クノイド波に関する研究(第1報) ―波形こう配および波形について―

Abstract

The conidal waves, which were discovered by Korteweg and de Vries in 1895, are notfamiliar for engineers in spite of a long history because of mathematical treatments includingthe Jacobian elliptic function and the complete elliptic integrals of the first and second kinds.Since, however, it is noticed that the theory of Stokes waves is not appropriate to periodicwaves progressing in shallow water whose depth is less than about one-tenth the wave length, but the theory of enoidal waves should he applied to those waves, it is necessary to modifythe theoretical results of cnoidal waves and provide the graphs to find easily the wavecharacteristics.This paper presents, as the first report, the graphs and the method to compute the waveprofile from given wave steepness and the water depth to wave height ratio based on theconidal wave theory developed by Laitone in 1960 and, in addition, compares the first andsecond approximations of his solution, Stokes waves of the third order approximation andthe solitary wave.