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Shoaling of Solitary Waves on Plane Beaches

Shoaling of solitary waves on both gentle (1:35) and steeper slopes ( 1:6.50) is analyzed up to breaking using both a fully nonlinear wave model and high-accuracy laboratory experiments. For the mildest slope, close agreement is obtained between both approaches up to breaking, where waves become very asymmetric and breaking indices reach almost twice the value for the largest stable symmetric wave. Bottom friction does not seem to affect the results at all. Wave celerity decreases during shoaling and slightly increases before breaking. At breaking, the crest particle velocity is almost horizontal and reaches 90% of the crest celerity, which is two to three times larger than the bottom velocity. The nonlinear shallow water equations and the Boussinesq approximation both fail to predict these results. Finally, shoaling rates for various wave heights and bottom slopes differ from the predictions of Green's or Boussinesq shoaling laws. On the mildest slope, shoaling rates roughly follow a "two-zone" model proposed earlier but on steeper slopes reflection becomes significant and wave heights change little during shoaling.