Moving mesh methods for ocean modelling

In this paper we introduce preliminary work on the use of mesh movement or r-adaptivity techniques in ocean modelling. The ultimate goal is to propose an alternative approach to isopycnal models by using a combination of mesh optimisation and node movement in a Lagrangian-like manner to follow isopycnals, surfaces of constant density, reduce levels of spurious numerical diapycnal mixing, and move with eddies and other flow features. We present different methods to define the grid velocity and additional terms to preserve mesh quality. For a simple test case we show that the method offers a way to produce meshes which dynamically adapt and move to follow density layers.