Convergence of outer iterations for vertically split pressure solves on real bathymetry

Determine the convergence of an outer iteration on the inter-column coupling for the vertically split non-hydrostatic pressure problem on realistic ocean bathymetry, including whether such an iteration must fail.

Background

The paper examines an exact vertical spectral split as a possible alternative to the AC/DC approach. On stretched grids and realistic bathymetry, neighboring columns have different vertical operators and eigenbases, so horizontal coupling destroys the independent two-dimensional modal decomposition. The authors therefore conclude that the split is not exact and that an iterative treatment of the inter-column coupling would be required.

However, the paper does not establish whether an outer iteration based on that coupling necessarily fails, nor does it determine its convergence behavior on realistic ocean geometry. This remains unresolved because topography, varying land–sea masks, sills, and disconnected basins may strongly affect the iteration.