一种改善了非线性和色散性的Boussinesq方程模型

推导了一种在不平底上的新的Boussinesq方程．在不增加方程的最高导数项的阶数的情况下提高了模型方程的非线性．为了提高模型的色散性，引入长波近似，通过调节待定系数来使模型的色散性达到Padé(2,2)．对模型方程进行了非线性、线性色散性和线性浅化性分析，分析表明此模型在非线性、色散性和浅化性上都有所提高．将计算结果与实验数据做了比较，结果显示模型更好的符合了实验数据．

A Boussinesq Model With Improved Nonlinearity and Dispersion

A new form of Boussinesq model over uneven bottom is derived.In the new model,the nonlinearity is improved without increasing the orders of the highest derivative of the differential equations.The dispersion relationship of the model was improved to the order of Pad (2,2)by adjusting a parameter in the model based on the long wave approximation.The analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the nonlinearity,dispersion and shoaling of this model are improved.The numerical results obtained for the present model were compared with the experimental data,and it is found that the predicted results agree with the experimental data.