A mathematical simulation model is used to study the relations among storm cycles, beach erosion, and nearshore bar migration. The model is based on Fourier analysis of weather and wave data collected on Lake Michigan during the summers of 1969 and 1970.
In the simulation of coastal processes, barometric pressure is used as the independent variable with longshore current velocity computed as the first derivative and breaker height as a filtered version of the second derivative of barometric pressure. The simulated curves are used to compute wave and longshore current energy for each storm cycle and poststorm recovery.
Daily profiles across the nearshore area provide data for topographic maps and maps of erosion and deposition. For simulation, the nearshore area is broken down into five components including beach, foreshore, plunge zone, trough, and bar. A gently sloping linear plus quadratic surface is used to represent the barless topography, with bars and troughs generated by normal curves. Bar distance is computed as a function of wave energy and bottom slope. Position of the bar and trough along the shore is determined by wave and longshore current energy. Simulated maps are produced for each storm cycle and poststorm recovery.