OSCILLATING TIDAL BARRIERS AND RANDOM WAVES

The interaction between sea waves and the oscillating gates designed t o close the three inlets of Venice lagoon and to protect the city from the phenomenon of high waters is studied. Previous studies of this to pic, which considered monochromatic waves, are extended to consider ra ndom waves characterized by a narrow-band wave spectrum, such that the incoming wave strongly resembles a monochromatic wave, slowly modulat ed by a random function of time and space. A linear stability analysis of basic synchronous response of the barrier to the incident wave sho ws that the excitation of subharmonic oscillations of the gates is pos sible. When the width S of the incoming wave spectrum tends to zero, the results of previous studies which considered an oscillatory forcin g of constant amplitude tends to be recovered. Unexpectedly, as the wi dth of the spectrum increases, the unstable regions in the parameter s pace widen. However, a weakly nonlinear stability analysis shows that the regime configuration, i.e., the configuration attained by gate osc illations for large time, is characterized by values of the amplitude of the subharmonic oscillations that decrease as the width of the spec trum increases. Present results suggest that for large band spectra th e subharmonic oscillations cannot be detected. These findings result f rom linear and nonlinear amplitude equations characterized by time-dep endent coefficients that introduce new interesting features in the tim e development of the amplitude of subharmonic perturbations of the gat e oscillations.