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On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number. (English) Zbl 1072.76067
Summary: Numerical simulations are used to study a series of reduced models of homogeneous, rotating flow at moderate Rossby numbers \(Ro\approx 0.1\), for which both numerical and physical experiments show the generation of quasi-two-dimensional vortices and symmetry breaking in favour of cyclones. A random force at intermediate scales injects energy at a constant average rate. The nonlinear term of reduced models is restricted to include only a subset of triad interactions in Fourier space. Reduced models of near-resonant, non-resonant and near two-dimensional triad interactions are considered. Only the model of near resonances reproduces all of the important characteristics of the full simulations: (i) efficient energy transfer from three-dimensional forced modes to two-dimensional large-scale modes, (ii) large-scale energy spectra scaling approximately as \(k_h^{-3}\), where \(k_h\) is the wavenumber in the plane perpendicular to the axis of rotation, and (iii) strong cyclone/anticyclone asymmetry in favour of cyclones. Non-resonances, defined as the complement to near resonances, act to reduce the energy transfer to large scales.

MSC:
76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
86A05 Hydrology, hydrography, oceanography
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