FN Archimer Export Format PT CHAP TI Linear Wave Solutions of a Stochastic Shallow Water Model BT 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 AF Mémin, Etienne Li, Long Lahaye, Noe Tissot, Gilles Chapron, Bertrand AS 1:1,2;2:1,2;3:1,2;4:1,2;5:3; FF 1:;2:;3:;4:;5:PDG-ODE-LOPS-SIAM; C1 ODYSSEY Team, Centre Inria de l’Université de Rennes, Rennes, France IRMAR – UMR CNRS 6625, Rennes, France Laboratoire d’Océanographie Physique et Spatiale, Ifremer, Plouzané, France C2 INRIA, FRANCE CNRS, FRANCE IFREMER, FRANCE SI BREST SE PDG-ODE-LOPS PDG-ODE-LOPS-SIAM UM LOPS UR https://archimer.ifremer.fr/doc/00856/96754/105301.pdf LA English DT Book section AB 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. PY 2024 DI 10.1007/978-3-031-40094-0_10 ID 96754 ER EF