一个大气定常波的非线性初始方程谱模式
A NONLINEAR PRIMITIVE EQUATION SPECTRAL MODEL OF STATIONARY WAVES IN THE ATMOSPHERE
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摘要: 本文提出了一个可以用于大气定常波数值模拟的非线性初始方程三维谱模式,模式的动力学框架与文献[1]中的线性模式是相互对应的。利用线性模式的定常解作为初值,通过Newton-Raphson迭代法求出了收敛的非线性定常解。文中给出了这一模式大气对于北半球大尺度地形和1979年1月平均非绝热加热场的响应作为计算实例,并与对应的线性响应以及观测事实进行了对比,证明在考虑了大气中波动之间的非线性相互作用之后数值模拟的结果确实比线性模式有显著的改进,尤其是对于低纬环流系统更是如此。这表明了非线性作用对于热带环流系统的极端重要性。Abstract: A nonlinear, steady-state, baroclinic, primitive equation, numerical model of forced stationary waves in the atmosphere is developed. In the model, the vertical structure is represented by truncated series of normalized Legendre polynomials with a as argument and the horizontal structure of each vertical mode is described in terms of spherical harmonics. Newtonian cooling, Rayleigh friction and biharmonic horizontal diffusion are included in the model. The method used in the computation of nonlinear terms is a generalization to three dimensions of the transform method. The solution of a linear model,which corresponds to the nonlinear one in all aspects except that the basic equations are linearized by the perturbation method, is used as the initial guess and then the steady-state, convergent, nonlinear solution is obtained by using Newton-Raphson iteration.Besides that the basic model and the numerical procedure are outlined, the results of some preliminary experimental tests of the model are also presented.Comparison of nonlinear model solution with corresponding linear solution for the response to the Northern Hemispheric topography and diabatic heating in January 1979 shows that the nonlineaYities are of primary importance in simulation of the stationary waves in the real atmosphere, especially in the tropical region.
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