SHOALING OF SOLITARY WAVES ON PLANE BEACHES

Shoaling of solitary waves on both gentle (1:35) and steeper slopes (l ess-than-or-equal-to 1:6.50) is analyzed up to breaking using both a f ully nonlinear wave model and high-accuracy laboratory experiments. Fo r the mildest slope, close agreement is obtained between both approach es up to breaking, where waves become very asymmetric and breaking ind ices reach almost twice the value for the largest stable symmetric wav e. Bottom friction does not seem to affect the results at all. Wave ce lerity decreases during shoaling and slightly increases before breakin g. At breaking, the crest particle velocity is almost horizontal and r eaches 90% of the crest celerity, which is two to three times larger t han the bottom velocity. The nonlinear shallow water (NSW) equations a nd the Boussinesq approximation both fail to predict these results. Fi nally, shoaling rates for various wave heights and bottom slopes diffe r from the predictions of Green's or Boussinesq shoaling laws. On the mildest slope, shoaling rates roughly follow a ''two-zone'' model prop osed earlier but on steeper slopes reflection becomes significant and wave heights change little during shoaling.