The re-examination of determining the coefficient of the amplitude evolution equation in the nonlinear theory of the hydrodynamic stability

1994 ◽  
Vol 15 (8) ◽  
pp. 745-748
Author(s):  
Luo Ji-sheng
Keyword(s):  
Evolution Equation ◽  
Nonlinear Theory ◽  
Hydrodynamic Stability ◽  
Amplitude Evolution

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

1997 ◽  
Vol 349 ◽  
pp. 295-325 ◽  
Author(s):  
PAOLO SAMMARCO ◽  
HOANG H. TRAN ◽  
CHIANG C. MEI
Keyword(s):  
Evolution Equation ◽  
Nonlinear Theory ◽  
Laboratory Experiments ◽  
Vertical Plane ◽  
Venice Lagoon ◽  
Subharmonic Resonance ◽  
Sea Waves ◽  
Stormy Weather ◽  
Incident Waves ◽  
Theoretical Results

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.

scholarly journals Weakly nonlinear theory for a gate-type curved array in waves

2019 ◽  
Vol 869 ◽  
pp. 238-263 ◽  
Author(s):  
S. Michele ◽  
E. Renzi ◽  
P. Sammarco
Keyword(s):  
Evolution Equation ◽  
Nonlinear Theory ◽  
Surface Curvature ◽  
Nonlinear Behaviour ◽  
Trapped Modes ◽  
Ginzburg Landau ◽  
Curved Boundaries ◽  
Weakly Nonlinear ◽  
Wave Energy Converters ◽  
Weakly Nonlinear Theory

We analyse the effect of gate surface curvature on the nonlinear behaviour of an array of gates in a semi-infinite channel. Using a perturbation-harmonic expansion, we show the occurrence of new detuning and damping terms in the Ginzburg–Landau evolution equation, which are not present in the case of flat gates. Unlike the case of linearised theories, synchronous excitation of trapped modes is now possible because of interactions between the wave field and the curved boundaries at higher orders. Finally, we apply the theory to the case of surging wave energy converters (WECs) with curved geometry and show that the effects of nonlinear synchronous resonance are substantial for design purposes. Conversely, in the case of subharmonic resonance we show that the effects of surface curvature are not always beneficial as previously thought.

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