plumes

This package contains solvers for various models of buoyant meltwater plumes under floating ice shelves. The solvers are implemented using the finite element modeling package Firedrake.

Code structure

The library is structured roughly as follows:

plumes
├── coefficients.py         # Physical constants
├── numerics.py             # Time discretization schemes
└── models/
    ├── forms.py            # Spatial discretization helper functions
    ├── advection.py        # Scalar advection equation; for testing
    ├── shallow_water.py    # Nonlinear shallow water equations
    └── thin_film.py        # Thin viscous film flow equations

The directory demo/ contains several Jupyter notebooks that show the features of this package.

References

Physics

• Jenkins (1991). A One-Dimensional Model of Ice Shelf-Ocean Interaction. JGR
• Jenkins et al. (2010). Observation and Parameterization of Ablation at the Base of Ronne Ice Shelf, Antarctica. JPO
• Lazeroms et al. (2018). Modelling present-day basal melt rates for Antarctic ice shelves using a parametrization of buoyant meltwater plumes. The Cryosphere
• Hoffman et al. (2019). Effect of Subshelf Melt Variability on Sea Level Rise Contribution From Thwaites Glacier, Antarctica. JGR Earth Surface

Numerics

• Aizinger, Dawson (2002). A discontinuous Galerkin method for two-dimensional flow andtransport in shallow water. Advances in Water Resources
• Dolejší, Feistauer (2015). Discontinuous Galerkin Method: Analysis and Applications to Compressible Flow. Springer
• Wimmer et al. (2020). Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations. JCP