Abstract
The small-amplitude wave theory was formulated as a solution to the Laplace equation with the required surface (two) and bottom (one) boundary conditions [Eqs. (2.1), (2.3), (2.4), and (2.6)]. But the two surface boundary conditions had to be linearized and then applied at the still water level rather than at the water surface. This requires that H/d and H/L be small compared to unity. Consequently, the small-amplitude wave theory can be applied over the complete range of relative water depths (d/L), but it is limited to waves of relatively small amplitude relative to the water depth (for shallow water waves) and wave length (for deep water waves).
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