Boundary layer formation in the quasigeostrophic model near nonperiodic rough coasts

DOI10.1007/S00205-023-01846-ZarXiv2108.02705MaRDI QIDQ6374601

Publication date: 5 August 2021

Abstract: 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 G'erard-Varet (Commun. Math. Phys. (1) 253: (2005), 81-119) in the context of periodic irregularities.

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Hydrology, hydrography, oceanography (86A05) Boundary-layer theory, separation and reattachment, higher-order effects (76D10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Geophysical flows (76U60)

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