Linear response of the gate system for protection of the Venice Lagoon. Note II: Excitation of transverse suhharmonic modes

Paolo Blondeaux; Giovanni Seminara; Giovanna Vittori

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 4, page 299-305
  • ISSN: 1120-6330

Abstract

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We show that the transverse subharmonic modes characterizing the free oscillations of the gate system proposed to defend the Venice Lagoon from the phenomenon of high water (see Note I[1]) can be excited when the gate system is forced by plane monochromatic waves orthogonal to the gates with the typical characteristics of large amplitude waves in the Adriatic sea close to the lagoon inlets. A linear stability analysis of the coupled motion of the system sea-gates-lagoon reveals that for typical values of the parameters of the problem modes 4, 5 and 6 may be unstable. The need for a nonlinear analysis of mode competion is pointed out.

How to cite

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Blondeaux, Paolo, Seminara, Giovanni, and Vittori, Giovanna. "Linear response of the gate system for protection of the Venice Lagoon. Note II: Excitation of transverse suhharmonic modes." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.4 (1993): 299-305. <http://eudml.org/doc/244162>.

@article{Blondeaux1993,
abstract = {We show that the transverse subharmonic modes characterizing the free oscillations of the gate system proposed to defend the Venice Lagoon from the phenomenon of high water (see Note I[1]) can be excited when the gate system is forced by plane monochromatic waves orthogonal to the gates with the typical characteristics of large amplitude waves in the Adriatic sea close to the lagoon inlets. A linear stability analysis of the coupled motion of the system sea-gates-lagoon reveals that for typical values of the parameters of the problem modes 4, 5 and 6 may be unstable. The need for a nonlinear analysis of mode competion is pointed out.},
author = {Blondeaux, Paolo, Seminara, Giovanni, Vittori, Giovanna},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Gates; Waves; Forced oscillations; forced oscillations; free oscillations; high water; plane monochromatic waves; linear stability analysis},
language = {eng},
month = {12},
number = {4},
pages = {299-305},
publisher = {Accademia Nazionale dei Lincei},
title = {Linear response of the gate system for protection of the Venice Lagoon. Note II: Excitation of transverse suhharmonic modes},
url = {http://eudml.org/doc/244162},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Blondeaux, Paolo
AU - Seminara, Giovanni
AU - Vittori, Giovanna
TI - Linear response of the gate system for protection of the Venice Lagoon. Note II: Excitation of transverse suhharmonic modes
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/12//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 4
SP - 299
EP - 305
AB - We show that the transverse subharmonic modes characterizing the free oscillations of the gate system proposed to defend the Venice Lagoon from the phenomenon of high water (see Note I[1]) can be excited when the gate system is forced by plane monochromatic waves orthogonal to the gates with the typical characteristics of large amplitude waves in the Adriatic sea close to the lagoon inlets. A linear stability analysis of the coupled motion of the system sea-gates-lagoon reveals that for typical values of the parameters of the problem modes 4, 5 and 6 may be unstable. The need for a nonlinear analysis of mode competion is pointed out.
LA - eng
KW - Gates; Waves; Forced oscillations; forced oscillations; free oscillations; high water; plane monochromatic waves; linear stability analysis
UR - http://eudml.org/doc/244162
ER -

References

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  1. BLONDEAUX, P. - SEMINARA, G. - VITTORI, G., Linear response of the gate system for protection of the Venice Lagoon. Note I: Transverse free modes. Rend. Mat. Acc. Lincei, s. 9, v. 4, 1993, 291-298. Zbl0801.76008MR1269619
  2. HALL, P. - SEMINARA, G., Nonlinear oscillations of non-spherical cavitation bubbles in acoustic fields. J. Fluid Mech., 101, 1980, 423-444. Zbl0448.76085MR605389DOI10.1017/S0022112080001735
  3. CILIBERTO, S. - GOLLUB, J. P., Chaotic mode competition in parametrically forced surface waves. J. Fluid Mech., 158, 1985, 381-398. MR813201DOI10.1017/S0022112085002701
  4. SIMONELLI, F. - GOLLUB, J. P., Surface wave mode interactions: effects of symmetry and degeneracy. J. Fluid Mech., 199, 1989, 471-494. MR985202DOI10.1017/S0022112089000443
  5. KARATSU, M., Nonlinear resonance and chaos of surface waves of water. Master thesis, University of Tokyo, 1988 (in Japanese). 
  6. FENG, Z. C. - SETHNA, P.R., Symmetry-breaking bifurcation in resonant surface waves. J. Fluid Mech., 199, 1989, 495-518. Zbl0659.76026MR985203DOI10.1017/S0022112089000455
  7. KAMBE, T. - UMEKI, M., Nonlinear dynamics of two-mode interactions in parametric excitation of surface waves. J. Fluid Mech., 212, 1990, 373-393. Zbl0692.76008MR1051336DOI10.1017/S0022112090002014
  8. FENG, Z. - WIGGINS, S., On the existence of chaos in a class of two-degree-of-freedom, damped, strongly parametrically forced mechanical systems with broken O(2) symmetry. ZAMP, 44, 1993, 201-248. Zbl0786.34050MR1214130DOI10.1007/BF00914282

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