Abstract: The theory of resonant interaction of planetary waves in a two layer model is extended from three-wave system to five-wave system. The evolution equations governing the amplitudes of the waves are derived and solved analytically. It is found that the solutions can be given in terms of Jacobi elliptic functions.

Key words: resonant interaction of planetary waves, Rossby wave, geophysical fluid

摘要： 本文将二层模式中的三波共振推广到五波共振，推得了五波共振时其振幅所满足的方程组，该方程组的解可用Jacob；椭圆函数表示。

关键词: 行星波共振, Rossby波, 地球物理流体