EFFECT OF DEPTH ON THE PATTERN-FORMATION OF FARADAY WAVES

The symmetry of standing wave patterns on the surface of a vertically oscillated fluid layer depends on the depth of the layer. In a large e xperiment we trace out the stability diagram. The dependency can be un derstood on the basis of the oscillatory character of the waves and th e dispersion relation. A simple amplitude equation can be constructed with the variation with depth of the dispersion relation and a general quadratic nonlinearity as its only ingredients. The predictions of th is model agree well with the experiment.