Stochastic Compressible Navier–Stokes Equations Under Location Uncertainty
Type | Book section | ||||||||
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Date | 2024 | ||||||||
Language | English | ||||||||
Author(s) | Tissot Gilles1, Mémin Étienne1, Jamet Quentin2, 3 | ||||||||
Affiliation(s) | 1 : INRIA Centre de l’Université de Rennes, IRMAR – UMR CNRS 6625, Rennes, France 2 : INRIA Centre de l’Université de Rennes, IRMAR – UMR CNRS 6625, Rennes, France 3 : LOPS, 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_14. pp.293-319 | ||||||||
DOI | 10.1007/978-3-031-40094-0_14 | ||||||||
Abstract | The aim of this paper is to provide a stochastic version under location uncertainty of the compressible Navier–Stokes equations. To that end, some clarifications of the stochastic Reynolds transport theorem are given when stochastic source terms are present in the right-hand side. We apply this conservation theorem to density, momentum and total energy in order to obtain a transport equation of the primitive variables, i.e. density, velocity and temperature. We show that performing low Mach and Boussinesq approximations to this more general set of equations allows us to recover the known incompressible stochastic Navier–Stokes equations and the stochastic Boussinesq equations, respectively. Finally, we provide some research directions of using this general set of equations in the perspective of relaxing the Boussinesq and hydrostatic assumptions for ocean modelling. |
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