Modeling the development of wave-cut shore platforms

Abstract

Abstract A mathematical model was used to investigate the development of wave-cut shore platforms with constant sea level. The model considered the effects of deep water wave height spectra, period and wavelength, breaker height and depth, breaker type, the width and bottom roughness of the surf zone, the gradient of the submarine slope, an erosional threshold related to the strength of the rocks, the number of hours each year in which the water level is at each intertidal elevation and the amount and persistence of the debris at the cliff foot. Intertidal erosion rates were calculated according to the force of the surf reaching the shoreline, whereas submarine erosion rates were determined using a depth decay variable. Each of the two hundred and fifty model runs consisted of 300,000 iterations. Platform width increased and gradient progressively decreased through model runs, and states of static equilibrium were attained by the end of one-hundred and nine runs when the wave induced force at each point in the intertidal zone had became too weak to continue eroding the rock. Runs with mesotidal spring tidal range (3 m) generally produced subhorizontal platforms with cliff-platform junctions at the mean low water neap tidal level. A greater variety of profiles was produced in runs with macrotidal spring tidal ranges (9 m). Although almost 30% of these runs produced gently sloping platforms, with average gradients of only 0.3°, about two-thirds of the simulated profiles had average gradients ranging from about 1 to 3°. Simulated platform width increased with tidal range and decreased with the rate of submarine erosion, rock resistance, the roughness or irregularity of the platform surface, the amount and persistence of the cliff foot debris and wave period. Because higher waves break in deeper water than lower waves, there was no consistent relationship between simulated platform width and wave height.