APPROXIMATIONS TO WAVE-TRAPPING BY TOPOGRAPHY

The trapping of linear water waves over two-dimensional topography is investigated by using the mild-slope approximation. Two types of bed p rofile are considered: a local irregularity in a horizontal bed and a shelf joining two horizontal bed sections at different depths. A numbe r of results are derived concerning the existence of trapped modes and their multiplicity. It is found, for example, that the maximum number of modes which can exist depends only on the gross properties of the topography and not on its precise shape. A range of problems is solved numerically, to inform and illustrate the analysis, using both the mi ld-slope equation and the recently derived modified mild-slope equatio n.