摘要
加权残值法可以统一处理任一学科的几乎所有问题,在应用加权残值法建立的变分原理导出线性波、孤立波和五阶斯托克斯波的基础上,应用加权残值法统一处理水重力波问题,不必应用不同的方法导出不同的波浪理论;直接处理运动自由表面边界条件和动力自由表面边界条件,不必应用其等价的条件,并得出惟一的最优化解。当用原有的导出波浪理论的方法所得的解为非惟一时,应用加权残值法建立的泛函可判断出合理的解。对于原有的导出波浪理论的方法,当波高h、周期T、水深d给定后,其结果也就确定了,如果发现其与实际情况不符,也不能再进行调整,但加权残值法则可以增加几个约束条件进行调整,例如根据波峰的精确位置等条件对波剖面的形状进行调整。文中实例表明,加权残值法导出的波浪理论在满足运动自由表面边界条件和动力自由表面边界条件方面,在误差平方和最小意义上优于原有的波浪理论。
For reason that the method of weighted residuals(MWR) can be used to solve almost all problems in any subject, and based deriving linear wave, solitary wave and fifth order Stocks wave with the variational principle established by MWR, the integral method for handling the problems of water gravity wave with MWR instead of deriving different wave theory with different methods is presented in this paper. In this paper, the kinetic free surface boundary condition(KFSBC) and dynamic free surface boundary condition (DFSBC) can be handled directly instead of using the equivalent conditions, and the unique optimum solution could be given. As the non-unique solutions are given with existing method for deriving wave theory, the reasonable solution can be judged with the functional established by MWR. For the existing method of deriving wave theory, as the wave height h, period t and water depth d are given, then the results are also determined, if they are not agreeable with the real case, the adjustment could be put up with adding several restricted conditions. For example, wave profile can be adjusted according to the accurate position of wave crest. The example given in this paper shows that the wave theory derived by MWR is better than the existing one in the meaning of minimum error squares by MWR for satisfying KFSBC and DFSBC.
