Computation of set-up, longshore currents, run-up and overtopping due to wind-generated waves

Abstract

The main problem dealt with in this thesis is the calculation of certain effects caused by random waves breaking on a slope. The solution to this problem is greatly complicated by the fact that wave breaking is a highly nonlinear process. The flow field is further complicated by far stronger in homogeneities than those occurring outside the breaker zone, by air entrainment and by generation of turbulence. No realistic deductive treatment of it has been developed so far. Even for the simpler case of periodic waves, empirical knowledge of certain macroscopic properties of the breakers is still an integral part of calculations relating to the surf zone. An attempt has been made in this thesis to apply this knowledge in a formulation incorporating the stochastic nature of wind-generated waves. The computations are of two distinct categories, those relating to comparatively gentle slopes and those relating to comparatively steep slopes. A summary of the results will be given in the following. The energy variation is calculated in chapter 5 by clipping a fictitious wave height distribution, which theoretically would be present if breaking did not occur, at an upper limit which is determined from an adapted breaking criterion for periodic waves. The computed results are in fair agreement with measurements carried out on a plane slope. Knowledge of the energy variation permits the radiation stresses to be evaluated, which in turn are necessary for the calculation of the set-up and the longshore current velocity profiles. A comparison of the calculated set-up profiles with empirical data has not given conclusive results. Good agreement has been found with field data, but not with laboratory data, which locally showed a systematically smaller rise towards the shore than would be expected on the basis of the measured or calculated wave height variations. However, there is some uncertainty with respect to the system used for measuring the set-up in the laboratory, so that is not known to which extent the differences are real or apparent.