Analysis of Effect on Forced Dissipation about Nonlinear Ross by Wave Packets

Abstract

本研究运用多尺度变换和摄动法简化具有耗散效应的正压准地转涡度方程，得到带有扰动项的非线性Shrӧdinger方程，在此基础上，分析了非线性Shrӧdinger孤立子的拓扑结构，并采用孤立子直接微扰理论研究强迫耗散对大气阻塞结构的作用。结果表明：1) 在没有耗散的情况下，当基本纬向速度和孤立子波幅满足不同的条件时，定常Shrӧdinger孤立子具有两种形态，当基本纬向速度较小而孤立子波幅较大时，流场具有偶极子型的孤立波，表征低指数的经向环流；当基本纬向速度较大而孤立子波幅较小时，流场是退化的中心结构，表征高指数的纬向环流。2) 耗散效应对大气阻塞发展具有抑制作用，这种抑制作用随时间的负指数函数变化。 The nonlinear Shrӧdinger equation with disturbance term is obtained, by simplifying the positive pressure quasi-geostrophic vorticity equation with dissipative effect through multi-scale trans-formation and perturbation method. On the base of this, topology of nonlinear Shrӧdinger soliton is analyzed. And effect of forced dissipation on the blocking structure is studied by using the direct perturbation theory of solitons. The results show that: 1) Without dissipation, there exit two forms for the stationary Shrӧdinger soliton: the flow field has a soliton-shaped solitary wave when the basic zonal velocity is small and the isolated wavelet amplitude is large enough, which represents a low-index circulation, as well as the flow field is a degenerate central structure when the basic zonal velocity is large and the isolated wavelet amplitude is small, which characterizes the low-index circulation. 2) The dissipative effect has an inhibitory effect on the development of obstruction, which inhibition changes with a negative exponential function of time.