Iceberg Melting

Dedalus is great for making beautiful simulations of fluid-solid interactions. The mathematical analysis of these methods is also deeply rewarding. But usefulness comes from applying your methods to a concrete scientific problem. That’s what I really like about my project on iceberg melting, which grew out of my 2017 Woods Hole Summer Fellowship with Claudia Cenedese and Craig McConnochie. See the paper here.

Icebergs are a significant part of freshwater flux from ice sheets to oceans. Where and when their meltwater is released depends on how quickly icebergs melt. Understanding how icebergs influence the climate therefore requires accurate predictions of iceberg melt rates.

This project investigates an often neglected aspect of iceberg melting — their shape. Icebergs come in an enormous range of shapes and sizes, and different processes affect melting on the base and sides of icebergs. However, common models do not take iceberg aspect ratio into account.

We combine experimental and numerical investigations to show that aspect ratio is an important determinant of iceberg melting. Our experiments measure melting of ice blocks in warm salt water at different relative velocities. The first video above shows a time lapse version of one experiment. We immerse a dyed ice-block in a recirculating flume with salinity 30 g/kg and temperature 20 C for 10 minutes, at speed 3.5 cm/s. By measuring the melting of each face after the experiment, we find significant differences in melt rates between different faces, and large non-uniformities in melting on each face. These complexities are not captured by existing parameterisations.

We reproduce and examined these findings using a phase-field model for melting in salt water. The second video above shows the temperature field (black : 0 C; yellow : 20 C) of a numerical simulation of the previous experiment. Cool stagnant water pools near the front, which becomes unstable due to shear gradients. The instability generates vortices, which upwell warm water and increase melt rates (indicated with the red line). This explains the non-uniform basal melting of our experiments. Previous research suggests the length scale of the accelerated basal melting scales with the depth of the iceberg. We therefore expect this non-uniformity to affect geophysical icebergs. We also find that double diffusive effects matter at low flow speeds.

We use these findings to propose simple improvements that capture the influence of aspect ratio on iceberg melting.