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1.
Periodic Structure of Equatorial Envelope Rossby Wave Under
Influence of Diabatic Heating 总被引:1,自引:0,他引:1
FUZun-Tao CHENZhe LIUShi-Da LIUShi-Kuo 《理论物理通讯》2004,42(1):43-48
A simple shallow-water model with influence of diabatic heating on a β-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the asymptotic method of multiple scales, the cubic nonlinear Schro^edinger (NLS for short) equation with an external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of Jacob/elliptic functions and elliptic equation. It is shown that phase-locked diabatic heating plays an important role in periodic structures of rational form. 相似文献
2.
FU Zun-Tao LIU Shi-Da LIU Shi-Kuo 《理论物理通讯》2004,42(10)
The cubic nonlinear Schrodinger (NLS for short) equation with a generalized external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of a new transformation, Jacobi elliptic functions,and elliptic equation. It is shown that different types of resonant phase-locked diabatic heating play different roles in structures of equatorial envelope Rossby wave. 相似文献
3.
SHI Yun-Long YANG Hong-Wei YIN Bao-Shu YANG De-Zhou XU Zhen-Hua FENG Xing-Ru 《理论物理通讯》2015,64(4):464-472
The dissipative nonlinear Schrödinger 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 β 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 Schrödinger equation and forced nonlinear Schrödinger 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. 相似文献
4.
A simple shallow-water model with influence of external forcing on
a β-plane is applied to investigate the nonlinear equatorial
Rossby waves in a shear flow. By the perturbation method, the
extended variable-coefficient KdV equation under an external
forcing is derived for large amplitude equatorial Rossby wave in a
shear flow. And then various periodic-like structures for these
equatorial Rossby waves are obtained with the help of Jacobi
elliptic functions. It is shown that the external forcing plays an
important role in various periodic-like structures. 相似文献
5.
In this paper,we investigate a(2+1)-dimensional nonlinear equation model for Rossby waves in stratified fluids.We derive a forced Zakharov–Kuznetsov(ZK)–Burgers equation from the quasigeostrophic potential vorticity equation with dissipation and topography under the generalized beta effect,and by utilizing temporal and spatial multiple scale transform and the perturbation expansion method.Through the analysis of this model,it is found that the generalized beta effect and basic topography can induce nonlinear waves,and slowly varying topography is an external impact factor for Rossby waves.Additionally,the conservation laws for the mass and energy of solitary waves are analyzed.Eventually,the solitary wave solutions of the forced ZK–Burgers equation are obtained by the simplest equation method as well as the new modified ansatz method.Based on the solitary wave solutions obtained,we discuss the effects of dissipation and slowly varying topography on Rossby solitary waves. 相似文献
6.
(2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect
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In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given. 相似文献
7.
The paper deals with the effects of non-stationary external source forcing and dissipation on algebraic Rossby solitary waves.From quasi-geostrophic potential vorticity equation,basing on the multiple-scale method,an inhomogeneous Korteweg-de Vries-Benjamin-Ono-Burgers(KdV-B-O-Burgers) equation is obtained.This equation has not been previously derived for Rossby waves.By analysis and calculation,four conservation laws associated with the above equation are first obtained.With the help of pseudo-spectral method,the waterfall plots are obtained and the evolutional characters of algebraic Rossby solitary waves are studied.The results show that non-stationary external source and dissipation have great effect on the generation and evolution of algebraic solitary Rossby waves. 相似文献
8.
The paper deals with the effects of non-stationary external source forcing and dissipation on algebraic Rossby solitary waves. From quasi-geostrophic potential vorticity equation, basing on the multiple-scale method, an inhomogeneous Korteweg-de Vries-Benjamin-Ono-Burgers (KdV-B-O-Burgers) equation is obtained. This equation has not been previously derived for Rossby waves. By analysis and calculation, four conservation laws associated with the above equation are first obtained. With the help of pseudo-spectral method, the waterfall plots are obtained and the evolutional characters of algebraic Rossby solitary waves are studied. The results show that non-stationary external source and dissipation have great effect on the generation and evolution of algebraic solitary Rossby waves. 相似文献
9.
Construction of doubly-periodic solutions to nonlinear partial differential equations using improved Jacobi elliptic function expansion method and symbolic computation 总被引:2,自引:0,他引:2
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Some doubly-periodic solutions of the Zakharov--Kuznetsov equation are
presented.
Our approach is
to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function
solutions to construct doubly-periodic solutions of the Zakharov--Kuznetsov
equation, which has been derived by Gottwald as a two-dimensional model for
nonlinear Rossby waves. When the modulus k \rightarrow 1, these solutions reduce
to the solitary wave solutions of the equation. 相似文献
10.
