Ultimate regimes in horizontal and internally heated convection

Abstract

We derive asymptotic models for the ultimate regimes in horizontal convection (HC) and pure internally heated convection (IHC), in analogy with our recent (2024) extension of the ultimate-regime model for Rayleigh-Benard convection (RBC). To derive the corresponding models for HC and IHC, we combine turbulent boundary-layer relations with the exact dissipation balances for these two systems. For HC, the resulting scaling relations are consistent with the rigorous transport bound of Siggers et al. (2004). For pure IHC, they are consistent with the exact HC-IHC balance analogy of Wang et al. (2021) and with the rigorous bounds on the convective-flux asymmetry in the equal-temperature-plates configuration (Arslan et al 2021). The main difference between RBC and HC/IHC is that, in the latter two cases, the global kinetic-energy balance does not contain the additional response factor (dimensionless convective heat flux in HC or inverse bulk temperature in IHC), whereas it does in RBC. As a consequence, for fixed Pr, the ultimate-regime scaling exponent is 1/3 for both HC and IHC, rather than 1/2 as in RBC.

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