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本文从非线性大气运动方程组出发,在力学的平衡点附近,用比较简洁的方法求得了非线性有限振幅的色散大气惯性波、重力内波、Rossby波均满足KdV方程,它的解为椭圆余弦波和孤立波。对有限振幅的Rossby波,建立了不同于Rossby公式的新的色散关系,它合有波的振幅因子。分析表明,对有限振幅的惯性波和重力内波,振幅大,宽度大的波传播越快;但对于Rossby孤立波,振幅大,宽度大的波传播越慢,极涡、阻塞切断系统可能属于这一类波。
In this paper, starting from the system of nonlinear atmospheric equations, the inertial wave with nonlinear finite amplitude is obtained by the simpler method near the equilibrium point of mechanics. The gravity and Rossby waves satisfy the KdV equation. The solution is elliptic Cosine wave and isolated wave. For a Rossby wave of finite amplitude, a new dispersion relation different from the Rossby equation is established, which combines the amplitude factor of the wave. The analysis shows that for the limited amplitudes of inertial and gravitational waves, the waves with larger amplitude and larger width propagate faster; however, for Rossby solitary waves, the wave propagation with larger amplitude and width is slower and the polar vortex and blocking and cutting systems may belong to This type of wave.