Boundary Layer Formation in the Quasigeostrophic Model Near Nonperiodic Rough Coasts

Abstract

We study the so-called homogeneous model of wind-driven ocean circulation or the 2D quasigeostrophic model. Our attention focuses on performing a complete asymptotic analysis that highlights boundary layer formation along the coastal line. We assume rough coasts without any particular structure, resulting in the study of a nonlinear PDE system for the western boundary layer in an infinite domain. As a consequence, we look for the solution in nonlocalized Sobolev spaces. Under this hypothesis, the eastern boundary layer exhibits a singular behavior at low frequencies far from the rough boundary, leading to issues with convergence. The problem is tackled by imposing ergodicity properties. We establish the well-posedness of the governing boundary layer equations and the asymptotic solution. Our results generalize the ones in Bresch and Gérard-Varet (Commun Math Phys 253(1):81–119, 2005) for periodic irregularities.