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

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-Bénard 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-Bénard 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 ~ 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.