The numerical models below demonstrate how GLNumericalModelingKit can be used to solve partial differential equations. All of the examples are open source and available for download.

**Kelvin Helmholtz Instability** This models an unstable shear flow. The model is initialized with a strong shear, then is given a small perturbation, resulting in the flow going unstable and the creation of Kelvin-Helmholtz billows. The code outputs the fluid velocity, vorticity and particle trajectories.

**Rossby Waves **This models the two-dimensional linearized quasigeostrophic potential vorticity equation. The model is initialized with a Gaussian shaped eddy, which quickly disperses into Rossby waves.

**Turbulence Spin Up **This models the forced-dissipative quasigeostrophic potential vorticity equation as it spins up with a constant forcing.

**Anisotropic Turbulence **This models the forced-dissipative quasigeostrophic potential vorticity equation *on a beta-plane*, which, in comparison to the isotropic example above, shows directional dependence in the fluid flow.

**Internal Waves **This model advects particles using the analytical solution to the three-dimensional linearized internal wave equation for arbitrary stratification. In the two cases shown here, the model is initialized with a single internal mode and the full Garrett-Munk spectrum.

**Shoaling surface gravity waves **This models surface gravity waves they approach a sandbar. Waves are generated in the deep water on the left of the domain, then propagate towards a shallowing continental slope, before impinging upon a sandbar.