Oscillating Tidal Barriers and Random Waves

The interaction between sea waves and the oscillating gates designed to close the three inlets of Venice lagoon and to protect the city from the phenomenon of high waters is studied. Previous studies of this topic, which considered monochromatic waves, are extended to consider random waves characterized by a narrow-band wave spectrum, such that the incoming wave strongly resembles a monochromatic wave, slowly modulated by a random function of time and space. A linear stability analysis of basic synchronous response of the barrier to the incident wave shows that the excitation of subharmonic oscillations of the gates is possible. When the width 𝒮* of the incoming wave spectrum tends to zero, the results of previous studies which considered an oscillatory forcing of constant amplitude tends to be recovered. Unexpectedly, as the width of the spectrum increases, the unstable regions in the parameter space widen. However, a weakly nonlinear stability analysis shows that the regime configuration, i.e., the configuration attained by gate oscillations for large time, is characterized by values of the amplitude of the subharmonic oscillations that decrease as the width of the spectrum increases. Present results suggest that for large band spectra the subharmonic oscillations cannot be detected. These findings result from linear and nonlinear amplitude equations characterized by time-dependent coefficients that introduce new interesting features in the time development of the amplitude of subharmonic perturbations of the gate oscillations.