The Sandpaper Theory of Flow‐Topography Interaction: The Non‐Local Formulation

Abstract The irregular seafloor variability at lateral scales of several kilometers can strongly influence large‐scale oceanic flows. However, these fine topographic patterns are currently unresolved by most global circulation models. To address this complication, we develop the “sandpaper” model of flow‐topography interaction. This theory uses asymptotic multiscale methods to parameterize the effects of small‐scale bathymetry in analytical and coarse‐resolution numerical models. The previously reported version of the sandpaper theory assumed that the direct effects of bottom roughness are limited to the deepest density layer. Its reliance on the local approximation fundamentally limited the model's ability to represent the vertical structure of abyssal flows. To overcome this deficiency, we develop a more general non‐local model, in which the effects of bottom roughness are distributed throughout the water column. The non‐local formulation enables the implementation of the sandpaper closure in isopycnal models designed for realistic simulations, in which density interfaces frequently intersect the bathymetry. Local closure in such regions exhibits unphysical singularities, whereas its non‐local counterpart remains well‐behaved. The non‐local sandpaper model is implemented in the HYbrid Coordinate Ocean Model (HYCOM), one of the mainstream oceanographic general circulation models. The parameterization is tested on the canonical vortex spin‐down problem.