Energy dissipation in breaking solitary and periodic waves

It is well known (see Divoky et al., 1970, for a review) that on gentle slopes (slope S < 1:30, say) the wave height after breaking does not decay in proportion to the mean depth. The curve H/Hb vs h/hb is concave upwards (for plane bottom). The concavity increases with decreasing S and with increasing Ho/Lo (Nakamura et al., 1966). The often-used hypothesis H(x) = gamma h(x), gamma = const. for given (S, Ho/Lo)' does not incorporate the effects mentioned above. Its success in the prediction of set-up can perhaps be ascribed Co the fact that it has been tested mainly on plane and relatively steep slopes, where indeed it is in reasonable agreement with the data. The hypothesis H = gamma h is not applicable in regions where the depth is constant or increasing in the propagation direction, such as in a bar-trough profile. Visual observations of the latter situation cannot fail but to give the impression that the immediate post-breaking behavior is governed primarily by the characteristics at breaking, with its own imposed length scale. The bottom slope is believed to affect this behavior only if it is sufficiently steep, so that the rate of change of wave height due to changes in depth ("shoaling" with either increasing or decreasing depth) is comparable to that due to breaking.Civil Engineering and Geoscience