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SLIM3D solves the three-dimensional hydrostatic equations under the Boussinesq approximation. The model variables are the 3D velocity, the surface elevation, the salinity and the temperature. The density is obtained by means of an equation of state. SLIM3D uses a mesh composed of triangular prismatic elements that are formed by extruding the 2D unstructured mesh in the vertical direction. The model equations are solved by means of the Discontinuous Galerkin finite element method.

3D mesh
Sketch of the 3D mesh obtained by vertically extruding a 2D triangular mesh. All variables are piecewise linear and discontinuous between elements.

One key aspect in any 3D ocean model is the coupling between the external and internal modes. SLIM3D uses a mode-splitting formulation in which the fast propagating gravity waves are solved in an external 2D mode. That mode can either be discretised explicitly with a small time step or implicitly with a larger time step.

Burdekin mesh
3D mesh used to simulate the sediment plume dynamics of the Burdekine River (Australia). The bathymetry being quite shallow and smooth, sigma layers are sufficient to provide an accurate solution.

In the vertical, SLIM3D allows a combination of z and sigma layers. For rather shallow environments with mild bathymetry gradients, sigma coordinates can be used over the entire water column. For deeper areas with sharp bathymetry gradients, sigma layers are generally used only near the surface while z layers are used in the rest of the domain. The number of z layers can be adapted to better approximate bathymetry gradients.

The accuracy of the mode coupling has been tested on a baroclinic test case described in Ilicak et al. (2012). The domain is a periodic (along the 500km-long boundaries) and closed (along the 160km-long boundaries) channel with a bathymetry of 1000m (exaggerated on the video). The large bottom drag coefficient and asymmetric initial condition trigger baroclinic instabilities in the channel. The 4km mesh resolution is similar to one of typical mesoscale eddy permitting models. SLIM3D is able to reproduce the development of baroclinic eddies, as illustrated by the evolution of the predicted temperature.

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