Continuous data assimilation closure for modeling statistically steady turbulence in large-eddy simulation

A closure model is presented for large-eddy simulation (LES) based on the three-dimensional variational data assimilation algorithm. The approach aims at reconstructing high-fidelity kinetic energy spectra in coarse numerical simulations by including feedback control to represent unresolved dynamics interactions in the flow as stochastic processes. The forcing uses statistics obtained from offline high-fidelity data and requires only a few parameters compared to the number of degrees of freedom of LES. This modeling strategy is applied to geostrophic turbulence on the sphere and enables simulating indefinitely at reduced cost. The method accurately recovers the energy spectra and the zonal velocity profiles in the coarse model for three generic situations.