HIGHLY NONLINEAR STANDING WATER-WAVES WITH SMALL CAPILLARY EFFECT

We calculate spatially and temporally periodic standing waves using a spectral boundary integral method combined with Newton iteration. When surface tension is neglected, the non-monotonic behaviour of global w ave properties agrees with previous computations by Mercer & Roberts ( 1992). New accurate results near the limiting form of gravity waves ar e obtained by using a non-uniform node distribution. It is shown that the crest angle is smaller than 90 degrees at the largest calculated c rest curvature. When a small amount of surface tension is included, th e crest form is changed significantly. It is necessary to include surf ace tension to numerically reproduce the steep standing waves in Taylo r's (1953) experiments. Faraday-wave experiments in a large-aspect-rat io rectangular container agree with our computations. This is the firs t time such high-amplitude, periodic waves appear to have been observe d in laboratory conditions. Ripple formation and temporal symmetry bre aking in the experiments are discussed.