Boundary zonal flows in rapidly rotating turbulent thermal convection [electronic resource]
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| Format: | Government Document Electronic eBook |
| Language: | English |
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Washington, D.C. : Oak Ridge, Tenn. :
United States. Department of Energy ; Distributed by the Office of Scientific and Technical Information, U.S. Department of Energy,
2021.
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| Abstract: | Recently, in Zhang <span class='italic'>et al.</span> (<span class='italic'>Phys. Rev. Lett.</span>, vol. 124, 2020, 084505), it was found that, in rapidly rotating turbulent Rayleigh?Bňard convection in slender cylindrical containers (with diameter-to-height aspect ratio <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\varGamma =1/2$</span></span></span></span>) filled with a small-Prandtl-number fluid (<span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${Pr}\approx 0.8$</span></span></span></span>), 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 (<span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${>}60\,\%$</span></span></span></span>) of the total heat transport for <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${Pr} < 1$</span></span></span></span>, but decreases rather abruptly for larger <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${Pr}$</span></span></span></span> to approximately <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$35\,\%$</span></span></span></span>. In this work, we show that the BZF is robust and appears in rapidly rotating turbulent Rayleigh?Bňard convection in containers of different <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\varGamma$</span></span></span></span> and over a broad range of <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${Pr}$</span></span></span></span> and <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${Ra}$</span></span></span></span>. Furthermore, tirect numerical simulations for Prandtl number <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$0.1 \leq {\textit {Pr}} \leq 12.3$</span></span></span></span>, Rayleigh number <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$10̂7 \leq {Ra} \leq 5\times 10̂{9}$</span></span></span></span>, inverse Ekman number <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$10̂{5} \leq 1/{\textit {Ek}} \leq 10̂{7}$</span></span></span></span> and <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\varGamma = 1/3$</span></span></span></span>, 1/2, 3/4, 1 and 2 show that the BZF width <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\delta _0$</span></span></span></span> scales with the Rayleigh number <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${Ra}$</span></span></span></span> and Ekman number <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${\textit {Ek}}$</span></span></span></span> as <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\delta _0/H \sim \varGamma ̂{0} Pr̂{\{-1/4, 0\}} {Ra}̂{1/4} {\textit {Ek}}̂{2/3}$</span></span></span></span> (<span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\{{\textit {Pr}}<1, {\textit {Pr}}>1\}$</span></span></span></span>) and with the drift frequency scales as <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\omega /\varOmega \sim \varGamma ̂{0} Pr̂{-4/3} {Ra}\,{\textit {Ek}}̂{5/3}$</span></span></span></span>, where <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$H$</span></span></span></span> is the cell height and <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\varOmega$</span></span></span></span> the angular rotation rate. The mode number of the BZF is 1 for <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\varGamma \lesssim 1$</span></span></span></span> and <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$2 \varGamma$</span></span></span></span> for <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>$\varGamma = \{1,2\}$</span></span></span></span> independent of <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${Ra}$</span></span></span></span> and <span class='inlineFormula'><span class='alternatives'><span class='mathjax-tex-wrapper' data-mathjax-type='texmath'><span class='tex-math mathjax-tex-math mathjax-on'>${Pr}$</span></span></span></span>. The BZF is quite reminiscent of wall mode states in rotating convection. |
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| Item Description: | Published through Scitech Connect. 03/17/2021. "la-ur-20-27752." "Journal ID: ISSN 0022-1120." Zhang, Xuan ; Ecke, Robert E. ; Shishkina, Olga ; |
| Physical Description: | Size: Article No. A62 : digital, PDF file. |