Linear Wave Solutions of a Stochastic Shallow Water Model
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.
Mémin Etienne, Li Long, Lahaye Noe, Tissot Gilles, Chapron Bertrand (2024). Linear Wave Solutions of a Stochastic Shallow Water Model. In 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. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-40094-0_10, https://archimer.ifremer.fr/doc/00856/96754/
Jamet Quentin, Mémin Etienne, Dumas Franck, Li Long, Garreau Pierre (2024). Toward a Stochastic Parameterization for Oceanic Deep Convection. In 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_6. pp.143-157. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-40094-0_6, https://archimer.ifremer.fr/doc/00856/96756/
Lobbe Alexander, Crisan Dan, Holm Darryl, Mémin Etienne, Lang Oana, Chapron Bertrand (2024). Comparison of Stochastic Parametrization Schemes Using Data Assimilation on Triad Models. In 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_7. pp.159-191. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-40094-0_7, https://archimer.ifremer.fr/doc/00856/96755/
Ouala Said, Chapron Bertrand, Collard Fabrice, Gaultier Lucile, Fablet Ronan (2024). Analysis of Sea Surface Temperature Variability Using Machine Learning. In 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_11. pp.247-260. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-40094-0_11, https://archimer.ifremer.fr/doc/00856/96753/
Resseguier Valentin, Zhen Yicun, Chapron Bertrand (2024). Constrained Random Diffeomorphisms for Data Assimilation. In 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, 10.1007/978-3-031-40094-0_13, pp.281-292. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-40094-0_13, https://archimer.ifremer.fr/doc/00856/96752/
Tissot Gilles, Mémin Étienne, Jamet Quentin (2024). Stochastic Compressible Navier–Stokes Equations Under Location Uncertainty. In 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_14. pp.293-319. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-40094-0_14, https://archimer.ifremer.fr/doc/00856/96751/
