Subharmonic resonance of Venice gates in waves. Part 2. Sinusoidally modulated incident waves

Abstract

In order to examine the effects of finite bandwidth of the incident sea spectrum on the resonance of the articulated storm gates for Venice Lagoon, we consider a narrow band consisting of the carrier frequency and two sidebands. The evolution equation for the gate oscillations now has a time-periodic coefficient, and is equivalent to a non-autonomous dynamical system. For small damping and weak forcing, approximate analysis for local and global bifurcations are carried out, and extended by direct numerical simulation. Typical bifurcation scenarios are also examined by laboratory experiments.

Weakly nonlinear theory for oscillating wave surge converters in a channel

“…For modulated waves, we find period doubling sequences, chaotic states and frequency downshift (Trulsen & Mei 1995;Trulsen & Dysthe 1997;Sammarco et al 1997b) by increasing the modulated wave amplitude. We detect the occurrence of homoclinic tangles and global chaos through usage of the Melnikov function (Guckenheimer & Holmes 1983;Jordan & Smith 2011).…”

“…The latter non-autonomous system is similar to that for Venice gates (Sammarco et al 1997b) and can exhibit chaos for a certain range of the long wave amplitudeÃ. There are different theoretical criteria to determine under what conditions the response of a dynamical system becomes chaotic.…”

“…Laboratory experiments have revealed that, for certain frequencies, the incident waves resonate subharmonically the trapped modes of the barrier (Mei et al 1994). The weakly nonlinear theory which explains this resonance mechanism has been developed by Sammarco, Tran & Mei (1997a), Sammarco et al (1997b) for uniform and modulated waves. A simplified model for the subharmonic resonance of sliding gates in shallow waters has been developed by Vittori, Blondeaux & Seminara (1996).…”

Motion-resonant modes of large articulated damped oscillators in waves

“…As a consequence, their interplay with incident waves can generate resonant interactions which cannot be explained with the traditional point-oscillator theory. Mei et al (1994) and Sammarco et al (1997a) showed for the first time that incident waves can trigger largeamplitude pitching motions of an array of narrowly spaced, large rectangular gates in a channel. Note that the gates of Mei et al (1994) and Sammarco et al (1997a) move in the absence of any power take-off damping.…”

“…Mei et al (1994) and Sammarco et al (1997a) showed for the first time that incident waves can trigger largeamplitude pitching motions of an array of narrowly spaced, large rectangular gates in a channel. Note that the gates of Mei et al (1994) and Sammarco et al (1997a) move in the absence of any power take-off damping. Lately, a resonant mechanism has been shown to occur for the same oscillators when located at the intersection of a straight channel and a semi-infinite domain (Adamo and Mei, 2005) and for multiple arrays of such oscillators in a channel (Sammarco et al, 2014).…”