An accurate momentum advection scheme for a z-level coordinate models

Abstract

In this paper, we focus on a conservative momentum advection discretisation in the presence of z-layers. While in the 2D case conservation of momentum is achieved automatically for an Eulerian advection scheme, special attention is required in the multi-layer case. We show here that an artificial vertical structure of the flow can be introduced solely by the presence of the z-layers, which we refer to as the staircase problem. To avoid this staircase problem, the z-layers have to be remapped in a specific way. The remapping procedure also deals with the case of an uneven number of layers adjacent to a column side, thus allowing one to simulate flooding and drying phenomena in a 3D model.