Two Examples from Geophysical and Astrophysical Turbulence on Modeling Disparate Scale Interactions

Turbulent flows are ubiquitous, and as manifestations of one of the last outstanding unsolved problems of classical physics, they form today the focus of numerous investigations. In view of the very large number of modes that are excited, a variety of modeling techniques can be used in conjunction with state of the art numerical methods. A few of the issues that need to be addressed by models of turbulence, such as the presence of strong localized structures, the degree of nonlocality of nonlinear interactions, the slow return to isotropy and homogeneity, and the interactions between eddies and waves, are reviewed here; all implicate a large number of scales in interactions. Two specific modeling examples are given, one for waves and eddies in oceanic flows, and one for the generation of magnetic fields in planetary and stellar bodies, both using variants of Lagrangian-averaged methods. Finally, it is also argued that in order to understand geophysical turbulence, there is a strong need for combining modeling methods and sophisticated numerical techniques, such as high-accuracy adaptive mesh refinement.