Stability analysis of a two-inlet bay system

Abstract

The stability analysis for a double-inlet bay system is applied to an inlet system resembling Big Marco Pass and Capri Pass on the lower west coast of Florida. Since the opening of Capri Pass in 1967, the length of Big Marco Pass has increased from 2000 m in 1967 to 3000 m in 1988 and the cross-sectional area has decreased from 1200 m 2 in 1967 to 1000 m 2 in 1988. Since 1967, the cross-sectional area of Capri Pass has steadily increased and in 1988 was 700 m 2. Tides off the inlets are of the mixed type with a diurnal range of 1 m. The gross littoral transport rate in the vicinity of the inlets is estimated at 150,000 m 3 yr −1. For each inlet the maximum tidal velocities are calculated as a function of the gorge cross-sectional areas using a lumped-parameter model to describe the hydrodynamics of the flow. In the model it is assumed that the bay level fluctuates uniformly and the bay surface area remains constant. The velocities are used to calculate the tidal maximum of the bottom shear stress in each inlet as a function of the cross-sectional areas of the two inlets (=closure surface). Values of the equilibrium shear stress are derived from an empirical relationship between cross-sectional area and tidal prism for stable inlets along the west coast of Florida. Closure surfaces and equilibrium stress values are calculated for values of friction factors ranging from F=4×10 −3 to F=6×10 −3. Using the closure surfaces and equilibrium stress values, the equilibrium flow curve for each inlet is determined. The equilibrium flow curve represents the locus of the combination of cross-sectional areas for which the actual bottom shear stress in the inlet equals the equilibrium shear stress. Based on the equilibrium flow curves and the known values of the cross-sectional areas of the two inlets in 1988, it is expected that, ultimately, Big Marco Pass will close and Capri Pass will remain as the sole inlet with a cross-sectional area of 1250 m 2 and a maximum tidal velocity pertaining to a diurnal tide of 0.85 m s −1.