地形及标量非线性作用下的Rossby孤立波机制研究

The Mechanism of Rossby Solitary Waves under Topography and Scalar Nonlinearity

地形及标量非线性作用下的Rossby孤立波具有不同的演化机制,为理解及解释实际大气运动提供了一定的理论依据。首先,从具有球面效应下的地转平衡和浅水模型出发,利用尺度分析等手段得到了具有标量非线性项意义下的位势涡度守恒方程。其次,利用多重尺度及摄动展开法,推导了非线性Rossby孤立波振幅演变所满足的Gardner方程。通过定性分析及定量数值计算模拟了Rossby孤立波的生成、发展过程。揭示了地形、标量非线性在Rossby孤立波的激发和传播中有着重要作用。

The evolution mechanism of Rossby solitary waves with topographic and scalar nonlinearity is studied.It provides some theoretical basis for knowing and explaining the actual atmospheric motion.Firstly,based on the geostrophic equilibrium and shallow water model with spherical effect,the conservation equation of potential vorticity with scalar nonlinear term is calculated by means of scaling analysis.Secondly,the Gardner equation for the amplitude evolution of nonlinear Rossby solitary waves are obtained by using multi-scale and perturbation expansion methods.The generation and development of Rossby solitary waves are simulated by qualitative analysis and quantitative numerical calculation.It is revealed that terrain and scalar nonlinearity play critical roles in excitation and propagation of Rossby solitary waves.