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 $$\varGamma =1/2$$) filled with a small-Prandtl-number fluid ($${Pr}\approx 0.8$$), 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 $$\varGamma$$ and over a broad range of $${Pr}$$ and $${Ra}$$. Furthermore, tirect numerical simulations for Prandtl number $$0.1 \leq {\textit {Pr}} \leq 12.3$$, Rayleigh number $$10^7 \leq {Ra} \leq 5\times 10^{9}$$, inverse Ekman number $$10^{5} \leq 1/{\textit {Ek}} \leq 10^{7}$$ and $$\varGamma = 1/3$$, 1/2, 3/4, 1 and 2 show that the BZF width $$\delta _0$$ scales with the Rayleigh number $${Ra}$$ and Ekman number $${\textit {Ek}}$$ as $$\delta _0/H \sim \varGamma ^{0} Pr^{\{-1/4, 0\}} {Ra}^{1/4} {\textit {Ek}}^{2/3}$$ ($$\{{\textit {Pr}}<1, {\textit {Pr}}>1\}$$) and with the drift frequency scales as $$\omega /\varOmega \sim \varGamma ^{0} Pr^{-4/3} {Ra}\,{\textit {Ek}}^{5/3}$$, where $$H$$ is the cell height and $$\varOmega$$ the angular rotation rate. The mode number of the BZF is 1 for $$\varGamma \lesssim 1$$ and $$2 \varGamma$$ for $$\varGamma = \{1,2\}$$ independent of $${Ra}$$ and $${Pr}$$. The BZF is quite reminiscent of wall mode states in rotating convection.
- Authors:
-
[1];
[2];
[1]
- Max Planck Inst. for Dynamics and Self-Organization, Gottingen (Germany)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS); Univ. of Washington, Seattle, WA (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program; German Research Foundation (DFG)
- OSTI Identifier:
- 1822786
- Report Number(s):
- LA-UR-20-27752
Journal ID: ISSN 0022-1120
- Grant/Contract Number:
- 89233218CNA000001; Sh405/8; Sh405/7
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Fluid Mechanics
- Additional Journal Information:
- Journal Volume: 915; Journal ID: ISSN 0022-1120
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Benard convection; rotating flows; rotating turbulence
Citation Formats
Zhang, Xuan, Ecke, Robert E., and Shishkina, Olga. Boundary zonal flows in rapidly rotating turbulent thermal convection. United States: N. p., 2021.
Web. doi:10.1017/jfm.2021.74.
Zhang, Xuan, Ecke, Robert E., & Shishkina, Olga. Boundary zonal flows in rapidly rotating turbulent thermal convection. United States. https://doi.org/10.1017/jfm.2021.74
Zhang, Xuan, Ecke, Robert E., and Shishkina, Olga. Wed .
"Boundary zonal flows in rapidly rotating turbulent thermal convection". United States. https://doi.org/10.1017/jfm.2021.74. https://www.osti.gov/servlets/purl/1822786.
@article{osti_1822786,
title = {Boundary zonal flows in rapidly rotating turbulent thermal convection},
author = {Zhang, Xuan and Ecke, Robert E. and Shishkina, Olga},
abstractNote = {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 $\varGamma =1/2$) filled with a small-Prandtl-number fluid (${Pr}\approx 0.8$), 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 $\varGamma$ and over a broad range of ${Pr}$ and ${Ra}$. Furthermore, tirect numerical simulations for Prandtl number $0.1 \leq {\textit {Pr}} \leq 12.3$, Rayleigh number $10^7 \leq {Ra} \leq 5\times 10^{9}$, inverse Ekman number $10^{5} \leq 1/{\textit {Ek}} \leq 10^{7}$ and $\varGamma = 1/3$, 1/2, 3/4, 1 and 2 show that the BZF width $\delta _0$ scales with the Rayleigh number ${Ra}$ and Ekman number ${\textit {Ek}}$ as $\delta _0/H \sim \varGamma ^{0} Pr^{\{-1/4, 0\}} {Ra}^{1/4} {\textit {Ek}}^{2/3}$ ($\{{\textit {Pr}}<1, {\textit {Pr}}>1\}$) and with the drift frequency scales as $\omega /\varOmega \sim \varGamma ^{0} Pr^{-4/3} {Ra}\,{\textit {Ek}}^{5/3}$, where $H$ is the cell height and $\varOmega$ the angular rotation rate. The mode number of the BZF is 1 for $\varGamma \lesssim 1$ and $2 \varGamma$ for $\varGamma = \{1,2\}$ independent of ${Ra}$ and ${Pr}$. The BZF is quite reminiscent of wall mode states in rotating convection.},
doi = {10.1017/jfm.2021.74},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 915,
place = {United States},
year = {Wed Mar 17 00:00:00 EDT 2021},
month = {Wed Mar 17 00:00:00 EDT 2021}
}
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