均匀连续分层流的自由面格林函数

Free-Surface Green's Function of Internal Waves in Uniformly Stratified Fluid

考虑自由表面的影响,理论上建立密度均匀连续分层流中脉动点源生成内波的数理模型和分析方法.应用Fourier变换和围道积分,推导出频率大于Brunt-Visl频率带自由面的连续分层流体中脉动点源格林函数,并给出了详细的解析表达式,讨论了解的性质和自由面的波动特征.当点源脉动频率大于Brunt-Visl频率时,格林函数解析解相应的是由于密度均匀连续分层对等密度流体中脉动点源格林函数的影响,在自由面上的辐射波项表现最为直观.

A mathematical model and analysis methods for the internal waves generated by pulsating point sources were theoretically established,and the analytic expression of the free-surface Green＇s function forω2N2 in uniformly density-stratified fluids was derived based on the Fourier transformation and contour integration technique,where N is the buoyancy（or Brunt-Visl）frequency.Compared with the previous Green＇s function of internal waves,this paper laid emphasis on the consideration of the free surface.A complete description of the properties of solution and the free-surface fluctuation characteristics were discussed in detail.In fact,the pulsating sources do not produce the real internal waves whenω2N2.The analytical solution corresponds to the influence of density uniformly stratified upon the commonly used Green＇s function,which is extremely intuitive on the radiation term.