The limitation of balanced dynamics which contain the coupling of slow Rossby mode and fast gravity mode are investigated in the f-plane shallow water system.
First, we investigate the linear stability of zonal jets in this system, and compare the stability characteristics with those obtained in the quasi-geostrophic system for a wide range of Rossby Ro, and Froude Fr, numbers. As for the maximum growth rate, quasi-geostrophic approximation is good for a wide parameter range of Fr2/Ro2 > 1 and Fr < 1, even for high Ro. However, unstable modes in this parameter range are different between high Ro and low Ro. In low Ro (Ro < O(1)), there is a regime in which geostrophic balance is dominant. In this regime, the ratio of the amplitude of divergent component ψ to that of rotational one φ, |φ|/|ψ| is proportional to Ro/Fr2, and φ is symmetric to the center of jet. On the other hand, in high Ro (Ro > O(1)), another regime does exist. Here dominant balance is related to the basic flow. |φ|/|ψ| is proportional to 1/Fr2, and antisymmetric component in φ is dominant. In addition, for high Ro and Fr (Ro > O(1), Fr > O(1)), there is a regime of gravity-wave instability. These all results can be explained by order estimate of the linearized equations.
Second, gravity wave radiations from balanced Rossby flow are investigated in the full nonlinear f-plane forced-dissipative shallow water system. We use two types of basic flow; zonal jets and hurricane-like vortices. Unlike the well known linear Rossby adjustment problem, gravity waves are continuously and intermittently radiated from these basic flows. Furthermore, these radiations are occurred for small Ro and Fr. Therefore, it is fundamentally different from gravity-wave instability which is found in the linear stability analysis for the case of high Ro and Fr. We analyze these radiations in detail for a wide range of parameters. |
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