Wavy Ice Patterns as a Result of Morphological Instability of an Ice-Water Interface with Allowance for the Convective-Conductive Heat Transfer Mechanism

In this research, the wavy ice patterns that form due to the evolution of morphological perturbations on the water-ice phase transition interface in the presence of a fluid flow are studied. The mathematical model of heat transport from a relatively warm fluid to a cold wall includes the mechanism of convective-conductive heat transfer in liquid and small sinusoidal perturbations of the water-ice interface. The analytical solutions describing the main state with a flat phase interface as well as its small morphological perturbations are derived. Namely, the migration velocity of perturbations and the dispersion relation are found. We show that the amplification rate of morphological perturbations changes its sign with variation of the wavenumber. This confirms the existence of two different crystallization regimes with (i) a stable (flat) interfacial boundary and (ii) a wavy interfacial boundary. The maximum of the amplification rate representing the most dangerous (quickly growing) perturbations is found. The theory is in agreement with experimental data.