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Stochastic Transport in Upper Ocean Dynamics

Part of the Mathematics of Planet Earth Book Series (volume 10)

Editors: Chapron, Bertrand; Crisan, Dan; Holm, Darryl; Mémin, Etienne; Radomska, Anna

DOI: 10.1007/978-3-031-18988-3

ISBN: 978-3-031-18987-6

Publisher: Springer International Publishing - Springer Journals

Sep 24, 2022

1 - 10 of 19 Chapters

LitStream

Chapter 1Blow-Up of Strong Solutions of the Thermal Quasi-Geostrophic Equation

Crisan, Dan; Mensah, Prince Romeo

Pages: 1 –14

[The Thermal Quasi-Geostrophic (TQG) equation is a coupled system of equations that governs the evolution of the buoyancy and the potential vorticity of a fluid. It has a local in time solution as proved in Crisan et al. (Theoretical and computational analysis of the thermal quasi-geostrophic...
LitStream

Chapter 2Modeling Under Location Uncertainty: A Convergent Large-Scale Representation of the Navier-Stokes Equations

Debussche, Arnaud; Hug, Berenger; Mémin, Etienne

Pages: 15 –26

[We construct martingale solutions for the stochastic Navier-Stokes equations in the framework of the modelling under location uncertainty (LU). These solutions are pathwise and unique when the spatial dimension is 2D. We then prove that if the noise intensity goes to zero, these solutions...
LitStream

Chapter 3A Stochastic Benjamin-Bona-Mahony Type Equation

Dinvay, Evgueni

Pages: 27 –41

[Considered herein is a particular nonlinear dispersive stochastic equation. It was introduced recently in Dinvay and Mémin (Proc. R. Soc. A. 478:20220050, 2022), as a model describing surface water waves under location uncertainty. The corresponding noise term is introduced through a Hamiltonian...
LitStream

Chapter 4Observation-Based Noise Calibration: An Efficient Dynamics for the Ensemble Kalman Filter

Dufée, Benjamin; Mémin, Etienne; Crisan, Dan

Pages: 43 –56

[We investigate the calibration of the stochastic noise in order to guide the realizations towards the observational data used for the assimilation. This is done in the context of the stochastic parametrization under Location Uncertainty (LU) and data assimilation. The new methodology is...
LitStream

Chapter 5A Two-Step Numerical Scheme in Time for Surface Quasi Geostrophic Equations Under Location Uncertainty

Fiorini, Camilla; Boulvard, Pierre-Marie; Li, Long; Mémin, Etienne

Pages: 57 –67

[In this work we consider the surface quasi-geostrophic (SQG) system under location uncertainty (LU) and propose a Milstein-type scheme for these equations, which is then used in a multi-step method. The SQG system considered here consists of one stochastic partial differential equation, which...
LitStream

Chapter 6The Dissipation Properties of Transport Noise

Flandoli, Franco; Luongo, Eliseo

Pages: 69 –85

[The aim of this work is to present, in a compact way, the latest results about the dissipation properties of transport noise in fluid mechanics. Starting from the reasons why transport noise is natural in a passive scalar equation for the heat diffusion and transport, several results about...
LitStream

Chapter 7Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes Equation with Stochastic Lie Transport

Goodair, Daniel

Pages: 87 –107

[We present here a criterion to conclude that an abstract SPDE possesses a unique maximal strong solution, which we apply to a three dimensional Stochastic Navier-Stokes Equation. Motivated by the work of Kato and Lai we ask that there is a comparable result here in the stochastic case whilst...
LitStream

Chapter 8Coupling of Waves to Sea Surface Currents Via Horizontal Density Gradients

Holm, Darryl D.; Hu, Ruiao; Street, Oliver D.

Pages: 109 –133

[The mathematical models and numerical simulations reported here are motivated by satellite observations of horizontal gradients of sea surface temperature and salinity that are closely coordinated with the slowly varying envelope of the rapidly oscillating waves. This coordination of gradients...
LitStream

Chapter 9Variational Stochastic Parameterisations and Their Applications to Primitive Equation Models

Hu, Ruiao; Patching, Stuart

Pages: 135 –158

[We present a numerical investigation into the stochastic parameterisations of the Primitive Equations (PE) using the Stochastic Advection by Lie Transport (SALT) and Stochastic Forcing by Lie Transport (SFLT) frameworks. These frameworks were chosen due to their structure-preserving introduction...
LitStream

Chapter 10A Pathwise Parameterisation for Stochastic Transport

Lang, Oana; Pan, Wei

Pages: 159 –178

[In this work we set the stage for a new probabilistic pathwise approach to effectively calibrate a general class of stochastic nonlinear fluid dynamics models. We focus on a 2D Euler SALT equation, showing that the driving stochastic parameter can be calibrated in an optimal way to match a set...

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