Séminaire
Geophysical and other turbulent flows spread other a wide range of temporal and spatial scales. Simulations, observations and mixing diagnoses of these flows generally neglect the smallest scales and must involve subgrid corrections. Besides, for ensemble forecasts and data assimilation, an appropriate randomization of the dynamics is needed to quantify the model errors.
The models under location uncertainty define a new type of stochastic subgrid parameterization. By injecting a random time-uncorrelated velocity, the structure of the transport is modified. The new material derivative involves an inhomogeneous and anisotropic diffusion, a drift correction and a multiplicative noise. As such, the ensuing transport equations remain conservative. This structure models instabilities, variabilities and energy transfers better than diffusive models.
Furthermore, this specific randomization efficiently quantifies model errors, bifurcations and extreme events. Subgrid parametrization can be helpful for mixing diagnoses as well. Similar to the Okubo-Weiss criterion, two Eulerian-based mixing diagnoses have been proposed. The first one -- valid at finite time -- neglects the subgrid velocity (as FTLE and FSLE computed from oceanic altimetry). Except near few saddle points, pairs of particles stretch linearly in time. Most large-scale tracer gradients are wrapped around vortices creating spiral-like structures. Our second mixing diagnosis relies on the modeling under location uncertainty to take into account the subgrid dynamics.