Optimal Closures in a Simple Model for Turbulent Flows

In this work we introduce a computational framework for determining optimal closures of the eddy-viscosity type for large-eddy simulations (LESs) of a broad class of PDE models, such as the Navier--Stokes equation. This problem is cast in terms of PDE-constrained optimization where an error functional representing the misfit between the target and predicted observations is minimized with respect to the functional form of the eddy viscosity in …