Yin Tianle, Du Yajun, Wang Weiqing, Pang Jing, Yan Zhenya
College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China.
Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling, Hohhot 010051, China.
Chaos. 2024 Sep 1;34(9). doi: 10.1063/5.0228604.
Starting from the classical quasi-geostrophic potential vorticity equation with equal depth two-layer fluid, the coupled cylindrical Kadomtsev-Petviashvili (KP) equations with variable coefficients for Rossby waves are studied. To be more general, the phase velocity is considered an indefinite integral about time and improves the analysis procedure. So the variable coefficients are obtained and some previous studies are reasonably explained. The cylindrical wave theory is therewith utilized to reduce the coupled cylindrical KP equations with variable coefficients, and based on the modified Hirota bilinear method, the lump solutions and interaction solutions are found. Through numerical simulations, the Rossby lump waves on both sides of the y axis move closer to the center, and their amplitude gradually decreases and tends to flatten with the generalized Rossby parameter growth. In the Rossby waves flow field, the dipole structures propagate to the east and lead to the appearance of the compress phenomenon during barotropic-baroclinic interaction. It is possibly useful for further theoretical research on atmospheric phenomena.
从具有等深两层流体的经典准地转位涡方程出发，研究了罗斯贝波的变系数耦合圆柱 Kadomtsev-Petviashvili（KP）方程。更一般地，将相速度视为关于时间的不定积分并改进了分析过程。由此得到了变系数并合理地解释了一些先前的研究。利用圆柱波理论化简了变系数耦合圆柱 KP 方程，并基于修正的广田双线性方法，找到了块状解和相互作用解。通过数值模拟，y 轴两侧的罗斯贝块状波向中心靠近，且随着广义罗斯贝参数的增大，其振幅逐渐减小并趋于平缓。在罗斯贝波流场中，偶极结构向东传播，并在正压-斜压相互作用期间导致压缩现象的出现。这可能对大气现象的进一步理论研究有用。
