Scaling of heat transport near onset in rapidly rotating convection

Autor: Robert E. Ecke
Rok vydání: 2015
Předmět:
Zdroj: Physics Letters A. 379:2221-2223
ISSN: 0375-9601
DOI: 10.1016/j.physleta.2015.06.053
Popis: We consider the scaling of heat transport in the geostrophic regime of rotating Rayleigh–Benard 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 = a ϵ + b ϵ 2 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.
Databáze: OpenAIRE
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