Convective-absolute nature of ripple instabilities on ice and icicles

Film hydrodynamics is crucial in water-driven morphological pattern formation. A prominent example is given by icicle ripples and ice ripples, which are regular patterns developing on freezing-melting inclined surfaces bounding open-channel flows. By a suitable mathematical model based on conservation principles and the use of the cuspmap method, in this paper we address the convective-absolute nature of these two kinds of instabilities. The obtained results show that icicle ripples, which develop at inverted (overhang) conditions, have subcentimetric wavelengths which are unstable when the Reynolds number of the liquid flow (Re) is small and the supercooling is intensive. With the increase in Re, the instability switches from absolute to convective. Ice ripples instead exhibit the opposite dependance on Re and are highly affected by the surface slope. In addition, the evaluation of the so-called absolute wave number, which is responsible for the asymptotic impulse response, suggests a different interpretation of some recent experiments about ice ripples.