Subharmonic resonance of Venice gates in waves. Part 1. Evolution equation and uniform incident waves

For flood protection against storm tides, barriers of box-like gates hinged along a bottom axis have been designed to span the three inlets of the Venice Lagoon. While on calm days the gates are ballasted to rest horizontally on the seabed, in stormy weather they are raised by buoyancy to act as a dam which is expected to swing to and fro in unison in response to the normally incident sea waves. Previous laboratory experiments with sinusoidal waves have revealed however that neighbouring gates oscillate out of phase, at one half the wave frequency, in a variety of ways, and hence would reduce the effectiveness of the barrier. Extending the linear theory of trapped waves by Mei et al. (1994), we present here a nonlinear theory for subharmonic resonance of mobile gates allowed to oscillate about a vertical plane of symmetry. In this part (1) the evolution equation of the Landau–Stuart type is first derived for the gate amplitude. The effects of gate geometries on the coefficients in the equation are examined. After accounting for dissipation effects semi-empirically the theoretical results on the equilibrium amplitude excited by uniform incident waves are compared with laboratory experiments.