Solitary wave transformation, breaking and run-up at a beach

<jats:p> A validated one-dimensional Boussinesq–non-linear shallow water equations numerical model was used to investigate the interaction of solitary waves with beaches. The numerical model requires two adjustable parameters: the bed friction coefficient and a wave breaking parameter. Excellent agreement was achieved between the numerical predictions of solitary wave transformation and run-up at a plane beach with two sets of high-quality laboratory measurements: one a large number of experiments in a wave flume by Synolakis, the other in the UK Coastal Research Facility. A parameter study investigated the effect of uniform offshore water depth, bed friction and bed slope on solitary wave run-up. A uniform water depth may be associated with a continental shelf region. The non-dimensional run-up was found to be an asymptotic function of non-dimensional wave amplitude at high and low values of initial wave steepness. Both asymptotes scale as (R/h<jats:sub>o</jats:sub>)∼α(A<jats:sub>o</jats:sub>/h<jats:sub>o</jats:sub>)<jats:sup>β</jats:sup> where R is run-up (defined as the vertical elevation reached by the wave uprush above still water level), A<jats:sub>o</jats:sub> is the offshore wave amplitude and h<jats:sub>o</jats:sub> is the uniform depth offshore of the beach. The empirical coefficients α and β depend on the beach characteristics. The model is then used to simulate the interaction of a full-scale tsunami event with an idealised beach profile representative of a beach in Eastern Kamchatka. </jats:p>