Wave parameter tuning for the application of the mild-slope equation on steep beaches and in shallow water

摘要

The linear mild-slope equation (MSE) is examined in the limit of very shallow water. This is done by means of a series comparison with the more 'exact' linear classical theory (E) valid over arbitrary uniform slopes and known to have a "minimum norm" solution basis pair, respectively, regular and logarithmically singular at the shore line. It is shown that the agreement between E and MSE is exact for the first three terms for the regular wave and the first two for the singular wave.