Ice ripple formation at large Reynolds numbers

Abstract

AbstractA free-surface-induced morphological instability is studied in the laminar regime at large Reynolds numbers ($\mathit{Re}= 1\text{{\ndash}} 1{0}^{3} $) and on sub-horizontal walls ($\vartheta \lt 3{0}^{\ensuremath{\circ} } $). We analytically and numerically develop the stability analysis of an inclined melting–freezing interface bounding a free-surface laminar flow. The complete solution of both the linearized flow field and the heat conservation equations allows the exact derivation of the upper and lower temperature gradients at the interface, as required by the Stefan condition, from which the dispersion relationship is obtained. The eigenstructure is obtained and discussed. Free-surface dynamics appears to be crucial for the triggering of upstream propagating ice ripples, which grow at the liquid–solid interface. The kinematic and the dynamic conditions play a key role in controlling the formation of the free-surface fluctuations; these latter induce a streamline distortion with an increment of the wall-normal velocities and a destabilizing phase shift in the net heat transfer to the interface. Three-dimensional effects appear to be crucial at high Reynolds numbers. The role of inertia forces, vorticity, and thermal boundary conditions are also discussed.