Linear Wave Solutions of a Stochastic Shallow Water Model
| Type | Book section | ||||||||
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| Date | 2024 | ||||||||
| Language | English | ||||||||
| Author(s) | Mémin Etienne1, 2, Li Long1, 2, Lahaye Noe1, 2, Tissot Gilles1, 2, Chapron Bertrand 3 |
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| Affiliation(s) | 1 : ODYSSEY Team, Centre Inria de l’Université de Rennes, Rennes, France 2 : IRMAR – UMR CNRS 6625, Rennes, France 3 : Laboratoire d’Océanographie Physique et Spatiale, Ifremer, Plouzané, France |
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| Book | Chapron, B., Crisan, D., Holm, D., Mémin, E., Radomska, A. (eds) Stochastic Transport in Upper Ocean Dynamics II. STUOD 2022. Part of the Mathematics of Planet Earth book series (MPE,volume 11). Springer, Cham. Print ISBN 978-3-031-40093-3 Online ISBN 978-3-031-40094-0. https://doi.org/10.1007/978-3-031-40094-0_10. pp.223-245 | ||||||||
| DOI | 10.1007/978-3-031-40094-0_10 | ||||||||
| Abstract | In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind or coming as the feedback of the ocean on the atmosphere and leading in a very fast way to the selection of some wavelength. This interwoven, yet simple, mechanism explains the emergence of typical wavelength associated with near inertial waves. Ensemble-mean waves that are not in phase with the random forcing are damped at an exponential rate, whose magnitude depends on the random forcing variance. Geostrophic adjustment is also interpreted as a statistical homogenization process in which, in order to conserve potential vorticity, the small-scale component tends to align to the velocity fields to form a statistically homogeneous random field. |
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