Effect of turbulence on zonal jet flows in equivalent-barotropic quasi-geostrophic model

The linear stability of zonal flows superposed upon a sinusoidal, slightly supercritical background flow in an equivalent-barotropic quasi-geostrophic model on a \(\beta\) plane is investigated using asymptotic analysis. Consistent with results of full numerical simulations, all the steady isolated zonal jet solutions were found to be linearly unstable, and specifically, the mode independent of longitudinal direction was found to be most unstable, even when the amplitude equation of the zonal flows has longitudinal dependence. References K. Obuse, S. Takehiro and M. Yamada, Long-time asymptotic states of forced two-dimensional barotropic incompressible flows on a rotating sphere. Phys. Fluids 22:156601, 2010. doi:10.1063/1.3407652 R. K. Scott and L. M. Polvani, Forced-dissipative shallow-water turbulence on the sphere and the atmospheric circulation of the giant planets. J. Atmos. Sci. 64:3158–3176, 2007. doi:10.1175/JAS4003.1 A. J. Manfroi and W. R. Young, Slow evolution of zonal jets on the beta plane. J. Atmos. Sci. 56:784–800, 1999. doi:10.1175/1520-0469(1999)056<0784:SEOZJO>2.0.CO;2 K. Obuse, S. Takehiro and M. Yamada, Linear stability of steady zonal jet flows induced by a small-scale forcing on a \(\beta \) plane. Physica D 240:1825–1834, 2011. doi:10.1016/j.physd.2011.08.009 S. Takehiro, M. Odaka, K. Ishioka, M. Ishiwatari, Y.-Y. Hayashi and SPMODEL Development Group, A series of hierarchical spectral models for geophysical fluid dynamics. Nagare Multimedia, 2006. http://www.nagare.or.jp/mm/2006/spmodel/