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

• Published in: Geophysical and astrophysical fluid dynamics Vol. 111; no. 3; pp. 149 - 176
• Main Authors: Resseguier, V., Mémin, E., Chapron, B.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.05.2017; Taylor & Francis Ltd
• Subjects: Atmospheric and Oceanic Physics; Computational fluid dynamics; Dye dispersion; Dynamics; Energy; Energy conservation; Engineering Sciences; ensemble forecasts; Fluid dynamics; Fluid mechanics; Geophysics; Mechanics; Physics; Representations; Signal and Image processing; Stochastic flows; Stochastic processes; Transport; uncertainty quantification; upper ocean dynamics; Velocity; uncertainty quantification; stochastic flows; ensemble forecasts; upper ocean dynamics
• ISSN: 0309-1929; 1029-0419
• DOI: 10.1080/03091929.2017.1310210

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.