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The presence of salt in ocean water strongly affects the melt rate and theshape evolution of ice, both of utmost relevance in geophysical and ocean flowand thus for the climate. To get a better quantitative understanding of thephysical mechanics at play in ice melting in salty water, we numericallyinvestigate the lateral melting of an ice block in stably stratified salinewater, using a realistic, nonlinear equation of state (EOS). The developing iceshape from our numerical results shows good agreement with the experiments andtheory from Huppert & Turner (J. Fluid Mech. 100, 367 (1980)). Furthermore, wefind that the melt rate of ice depends non-monotonically on the mean ambientsalinity: It first decreases for increasing salt concentration until a localminimum is attained, and then increases again. This non-monotonic behavior ofthe ice melt rate is due to the competition among salinity-driven buoyancy,temperature-driven buoyancy, and salinity-induced stratification. We develop atheoretical model based on the energy balance which gives a prediction of thesalt concentration for which the melt rate is minimal, and is consistent withour data. Our findings give insight into the interplay between phasetransitions and double-diffusive convective flows.

Ice melting in salty water: layering and non-monotonic dependence on the mean salinity