Two-phase Temperature Reconstruction in Ice-Water Systems

Abstract

What controls heat transport when liquid water interacts with ice? Answering this question is essential for understanding water bodies undergoing phase change. Yet experimental progress remains limited by the lack of a minimally invasive methodology for simultaneously resolving temperature fields in coupled liquid water and non-isothermal ice systems. Here, we introduce a physics-based data-assimilation method for reconstructing temperature fields in buoyancy-driven flows interacting with non-isothermal ice. Particle tracking velocimetry provides the liquid velocity field, while thermal and kinematic boundary conditions constrain the inverse problem. The method couples advection--diffusion in liquid water with conduction in ice to reconstruct simultaneous mean temperature fields and quantify heat transport across the water--ice interface, while remaining minimally invasive and compatible with free-surface systems. We demonstrate the method in laboratory experiments in which the temperature range across the liquid water in contact with ice drives cabbeling-induced convection. This framework enables investigation of coupled thermo-fluid dynamics in cryospheric aquatic systems, including heat exchange at the ice-water interface and liquid-phase energetics, with broader applications to phase-change processes in food and energy industries.