Cnoidal Standing Waves and the Transition to the Traveling Hydraulic Jump.

摘要

Standing waves of finite amplitude in an enclosed basin are considered. it is shown that the existing theory of Tadjbakhsh and Keller (1960) breaks down at a critical value of the amplitude dependent upon the depth. By formal perturbation expansion it is found that the solutions change to cnoidal standing waves at this critical value of the amplitude. An experiment is constructed which verifies this theory and also elucidates the wavefield when the amplitude is much larger than the critical amplitude. Based on the experimental observations, a cascade theory is proposed to explain the transition to a traveling hydraulic jump. Keywords: Cnoidal waves; Bifurcation; Experimental observations. (Reprints)