We consider the profile of two-dimensional standing gravity waves and their linear stabilities. We have obtained the result that the maximum wave steepness is 0.61. The instability with maximum growth rate is three-dimensional for the wave steepness 0.1. Instabilities due to the four-wave resonance occur but those due to the five-wave resonance are not found for wave steepness smaller than 0.15.
!!!All Science Journal Classification (ASJC) codes