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摘要
The time-evolution of two-dimensional decaying turbulence governed by the long-wave limit, in which L-D/L -> 0, of the quasi-geostrophic equation is investigated numerically. Here, L-D is the Rossby radius of deformation, and L is the characteristic length scale of the flow. In this system, the ratio of the linear term that originates from the beta-term to the nonlinear terms is estimated by a dimensionless number, gamma = beta L-D(2)/U, where beta is the latitudinal gradient of the Coriolis parameter, and U is the characteristic velocity scale. As the value of. increases, the inverse energy cascade becomes more anisotropic. When gamma >= 1, the anisotropy becomes significant and energy accumulates in a wedge-shaped region where vertical bar l vertical bar > root 3 vertical bar k vertical bar in the two-dimensional wavenumber space. Here, k and l are the longitudinal and latitudinal wavenumbers, respectively. When gamma is increased further, the energy concentration on the lines of l = +/-root 3k is clearly observed. These results are interpreted based on the conservation of zonostrophy, which is an extra invariant other than energy and enstrophy and was determined in a previous study. Considerations concerning the appropriate form of zonostrophy for the long-wave limit and a discussion of the possible relevance to Rossby waves in the ocean are also presented.
- 出版日期2013-7
