Two-dimensional solidification and melting in potential flows
L. Cummings, Yuri Evgenyevich Hohlov, Sam Howison, Konstantin G. Kornev · Journal of Fluid Mechanics · 1999
The problem of solidification or melting under the action of a forced hydrodynamic flow is considered. In the appropriate parameter régime, the problem admits a formulation in terms of analytic functions. It is shown that a crystal with a parabolic tip propagates without change of shape at a steady velocity. Some novel explicit solutions are presented.