Large‐scale flows under location uncertainty: a consistent stochastic framework

Using a classical example, the Lorenz‐63 model, an original stochastic framework is applied to represent large‐scale geophysical flow dynamics. Rigorously derived from a reformulated material derivative, the proposed framework encompasses several meaningful mechanisms to model geophysical flows. The slightly compressible set‐up, as treated in the Boussinesq approximation, yields a stochastic transport equation for the density and other related thermodynamical variables. Coupled to the momentum equation through a forcing term, the resulting stochastic Lorenz‐63 model is derived consistently. Based on such a reformulated model, the pertinence of this large‐scale stochastic approach is demonstrated over classical eddy‐viscosity based large‐scale representations. We describe an original stochastic framework derived through a stochastic transport formalism. The proposed framework encompasses several meaningful mechanism to model geophysical flows. The pertinence of this large‐scale stochastic approach over classical eddy‐viscosity based representations is demonstrated on the Lorenz 63 model.