ANALYSIS OF DISPERSION AND SHOALING CHARACTERISTICS OF LINEARIZED MILD-SLOPE EQUATIONS

摘要

In this paper, the linearized form of the nonlinear mild-slope equations derived by Isobe (1994) is considered and analyzed for the dispersion, group velocity and shoaling charac- teristics. It is found that the dispersion relation is just a Pade's expansion of that obtained by the small amplitude wave theory. The agreement of the dispersion relation, group ve- locity and gradient of shoaling coefficient with the small amplitude wave theory is good from shallow to deep water even with small numbers of terms of the series in the mild- slope equations. The dispersion relation is also examined for evanescent waves. Further- more, the vertical distribution functions for progressive and evanescent waves are analyzed and compared with the small amplitude wave theory. Then, the water depth limitation corresponding to the number of terms in the even-order polynomial vertical distribution functions is suggested.