Dynamical Models for Cross-Shore Transport and Equilibrium Bottom Profiles

Abstract

The long-term cross-shore dynamics of the surf zone affected by storms is investigated. The validity of the hypothesis of equilibrium bottom profiles in the coastal zone is examined using bathymetric measurements of some coastal regions in Israel for the period 1968–1995. It is shown that the power law of depth variation as a function of offshore coordinate (Dean's profile) is satisfied on the average for nonbarred profiles. Bar development for the period of the last five years is analyzed. A mathematical model for description of time-dependent sea bottom deformation under the action of wind waves in the surf zone is developed. It is found that, besides the known static solutions of the balance equation for sediment transport, which correspond to the equilibrium bottom profile with zero net sediment transport, there exists a solution corresponding to the profiles of dynamic equilibrium when the surf zone is a “carrier” of sediment transport from the coast to the sea or in the opposite direction. Both equilibrium bottom profiles satisfy the power asymptotic law near shore. A class of steady-state solutions of the sediment balance equation, which correspond to the “traveling” bottom profiles, is studied also. Such “wave” solutions may be used for the description of the long-term processes of the beach migration. Data available on the deviation of bottom profiles from equilibrium are used to estimate an anticipated speed of the long-term beach deformation.