On gravity waves in channels

The general problem of the free oscillations under gravity of a body of water in basins of variable depth, or travelling gravity waves over the free surface in canals of variable depth, has a long history. A theoretical treatment of such problems is usually based on the linearized three-dimensional theory of an incompressible inviscid fluid. Some exact solutions of these equations have been obtained for certain special basin profiles, which include those in the references cited in Lamb [1, pp. 276, 443–444], in Wehausen and Laitone [2, pp. 537–552 and 624–627] and those contained in the papers of Sen [3] and Storchi [4, 5].