SMALL-AMPLITUDE WAVES IN A STRAIGHT CHANNEL OF UNIFORM TRIANGULAR CROSS-SECTION

Abstract

The symmetric modes of oscillation are obtained for infinitesimal waves in a uniform channel whose cross-section is a triangle with sides inclined at 30° to the horizontal. The two lowest-order modes are those found by Macdonald. The higher-order modes are generalisations of those in Greenhili's solution for purely transverse oscillations in the same channel which is found to be in need of modification since the assumed form of solution excludes certain of the modes whilst at the same time other spurious modes have been introduced. Greenhill's solution is the limit as the wavelength along the channel tends to infinity. For short waves the modes tend to those for a rectangular channel whose width is the free surface width of the channel.