Dissipative Nonlinear Schrödinger Equation with External Forcing in Rotational Stratified Fluids and Its Solution
Dissipative Nonlinear Schrödinger Equation with External Forcing in Rotational Stratified Fluids and Its Solution
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DOI：
10.1088/0253-6102/64/4/464
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发表时间：
2015-10
影响因子：
3.1
通讯作者：
Shi Yun-long;Yang Hong-wei;Y. Bao-shu;Yang De-zhou;Xu Zhen-hua;Feng Xing-Ru
中科院分区：
文献类型：
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作者：
Shi Yun-long;Yang Hong-wei;Y. Bao-shu;Yang De-zhou;Xu Zhen-hua;Feng Xing-Ru
采用多尺度分析和微扰方法，导出了带强迫项的耗散非线性薛定谔方程，作为描述旋转分层流体中具有耗散效应和外强迫的包络孤立罗斯比波的数学模型。通过对包络孤立罗斯比波振幅演变的分析，发现基流剪切、布朗特维萨拉频率和1,13效应是包络孤立罗斯比波形成的重要因素。采用Jacobi椭圆函数展开法和Hirota直接法分别导出了耗散非线性薛定谔方程和强迫非线性薛定谔方程的解析解，并利用这些解详细讨论了耗散和外强迫对包络孤立罗斯比波演化的影响。结果表明：耗散导致包络孤立罗斯比波振幅缓慢减小，宽度缓慢增大，但对传播速度没有影响，不同类型的外强迫可以激发相同的包络孤立罗斯比波。值得注意的是，耗散和不同类型的外强迫对包络孤立罗斯比波的载频有一定的影响。
The dissipative nonlinear Schrodinger equation with a forcing item is derived by using of multiple scales analysis and perturbation method as a mathematical model of describing envelope solitary Rossby waves with dissipation effect and external forcing in rotational stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt Vaisala frequency and,13 effect are important factors in forming the envelope solitary Rossby waves. By employing Jacobi elliptic function expansion method and Hirota's direct method, the analytic solutions of dissipative nonlinear Schrodinger equation and forced nonlinear Schrodinger equation are derived, respectively With the help of these solutions, the effects of dissipation and external forcing on the evolution of envelope solitary Rossby wave are also discussed in detail. The results show that dissipation causes slowly decrease of amplitude of envelope solitary Rossby waves and slowly increase of width, while it has no effect on the propagation speed and different types of external forcing can excite the same envelope solitary Rossby waves. It is notable that dissipation and different types of external forcing have certain influence on the carrier frequency of envelope solitary Rossby waves.