The (2 1)-dimensional nonlinear barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a beta-plane channel is investigated by using the classical Lie symmetry approach. Some types of group-invariant wave solutions are expressed by means of the lower-dimensional similarity reduction equations. In addition to the known periodic Rossby wave solutions, some new types of exact solutions such as the ring solitary waves and the breaking soliton type of vorticity solutions with nonlinear and nonconstant shears are also obtained. 相似文献
11.
The two-dimensional (2D) nonlinear Rossby waves described by the Petviashvili equation, which has been invoked as an ageostrophic extension of the barotropic quasi-geostrophic
potential vorticity equation, can be investigated through the exact periodic-wave solutions for the Petviashvili equation, while the exact analytical periodic-wave solutions to the
Petviashvili equation are obtained by using the Jacobi elliptic function expansion method. It is shown that periodic-wave 2D Rossby solutions can be obtained by this method, and in the limit cases, the 2D Rossby soliton solutions are also obtained. 相似文献
12.
The (2 1)-dimensional nonlinear barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a beta-plane channel is investigated by using the classical Lie symmetry approach. Some types of group-invariant wave solutions are expressed by means of the lower-dimensional similarity reduction equations. In addition to the known periodic Rossby wave solutions, some new types of exact solutions such as the ring solitary waves and the breaking soliton type of vorticity solutions with nonlinear and nonconstant shears are also obtained. 相似文献
13.
In this paper, we investigate the dimensional nonlinear Rossby waves under non-traditional approximation. Using the asymptotic methods of multiple scales and weak nonlinear perturbation expansions, we derive a new modified Zakharov–Kuznetsov equation from the barotropic potential vorticity equation with the complete Coriolis parameter, the topography and the dissipation. Based on the new auxiliary equation method, new exact solutions of the new mZK equation are obtained when the dissipation is absent. However, the new auxiliary equation method fails to solve the new mZK equation with the dissipative term. Therefore, the weak nonlinear method and the homotopy perturbation method are developed to solve the obtained new mZK equation. Through numerical simulations, the results show the effects of different parameters on Rossby waves. 相似文献
14.
从准地转位涡方程出发,采用摄动方法和时空伸长变换推导了在缓变下垫面和耗散共同作用的Rossby代数孤立波方程,得到Rossby波振幅满足带有缓变下垫面的非齐次Benjamin-Davis-Ono-Burgers(BDOBurgers)方程的结论.指出地形效应和耗散是诱导非线性Rossby波产生的重要因素,说明了在缓变下垫面强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次BDO-Burgers方程,给出在切变基本气流下缓变下垫面和正压流体中Rossby波的相互作用. 相似文献
15.
DOU Fu-Quan SUN Jian-An DUAN Wen-Shan LU Ke-Pu 《理论物理通讯》2007,48(4):584-590
Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the (3+1)-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures (new dromions) are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures (dromions) are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic. 相似文献
16.
在层结流体中, 从带有地形、热外源耗散的下边界条件以及带有热外源的准地转位涡方程开始, 使用小参数展开方法和多尺度时空伸长变换推导出了具有热外源、β效应和地形效应的强迫Rossby孤立波方程, 得到孤立Rossby振幅满足的带有地形与热外源的非齐次非线性的Schrödinger方程. 通过分析Rossby孤立波振幅的变化, 指出了热外源、β效应和地形效应都是诱导Rossby孤立波产生的重要因素, 给出了切变基本流下地形、热外源和层结流体中Rossby的相互作用. 相似文献
17.
Robert Conte K.W. Chow 《理论物理通讯》2006,46(6):961-965
The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system. 相似文献
18.
Third and fifth order nonlinear wave equations which arise in the theory of water waves possess solitary and periodic traveling waves. Solitary waves also arise in systems with dissipation and instability where a balance between these effects allows the existence of dissipative solitons. Here we search for a model equation to describe long wave dissipative solitons including fifth order dispersion. The equation found includes quadratic and cubic nonlinearities. For periodic solutions in a small box we characterize the rate of growth, and show that they do not blow up in finite time. Analytic solutions are constructed for special parameter values. 相似文献
19.
By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg-de Vries (KdV)-Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influence of dissipation and slowly varying topography with time. The analysis indicates that dissipation and slowly varying topography with time are important factors in causing variation in the mass and energy of solitary waves. 相似文献
20.
By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg-de Vries (KdV)-Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influence of dissipation and slowly varying topography with time. The analysis indicates that dissipation and slowly varying topography with time are important factors in causing variation in the mass and energy of solitary waves. 相似文献