Conventional ocean models can be divided in two main categories: level models treat the ocean dynamics on fixed vertical levels, while layered models consider the ocean to consist of layers. Level models have the edge dealing with the pressure gradient, while layer models are superior in the treatment of tracer fields by reducing spurious diapycnal mixing.
In the COSIM group of LANL we are developing a hybrid model HYPOP that aims to combine the best of both worlds. It treats the momentum equations on a level grid, while the tracer equations are solved on a Lagrangian grid. John Dukowicz conceived a method to interpolate pressure and velocity between the two grids in an energetically consistent way.