On the accurate and stable reconstruction of tangential velocities in C-grid ocean models

The Arakawa C-grid is in widespread use in structured grid atmospheric and oceanic models. It now forms the grid of choice for a number of efficient and compact unstructured grid codes. In order to calculate the Coriolis terms, the C-grid requires the interpolation of the tangential velocities. In the case of a finite volume and or finite difference C-grid model, the tangential velocities have to be reconstructed from the cell normal velocities. This has to be handled with care otherwise the calculated Coriolis terms can be inaccurate, and even lead to instabilities. The interpolation matrix used to calculate the tangential velocities has to be skew-symmetric otherwise it can be shown to be unstable. Moreover, we show that the velocity reconstruction should be consistent with the discretized flow equations. Here a number of reconstructions for the tangential velocity components are described. We show that one has superior properties in the case of variable topography. Furthermore, we show that it is applicable for both structured and unstructured grids consisting of any cyclic polygons. We believe the result is therefore of general applicability to both structured and unstructured grid modellers who employ a classic Arakawa C-grid.