Irrotational, two-dimensional surface waves in fluids

Abstract

The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying bottom topography. Most importantly, the conserved norm for the surface waves is derived, important for quantisation of these waves and their use in analogue models for black holes. © Springer International Publishing Switzerland 2013.