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Title: Scaling of heat transport near onset in rapidly rotating convection

Abstract

Here, we consider the scaling of heat transport in the geostrophic regime of rotating Rayleigh–Bénard convection near onset for small Ekman number Ek from the perspective of weakly nonlinear theory. We show that available heat transport data from numerical simulation [1] for Ek < 10-5 for Pr = 1 are consistent with weakly nonlinear theory for ϵ = Ra / Rac - 1 < 1. In particular, we show that the numerical data are consistent with Nu - 1 = aϵ + bϵ2 with a ≈ 2 and b ≈ 3 with weak dependence of the coefficients on Ek. The coefficient a is consistent with calculations of weakly nonlinear theory and with experimental data at much higher Ek. The positive sign of b is also suggested by those experimental data. The magnitude and trend of the numerical data for larger Ra are consistent with experimental data with similar Pr ~ 1. The steep scaling of Nu ~ (Ra / Rac)3 noted elsewhere for Ra / Rac < 2 is shown to be an artifact of being close to onset where the effective power-law slope depends sensitively on the magnitude of the coefficients a and b. Similar arguments apply to Prmore » = 7 numerical data although the weakly nonlinear expansion appears valid for a smaller range of ϵ than in the Pr = 1 case.« less

Authors:
 [1]
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  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1457247
Alternate Identifier(s):
OSTI ID: 1359747
Report Number(s):
LA-UR-15-24568
Journal ID: ISSN 0375-9601; TRN: US1901330
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physics Letters. A
Additional Journal Information:
Journal Volume: 379; Journal Issue: 37; Journal ID: ISSN 0375-9601
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; Planetary Sciences; rotation; convection; heat transport

Citation Formats

Ecke, Robert E. Scaling of heat transport near onset in rapidly rotating convection. United States: N. p., 2015. Web. doi:10.1016/j.physleta.2015.06.053.
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Ecke, Robert E. Scaling of heat transport near onset in rapidly rotating convection. United States. https://doi.org/10.1016/j.physleta.2015.06.053
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Ecke, Robert E. Thu . "Scaling of heat transport near onset in rapidly rotating convection". United States. https://doi.org/10.1016/j.physleta.2015.06.053. https://www.osti.gov/servlets/purl/1457247.
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@article{osti_1457247,
title = {Scaling of heat transport near onset in rapidly rotating convection},
author = {Ecke, Robert E.},
abstractNote = {Here, we consider the scaling of heat transport in the geostrophic regime of rotating Rayleigh–Bénard convection near onset for small Ekman number Ek from the perspective of weakly nonlinear theory. We show that available heat transport data from numerical simulation [1] for Ek < 10-5 for Pr = 1 are consistent with weakly nonlinear theory for ϵ = Ra / Rac - 1 < 1. In particular, we show that the numerical data are consistent with Nu - 1 = aϵ + bϵ2 with a ≈ 2 and b ≈ 3 with weak dependence of the coefficients on Ek. The coefficient a is consistent with calculations of weakly nonlinear theory and with experimental data at much higher Ek. The positive sign of b is also suggested by those experimental data. The magnitude and trend of the numerical data for larger Ra are consistent with experimental data with similar Pr ~ 1. The steep scaling of Nu ~ (Ra / Rac)3 noted elsewhere for Ra / Rac < 2 is shown to be an artifact of being close to onset where the effective power-law slope depends sensitively on the magnitude of the coefficients a and b. Similar arguments apply to Pr = 7 numerical data although the weakly nonlinear expansion appears valid for a smaller range of ϵ than in the Pr = 1 case.},
doi = {10.1016/j.physleta.2015.06.053},
journal = {Physics Letters. A},
number = 37,
volume = 379,
place = {United States},
year = {Thu Jul 02 00:00:00 EDT 2015},
month = {Thu Jul 02 00:00:00 EDT 2015}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1016/j.physleta.2015.06.053
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Cited by: 7 works
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Figures / Tables:

Figure 1 Figure 1: (a) $Nu$ vs $R̂a$, Nu = $R̂a$ 2.8 (solid line); (b) $Nu$− 1 vs ϵ, $Nu$− 1 = 2.2ϵ+3.5ϵ2 (solid line), Nu− 1 = 5ϵ1.4(dashed line). $Pr$ = 1 and Ek: 10−7 (solid square, black), 10−6 (open square, blue), 10−5 (solid circle, red).
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Works referenced in this record:

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    Works referencing / citing this record:

    A heuristic framework for next-generation models of geostrophic convective turbulence
    journal, July 2018

    • Cheng, Jonathan S.; Aurnou, Jonathan M.; Julien, Keith
    • Geophysical & Astrophysical Fluid Dynamics, Vol. 112, Issue 4
    • DOI: 10.1080/03091929.2018.1506024

    A nonlinear model for rotationally constrained convection with Ekman pumping
    journal, May 2016

    • Julien, Keith; Aurnou, Jonathan M.; Calkins, Michael A.
    • Journal of Fluid Mechanics, Vol. 798
    • DOI: 10.1017/jfm.2016.225

    Transition to geostrophic convection: the role of the boundary conditions
    journal, June 2016

    • Kunnen, Rudie P. J.; Ostilla-Mónico, Rodolfo; van der Poel, Erwin P.
    • Journal of Fluid Mechanics, Vol. 799
    • DOI: 10.1017/jfm.2016.394

    A nonlinear model for rotationally constrained convection with Ekman pumping
    text, January 2016

    A heuristic framework for next-generation models of geostrophic convective turbulence
    journal, July 2018

    • Cheng, Jonathan S.; Aurnou, Jonathan M.; Julien, Keith
    • Geophysical & Astrophysical Fluid Dynamics, Vol. 112, Issue 4
    • DOI: 10.1080/03091929.2018.1506024
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