- 著者
-
Takahiro ITO
Hirotada KANEHISA
- 出版者
- Meteorological Society of Japan
- 雑誌
- 気象集誌. 第2輯 (ISSN:00261165)
- 巻号頁・発行日
- vol.91, no.6, pp.775-788, 2013
- 被引用文献数
-
4
The initial value problem of vortex Rossby waves (VRWs) is analytically solved in a linearized barotropic system on an <i>f</i> plane. The basic axisymmetric vorticity <span style="text-decoration: overline;"><i>q</i></span> is assumed to be piecewise uniform in the radial direction so that the radial gradient <i>d<span style="text-decoration: overline;"><i>q</i></span>/dr</i> and the disturbance vorticity <i>q</i> are expressed in terms of Dirac delta functions. After Fourier transformation in the azimuthal direction with the wavenumber <i>m</i>, the linearized vorticity equation becomes a system of ordinary differential equations with respect to time; these can be analytically solved to give a closed-form solution with a prescribed initial value.<br> For a monopolar <span style="text-decoration: overline;"><i>q</i></span>, the solution of <i>q</i> starting from the innermost radius exhibits the outward propagation of VRWs. As the outer disturbances are generated, the inner disturbance is diminished. On the other hand, in the case of a solution forced at the innermost radius, the inner disturbance is not diminished, and the outward propagation of VRWs forms a distribution of spiral-shaped disturbance vorticity.<br> For a basic vorticity <span style="text-decoration: overline;"><i>q</i></span> with a moat, and if the radial distribution of <span style="text-decoration: overline;"><i>q</i></span> satisfies a certain additional condition, the solution of <i>q</i> with |<i>m</i>| ≠ 1 grows exponentially or linearly in time as a result of the interaction of counterpropagating VRWs near the moat. Although the solution of <i>q</i> with |<i>m</i>| = 1 cannot grow exponentially for any <span style="text-decoration: overline;"><i>q</i></span>, it can grow as a linear function of time. This linear growth may be regarded as a result of resonance between two internal modes of the system.