非定常基本流作用下的高维Rossby孤立波模型及机制研究  

High Dimensional Rossby Solitary Wave Model and its Mechanism under Unsteady Flow

作　　者：张志慧 刘全生[1] 尹晓军[2] 杨联贵[1] 张瑞岗[1] Zhang Zhihui;Liu Quansheng;Yin Xiaojun;Yang Liangui;Zhang Ruigang(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;College of Science,Inner Mongolia Agriculture University,Hohhot 010018,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古农业大学理学院,时呼和浩特010018

出　　处：《水动力学研究与进展(A辑)》2024年第6期874-882,共9页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金项目(Nos.12102205,12262025及12362027);内蒙古自治区高等学校“青年科技英才支持项目”(NJYT23098);内蒙古自治区高等学校创新团队(No.NMGIRT2208);内蒙古自治区研究生科研创新项目(S20231025Z)。

摘　　要：基于揭示非线性Rossby波动物理机制的主要目标,该文从浅水方程组出发,通过进一步简化方程,推导得到了无量纲准地转位涡守恒方程。利用时空变换和摄动法推导了地形作用下的Rossby波振幅演变所满足的(2+1)维变系数Zakharov-Kuznetsov(Z-K)方程,利用Jacobi椭圆函数展开法对其求解。随后,数值分析表明了基本西风气流强度、地形效应和基本流剪切效应对偶极子阻塞和振幅的影响。该研究结果丰富了大气阻塞现象的理论解释。The primary objective of this paper is to reveal the dynamic mechanism of nonlinear Rossby waves.By simplifying the shallow water equation system,the dimensionless quasi-geostrophic vortex conservation equation is derived.The equation displaying the amplitude evolution of the Rossby wave influenced by topography is derived using the spatio-temporal strain transformation and perturbation method as a(2+1)-dimensional Zakharov-Kuznetsov(Z-K)equation with variable coefficients.And the solution is obtained by utilizing the expansion method of Jacobi elliptic function.Numerical analysis demonstrates the impact of basic westerly wind strength,topography and basic flow shear on dipole blocking and amplitude.The results enrich the theoretical explanation of the atmospheric blocking phenomenon.

关 键 词：ROSSBY波 变系数Z-K方程 偶极子阻塞 JACOBI椭圆函数展开法 

分 类 号：O352[理学—流体力学]