Morphology and flow structure evolution in thermally coupled convection with ice-sheet melting

We performed direct numerical simulations coupled with the phase-field method to simulate thermally coupled two-layer convection beneath a melting solid layer. These simulations were conducted for Rayleigh numbers in the range of 105 ⩽ Ra ⩽ 109. As the effective Rayleigh number of the upper fluid layer increases, the convective flow intensifies, progressing through three distinct flow regimes over time: initially, a thermal conduction stage, followed by thermal convection with eddy convergence, and ultimately transitioning to thermal convection with large-scale circulation. We quantified the melting rate influenced by the intermediate partition temperature, observing that the relationship with the vortex transitions from “locking in” to “fusion.” The scaling relationship between the Nusselt number in the middle partition and the effective Rayleigh number of the upper fluid layer shifts from 1/3 to approximately −1/3. Furthermore, we obtain a scaling relation of 1/3 between the Nusselt number and the effective Rayleigh number on the solid–liquid surface. The fluctuation of the solid–liquid interface is mainly dominated by the effective Rayleigh number in the thermal convection stage of vortex convergence. In addition, the statistical analysis presents that the lower layer's flow field transitions from thermal conduction to convection, with multiple eddies forming and merging as the system evolves. The number of eddies decreases exponentially until a quasi-steady state is reached. As the Rayleigh number increases, the system transitions rapidly to thermal convection with enhanced large-scale circulation. These insights contribute to a better understanding of transitions during phase change, with implications for accurately estimating melt rates and flow regimes.