Estimation of kinetic dissipation in thermal convection systems based on mechanical energy conservation

Abstract: In the theoretical analysis of convective heat transfer processes, the global kinetic dissipation plays an important role. In this study, we introduce a framework to derive the scaling laws for global kinetic dissipation by establishing its linkage with potential energy conversion. This potential energy-based dissipation relationship provides a rigorous theoretical foundation for characterizing universal global kinetic dissipation scaling. The proposed universal scaling laws successfully reconcile previously divergent results of classical Rayleigh-B\'enard and horizontal convection. Leveraging this framework, we can extend the Grossmann-Lohse (GL) theory to a unified description of thermal convective transport processes. Our study enables unified scaling laws for heat transfer and flow intensity in general confined thermal convection systems including horizontal, vertical, and Rayleigh-B\'enard convection, while accounting for the non-Oberbeck-Boussinesq effect. Remarkably, in horizontal convection with non-monotonic temperature dependence of density, our analysis reveals that a transition in the scaling laws occurs when thermal plumes reach a characteristic height scaling as $\sim H$. Through direct numerical simulations, we quantitatively verify these findings. Our study enhances the theoretical understanding of scaling laws and provides predictive capabilities for buoyancy-driven flows in various boundary conditions, with implications for geophysical and engineering applications.