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Abstract

Recently, in Zhang et al. (Phys. Rev. Lett., vol. 124, 2020, 084505), it was found that, in rapidly rotating turbulent Rayleigh–Bénard convection in slender cylindrical containers (with diameter-to-height aspect ratio Γ=1/2) filled with a small-Prandtl-number fluid (Pr≈0.8), the large-scale circulation is suppressed and a boundary zonal flow (BZF) develops near the sidewall, characterized by a bimodal probability density function 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 approximately 35%. In this work, we show that the BZF is robust and appears in rapidly rotating turbulent Rayleigh–Bénard convection in containers of different Γ and over a broad range of Pr and Ra. Direct numerical simulations for Prandtl number 0.1≤Pr≤12.3, Rayleigh number 107≤Ra≤5×109, inverse Ekman number 105≤1/Ek≤107 and Γ=1/3, 1/2, 3/4, 1 and 2 show that the BZF width δ0 scales with the Rayleigh number Ra and Ekman number Ek as δ0/H∼Γ0Pr{−1/4,0}Ra1/4Ek2/3 ({Pr<1,Pr>1}) and with the drift frequency scales as ω/Ω∼Γ0Pr−4/3RaEk5/3, where H is the cell height and Ω the angular rotation rate. The mode number of the BZF is 1 for Γ≲1 and 2Γ for Γ={1,2} independent of Ra and Pr. The BZF is quite reminiscent of wall mode states in rotating convection.