$ (${Pr<1, Pr>1}$) and the drift frequency as $ω/Ω\sim Γ^{0} Pr^{-4/3} Ra Ek^{5/3}$, where $H$ is the cell height and $Ω$ the angular rotation rate. The mode number of the BZF is 1 for $Γ\lesssim 1$ and $2 Γ$ for $Γ$ = {1,2} independent of $Ra$ and $Pr$. The BZF is quite reminiscent of wall mode states in rotating convection.

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Xuan Zhang, Robert E. Ecke, Olga Shishkina. 2021-03-08. Boundary zonal flows in rapidly rotating turbulent thermal convection. https://doi.org/10.1017/jfm.2021.74

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