Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,...Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.展开更多
在实现e^(N)方法时,需要搜索流场中的不稳定波,并大量求解当地边界层的稳定性问题,因此为高效求解当地边界层的不稳定波参数,提出了一种基于神经网络的线性稳定性分析方法(neural network-based linear stability analysis,NNLSA)。采...在实现e^(N)方法时,需要搜索流场中的不稳定波,并大量求解当地边界层的稳定性问题,因此为高效求解当地边界层的不稳定波参数,提出了一种基于神经网络的线性稳定性分析方法(neural network-based linear stability analysis,NNLSA)。采用卷积神经网络给出最不稳定波频率ω、展向波数β、流向波数αr和增长率σmax的初值对,再通过迭代法计算失稳扰动波的实际空间失稳波数和增长率。使用平板数据集训练神经网络模型,并利用平板和尖锥算例对NNLSA方法的准确性和计算效率进行验证。结果表明:神经网络部分对不稳定波参数的预测结果与线性稳定性理论的计算结果吻合较好;LSA部分可根据神经网络提供的预测值,通过迭代法找到最不稳定波;NN-LSA方法的求解效率较高,求解时间比全局搜索方法约低20~50倍,大大减小了人为因素在计算过程中的影响。本文提出的NN-LSA方法可以实现自动分析边界层流动的线性稳定性,具有一定的应用潜力。展开更多
文摘Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.
文摘在实现e^(N)方法时,需要搜索流场中的不稳定波,并大量求解当地边界层的稳定性问题,因此为高效求解当地边界层的不稳定波参数,提出了一种基于神经网络的线性稳定性分析方法(neural network-based linear stability analysis,NNLSA)。采用卷积神经网络给出最不稳定波频率ω、展向波数β、流向波数αr和增长率σmax的初值对,再通过迭代法计算失稳扰动波的实际空间失稳波数和增长率。使用平板数据集训练神经网络模型,并利用平板和尖锥算例对NNLSA方法的准确性和计算效率进行验证。结果表明:神经网络部分对不稳定波参数的预测结果与线性稳定性理论的计算结果吻合较好;LSA部分可根据神经网络提供的预测值,通过迭代法找到最不稳定波;NN-LSA方法的求解效率较高,求解时间比全局搜索方法约低20~50倍,大大减小了人为因素在计算过程中的影响。本文提出的NN-LSA方法可以实现自动分析边界层流动的线性稳定性,具有一定的应用潜力。
