Numerical Methods

ISOFT simulates the evolution of ice shelves and meltwater plumes beneath them. A cartoon diagram of such a can be found below. The ice flow has a vertically integrated velocity $\vec{u}$, with longitudinal and transverse components $u$ and $v$, respectively. $h$ is the thickness of the ice shelf, while $b$ is the depth of its lower surface below sea level. Subglacial discharge at the grounding line, with volume flux $Q_g$, feeds a plume of thickness $D$ flowing underneath the ice shelf with vertically integrated velocity $\vec{U}$. This velocity also has longitudinal, $U$, and transverse, $V$, components. The plume has a temperature, $T$, and salinity, $S$, which drive melting $m$ at the base of the ice shelf. The plume is further fed by turbulent entrainment, $e$, of the ambient ocean water. This water has its own temperature and salinity: $T_a$ and $S_a$, respectively.

This section of the documentation describes the mathematics behind ISOFT. First, the equations describing ice shelf and plume behaviour are provided. The solvers used for the shelf and plume components are described in turn. Finally, an overview of a benchmarking problem is provided.