A Regression Analysis Result for Water Waves on Irrotational Flow over a Horizontal Bed

摘要

For the purposes of engineering applications in offshore structure design, an analytical approximation is presented. The solution is based on a Fourier series expansion. An approximation is derived with a geometric series, which is simple and closer to a Jacobi elliptic function in shallow water or the trochoid in deep water. By applying the approximation to the two boundary conditions on the free surface, the total error is obtained, which gives a functional to determine the related constants by regression analysis. As a regression analysis, the least squares method is considered. For the regression analysis, all field quantities are represented in dimensionless forms. The constants are presented with closed forms. The approximation is simple and valid for all waves including those in the solitary wave limit and in the deepwater wave limit.