Data-driven modeling of non-local mixing phenomena in geophysical flows

Geophysical flows often feature mixing phenomena with a wide range of eddy sizes due to the effects of forcing and dissipation on large scales. In addition, many of them tend to exhibit mixing and no-mixing regions in statistically steady states, with eddies propagating finite distances between them. Therefore, a local closure model is sometimes not enough to accurately describe the mixing phenomena in geophysical flows, motivating us to explore non-local models that better account for mixing in geophysical flows. In this work, we propose an approach to construct neural-network-based model of non-local mixing that builds upon data-driven kernels. We test this approach by studying a barotropic flow driven by linear relaxation toward an unstable zonal jet. The results show that our approach achieves better extrapolation capability when training and testing on flows with different relaxation time and the reference unstable zonal jet. The approach also demonstrates the potential of constructing data-driven models of non-local mixing phenomena that can be generalized to different types of geophysical flows.