Boundary zonal flows in rapidly rotating turbulent thermal convection

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 Λ = 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 Λ 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 Λ = 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 ∼ Λ0Pr{-1/4,0}Ra1/4Ek2/3 ({Pr < 1, Pr > 1}) and with the drift frequency scales as ω/Ω ∼ Λ0Pr-4/3Ra Ek5/3, where H is the cell height and Ω the angular rotation rate. The mode number of the BZF is 1 for Λ ≲ 1 and 2Λ for Λ = {1, 2} independent of Ra and Pr. The BZF is quite reminiscent of wall mode states in rotating convection.