In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A...In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.展开更多
By using the multiple-scale perturbation method a set of equations which describes two interacting nonlinear Rossby waves in the barotropic atmosphere is derived. The equations are used to study the collision of two e...By using the multiple-scale perturbation method a set of equations which describes two interacting nonlinear Rossby waves in the barotropic atmosphere is derived. The equations are used to study the collision of two envelope solitary Rossby waves. It is found that for a range of parameters, the collision interactions are envelope soliton-like in that the properties of the two envelope solitary waves change very little. For other parameters, new "inelastic" effects are observed, including speed changes, fission of envelope solitary waves and energy dispersion. It is also found that despite of the complexity of the interacting process, the energy of each wave is conserved.展开更多
Under a semi-geostrophic approximation, the equations goyeming motions in a baroclinic atmosphere read in which （2） is the condition of geostrophic balance; N, the Brunt-Visl frequency characterizing stratification;...Under a semi-geostrophic approximation, the equations goyeming motions in a baroclinic atmosphere read in which （2） is the condition of geostrophic balance; N, the Brunt-Visl frequency characterizing stratification; ρ<sub>0</sub>, the motionless air density; φ, ρ’/ρ<sub>0</sub>, with ρ’ denoting the pressure deviation from that of motionless air; ξ<sup>（0）</sup>, the geostrophic vorticity; ▽<sup>2</sup>, the twodimensional Laplace operator; and the othees are of usual implications in展开更多
利用多重尺度摄动法,推导出非线性涡旋Rossby波波包的演变方程是非线性Schr d inger方程。对该非线性Schr d inger方程的周期波动解及其稳定性进行了研究,得到了有关稳定和不稳定的判据。数值计算表明:非线性涡旋Rossby波的相速值为100...利用多重尺度摄动法,推导出非线性涡旋Rossby波波包的演变方程是非线性Schr d inger方程。对该非线性Schr d inger方程的周期波动解及其稳定性进行了研究,得到了有关稳定和不稳定的判据。数值计算表明:非线性涡旋Rossby波的相速值为100m/s量级,这和台风中的螺旋雨带实测移速的量级是一致的,可以从涡旋Rossby波说中较好地解释台风中的螺旋雨带的形成和维持。展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11562014,11762011,11671101,71471020,51839002the Natural Science Foundation of Inner Mongolia under Grant No.2017MS0108+4 种基金Hunan Provincial Natural Science Foundation of China under Grant No.2016JJ2061the Scientific Research Fund of Hunan Provincial Education Department under Grant No.18A325the Construct Program of the Key Discipline in Hunan Province under Grant No.201176the Aid Program for Science and Technology Innovative Research Team in Higher Educational Instituions of Hunan Province under Grant No.2014207Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering of Changsha University of Science and Technology under Grant No.018MMAEZD191
文摘In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.
文摘By using the multiple-scale perturbation method a set of equations which describes two interacting nonlinear Rossby waves in the barotropic atmosphere is derived. The equations are used to study the collision of two envelope solitary Rossby waves. It is found that for a range of parameters, the collision interactions are envelope soliton-like in that the properties of the two envelope solitary waves change very little. For other parameters, new "inelastic" effects are observed, including speed changes, fission of envelope solitary waves and energy dispersion. It is also found that despite of the complexity of the interacting process, the energy of each wave is conserved.
基金Project supported by the National Natural Science Foundation of China
文摘Under a semi-geostrophic approximation, the equations goyeming motions in a baroclinic atmosphere read in which （2） is the condition of geostrophic balance; N, the Brunt-Visl frequency characterizing stratification; ρ<sub>0</sub>, the motionless air density; φ, ρ’/ρ<sub>0</sub>, with ρ’ denoting the pressure deviation from that of motionless air; ξ<sup>（0）</sup>, the geostrophic vorticity; ▽<sup>2</sup>, the twodimensional Laplace operator; and the othees are of usual implications in
文摘利用多重尺度摄动法,推导出非线性涡旋Rossby波波包的演变方程是非线性Schr d inger方程。对该非线性Schr d inger方程的周期波动解及其稳定性进行了研究,得到了有关稳定和不稳定的判据。数值计算表明:非线性涡旋Rossby波的相速值为100m/s量级,这和台风中的螺旋雨带实测移速的量级是一致的,可以从涡旋Rossby波说中较好地解释台风中的螺旋雨带的形成和维持。
