海气耦合非线性随机模式求解探讨

Analysis of Solution of Nonlinear Stochastic Model with Air-Sea Interaction

本文首先对一个假定随机强迫为高斯白噪声的四次方非线性海气耦合随机模式进行了ε一阶近似的摄动处理，将非线性随机模式化为显含随机项的线性系统和隐含随机项的非线性系统，通过对输出响应的分析表明：该模式结构和随机项的特性使得随机强迫输出的响应只能通过模式的线性区；非线性项仅对气候系统的方差及其对应的频谱有一定量的偏差作用．而对一般输出特性没有贡献。在这基础上，求出了模式输出谱，并给出了计算。

In this paper, using perturbation teChnique of one order approximation, a quartic nonlinear stochastic model of air-sea interaction is deduced to a linear system with random item and a nonlinear system without random item. By analyzing the output response, it is found that the model's self-orrelation function and its power speCtral density is not affected by nonlinear item and the variance of climatic system as well as its speCtrum is only affeCted under the condition that random process is a Gaussian process. On the basis of above, the response spectral density and calculations of the model are carried out.