DYNAMICAL MODELS FOR CROSS-SHORE TRANSPORT AND EQUILIBRIUM BOTTOM PROFILES

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 measuremen ts of some coastal regions in Israel for the period 1968-1995. It is s hown that the power law of depth variation as a function of offshore c oordinate (Dean's profile) is satisfied on the average for nonbarred p rofiles. Bar development for the period of the last five years is anal yzed. A mathematical model for description of time-dependent sea botto m deformation under the action of wind waves in the surf zone is devel oped. It is found that, besides the known static solutions of the bala nce equation for sediment transport, which correspond to the equilibri um bottom profile with zero net sediment transport, there exists a sol ution corresponding to the profiles of dynamic equilibrium when the su rf zone is a ''carrier'' of sediment transport from the coast to the s ea or in the opposite direction. Both equilibrium bottom profiles sati sfy the power asymptotic law near shore. A class of steady-state solut ions of the sediment balance equation, which correspond to the ''trave ling'' bottom profiles, is studied also. Such ''wave'' solutions may b e used for the description of the long-term processes of the beach mig ration. Data available on the deviation of bottom profiles from equili brium are used to estimate an anticipated speed of the long-term beach deformation.