ON STEP APPROXIMATIONS FOR WATER-WAVE PROBLEMS

The scattering of water waves by a varying bottom topography is consid ered using two-dimensional linear water-wave theory. A new approach is adopted in which the problem is first transformed into a uniform stri p resulting in a variable free-surface boundary condition. This is the n approximated by a finite number of sections on which the free-surfac e boundary condition is assumed to be constant. A transition matrix th eory is developed which is used to relate the wave amplitudes at +/-in finity. The method is checked against examples for which the solution is known, or which can be computed by alternative means. Results show that the method provides a simple accurate technique for scattering pr oblems of this type.