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Boundary Layer Formation in the Quasigeostrophic Model Near Nonperiodic Rough Coasts

Boundary Layer Formation in the Quasigeostrophic Model Near Nonperiodic Rough Coasts 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Rational Mechanics and Analysis Springer Journals

Boundary Layer Formation in the Quasigeostrophic Model Near Nonperiodic Rough Coasts

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References (18)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0003-9527
eISSN
1432-0673
DOI
10.1007/s00205-023-01846-z
Publisher site
See Article on Publisher Site

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.

Journal

Archive for Rational Mechanics and AnalysisSpringer Journals

Published: Jun 1, 2023

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