Brinkman volume penalization for bathymetry in three-dimensional ocean models

Accurate and stable implementation of bathymetry boundary conditions remains a challenging problem. The dynamics of ocean flow often depend sensitively on satisfying bathymetry boundary conditions and correctly representing their complex geometry. Generalized (e.g.  σ ) terrain-following coordinates are often used in ocean models, but they require smoothing the bathymetry to reduce pressure gradient errors (Mellor et al., 1994). Geopotential z …