Irrotational, two-dimensional Surface waves in fluids
  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 analog models for black holes. 
W. G. Unruh
gr-qc physics.flu-dyn