Built on

Joseph B. Keller ”Surface waves on water of non-uniform depth” J. fluid Mech. 4
1972
Earlier work this paper cites.
C. M. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation
1973
Earlier work this paper cites.

Similar

S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-time
1973
Cited alongside, same era.
R.M. Wald ”General Relativity” U. Chicago Press (1984)
1984
Cited alongside, same era.

Then

¨ R. Schützhold and W. G. Unruh, Phys. Rev. D 66
2002
Later among the works it cites.
http://en.wikipedia.org/wiki/Mild-slope_equation (retrieved Oct 10,2011)
2011
Later among the works it cites.

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2012

Irrotational, two-dimensional Surface waves in fluids

Unruh, W. G.

Understand

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.