Polar regions are strongly affected by global warming and heat up rapidly under anthropogenic climate change. In consequence, the ice in Greenland and Antarctica melts with increasing rates, which is a major contributor to global sea level rise. We study the melting of glacial ice tongues that flow into the ocean and are thus not only melted by the sun from above, but also from below due to processes at the ice–ocean interface. To investigate these interactions in-depth , we employ our coastal ocean model GETM, extended by a consistent melt parametrization, to glacier fjords in the polar regions. The adaptive vertical coordinates of GETM allow us to resolve the buoyant plume of meltwater under the ice in great detail. Our main focus is the 79°N Glacier in Greenland, as part of the research project GROCE (Greenland Ice Sheet–Ocean Interaction).