| Abstract: |
| Despite the increasing accuracy of geophysical flows observations and numerical simulations, full resolution is far beyond our current technological capacities. Progress will occur as measurements and simulations are optimally combined using a quantification of the error in these two information sources. Uncertainty quantification remains a challenge in computational fluid dynamics. Thus, we propose to introduce stochasticity into the fluid dynamics equations. Part of the transport velocity -- representing its unresolved small-scale component -- is assumed to be random and uncorrelated in time. Two similar but independent approaches -- location uncertainty (LU) and Stochastic Advection by Lie Transport (SALT) -- have followed this path. Both models conserve essential physical invariants. Numerous methods exist to specify the small-scale velocity statistics and thereby fully parametrize these random models. After presenting the LU and the SALT formalisms, the talk will numerically compare two tuning-free parametrizations: a data-driven heterogeneous one and a self-adaptive homogeneous one. For a Surface Quasi-Geostrophic (SQG) flow, both parametrizations lead to similar and accurate uncertainty quantification. A non-stationary and heterogeneous modulation based on an important third-order moment -- the energy flux -- will also be discussed. |
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