Scaling of heat transport near onset in rapidly rotating convection

Journal Article · Thu Jul 02 00:00:00 EDT 2015 · Physics Letters. A

DOI:https://doi.org/10.1016/j.physleta.2015.06.053· OSTI ID:1457247

Ecke, Robert E. ^[1]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)

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 / Ra_c - 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 / Ra_c)³ noted elsewhere for Ra / Ra_c < 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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1457247
• Alternate ID(s): OSTI ID: 1359747
• Report Number(s): LA-UR-15-24568; TRN: US1901330
• Journal Information: Physics Letters. A, Vol. 379, Issue 37; ISSN 0375-9601
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
Planetary Sciences
rotation
convection
heat transport