2021/08/05 by Gabriela López Ruiz, Ruiz, Gabriela López
Earth and Planetary Sciences · Environmental Science · #Ocean Waves and Remote Sensing #Geological formations and processes #Methane Hydrates and Related Phenomena
paper · pdf · doi:10.48550/arxiv.2108.02705
We study the so-called homogeneous model of wind-driven ocean circulation, also known as the single-layer 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 approximate solution. Our results generalize the ones in the paper of Bresch and Gérard-Varet (Commun. Math. Phys. (1) 253: (2005), 81-119) in the context of periodic irregularities.