Wave overtopping discharge for very gently sloping foreshores

Abstract

The spectral wave period Tm-1,0 at the toe of sea-dikes is a crucial parameter to predict wave overtopping discharge over sea-dikes. It is known from literature that this period quickly increases when waves reach shallow foreshores; however, sometimes the assumption is made that the wave period remains constant from offshore to near-shore, leading to an underestimation of the near-shore wave period. Several formulae have been proposed to resolve the underestimation of wave overtopping discharges for very shallow foreshores. These corrective formulations confirm the tendency of underestimating the overtopping discharges over a very gently sloping foreshore but are not validated for foreshore slopes gentler than 1:500. The "equivalent slope" method based on a recent study is inappropriate for these very gently sloping foreshores due to the breaker parameter being much smaller than seven. This study proposes an extension of the correction and finds that spectral wave periods can reach values two times those offshore.