# zbMATH — the first resource for mathematics

On the formation of geophysical and planetary zonal flows by near-resonant wave interactions. (English) Zbl 1110.76053
Summary: Numerical simulations on a $$\beta$$-plane are used to further understand the formation of zonal flows from small-scale fluctuations. The dynamics of ‘reduced models’ are computed by restricting the nonlinear term to include a subset of triad interactions in Fourier space. Reduced models of near-resonant triads are considered, as well as the complement set of non-resonant triads. At moderately small Rhines number, near-resonant triad interactions are shown to be responsible for the generation of large-scale zonal flows from small-scale random forcing. Without large-scale drag, both the full system and the reduced model of near resonances produce asymmetry between eastward and westward jets, in favour of stronger westward jets. When large-scale drag is included, the long-time asymmetry is reversed in the full system, with eastward jets that are thinner and stronger than westward jets. Then the reduced model of near resonances exhibits a weaker asymmetry, but there are nevertheless more eastward jets stronger than a threshold value.

##### MSC:
 76U05 General theory of rotating fluids 86A05 Hydrology, hydrography, oceanography