The latter complemented his experimental results with an analytical runup calculation using shallow water

theory (3), which is valid for non-breaking waves. The runup was defined in the mathematical model as the maximum wave amplitude above the initial shoreline position, at the maximum penetration of the wave (also in Tadepalli and Synolakis (1996)). Runup regimes were observed to be different according to the breaking or non-breaking nature of the waves. Experimental results agree with (3) for non-breaking waves. However, the predicted trend moves away from the non-breaking wave data at higher amplitudes, suggesting that wave amplitude does not account for the total variability in runup for highly non-linear waves. Similarly to Eq. (2), Eq. (3) highlights a strong dependence of runup on wave amplitude and takes into account Androgen Receptor antagonist the beach slope. Generally, previous Everolimus supplier research highlights that beach slope is an influential parameter on wave runup (i.e., Fuhrman and Madsen, 2008). The dependence of runup on this parameter appears complex. For example, the results from Li and Raichlen (2002) show that non-breaking waves runup higher for milder slopes, while breaking waves exhibit the opposite trend. In the field, shallow slopes

bordering continental coasts are a common feature. The analysis of the 2011 Japan tsunami field-based data by Nassirpour (2012) indicates that local variations in slope along transects of the continental shelf (East coast of Japan) do not seem to correlate with learn more high local variations in runup. Another interesting result from the numerical study of Borthwick et al. (2006) suggests that there is an upper value to the wave runup for beach slopes between 1:100 and 1:5 – irrespective of the wave height, which corresponds to Eq. (2) with α = 3.02 and γ = 0.91. Table 2 summarizes the values for α and γ obtained in previous studies ( Hall and Watts, 1953, Synolakis, 1987 and Borthwick et al., 2006). Despite the range of slopes and variety of experiments, there are only weak variations in the empirical values of α and

γ, with γ close to the value of 1- result consistent with a contribution of H of the same magnitude as the runup itself. Without knowing the form of the functional relationships for α and γ, it is not possible to know from (2) how slope influences runup. Eq. (3) would indicate that the runup is larger on shallower beaches for non-breaking waves, which agrees with the results from Li and Raichlen (2002). Indeed, the effects of shoaling are paramount on shallower slopes. It is worth noting that the effects of bed friction on shallow slopes are also important, and may lead to some dissipation of wave energy. The influence of wave shape on runup has been partially addressed in the analytical and numerical studies of Tadepalli and Synolakis, 1994 and Tadepalli and Synolakis, 1996, where waves with different profiles, namely solitary and N-waves, are treated separately.