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 experiment we trace out the stability diagram. The dependency can be understood on the basis of the oscillatory character of the waves and the 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 this model agree well with the experiment.