Geophysical flows under location uncertainty, Part I Random transport and general models

Abstract

A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction , an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics.

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• Geophysical flows under location uncertainty, Part III: SQG and frontal dynamics under strong turbulence conditions
• Theoretical tools for understanding the climate crisis from Hasselmann's program and beyond
• Rotating shallow water flow under location uncertainty with a structure-preserving discretization
• Semi-martingale driven variational principles
• Variational approach to closure of nonlinear dynamical systems: Autonomous case
• Stochastic modelling and diffusion modes for proper orthogonal decomposition models and small-scale flow analysis
• Implications of Kunita-Itô-Wentzell formula for $k$-forms in stochastic fluid dynamics
• Analytical Properties for a Stochastic Rotating Shallow Water Model under Location Uncertainty
• Circulation and Energy Theorem Preserving Stochastic Fluids
• A consistent stochastic large-scale representation of the Navier-Stokes equations
• Stochastic Parametrization of the Richardson Triple
• A Hamiltonian Mean-Field System for the Navier-Stokes Equation
• An eddifying Stommel model: Fast eddy effects in a two-box ocean
• A Hamiltonian interacting particle system for compressible flow