Non-uniform adaptive vertical grids in one-dimensional numerical ocean models

It is demonstrated in this paper how the concept of general vertical coordinates can be exploited for constructing adaptive grids in primitive equation ocean models. The term adaptive is used here in the sense of coordinate iso-surfaces which follow certain internal structures of the flow in such a way that higher vertical resolution is obtained in locations where vertical gradients are large. The internal structures considered here are shear and stratification. In this paper, one-dimensional models are applied in order to demonstrate the ability of such grid adaptation methods to follow internal structures even in flow situations dominated by vertical mixing processes. Here, a variational approach is considered for the generation of grids which results in a diffusion equation for the vertical coordinate. The method is tested for five different idealised and realistic scenarios with the result that the discretisation error can be significantly reduced in comparison to equidistant Cartesian grids. Some recommendations for extending these methods for three-dimensional models are given at the end of this paper.