Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T14:01:40.392Z Has data issue: false hasContentIssue false
  • English
  • Français

Gap resonance from linear to quartic wave excitation and the structure of nonlinear transfer functions

Published online by Cambridge University Press:  06 September 2021

W. Zhao Open the ORCID record for W. Zhao [Opens in a new window] ,
P.H. Taylor ,
H.A. Wolgamot  and
R. Eatock Taylor
W. Zhao*
Affiliation:
Oceans Graduate School, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
P.H. Taylor
Affiliation:
Oceans Graduate School, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
H.A. Wolgamot
Affiliation:
Oceans Graduate School, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
R. Eatock Taylor
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Resonant response of water waves in a narrow gap, with the interaction of multiple highly resonant modes, is an interesting hydrodynamic phenomenon with practical applications. Gap resonances between two identical fixed rectangular boxes are experimentally investigated for unidirectional waves with broadside incidence. We show that gap resonances can be driven through both linear wave excitation and nonlinear processes, i.e. frequency doubling, tripling and quadrupling – apparently new observations. It is striking that the time histories of the gap resonances excited through different nonlinear interactions are remarkably similar to each other. It seems likely that the nonlinear sum-frequency transfer functions for gap resonances depend strongly on the output frequency sum of the interacting linear components, but only weakly on the frequency difference. In terms of their structure in multiple frequency space (at second order the bi-frequency plane for two components), these transfer functions must then have a near-flat form in the direction(s) perpendicular to the leading diagonal. This is supported by our potential flow calculations of the quadratic transfer functions (QTFs). It is therefore convenient to approximate the QTF matrix as ‘flat’ in the direction perpendicular to the leading diagonal. This approximation is justified through experimental data that includes viscous damping. It is too complex, if not impossible, to calculate the full cubic or quartic transfer functions as direct evidence. However, the experimental analysis does provide some support for the near-flat structure being applicable to transfer functions above second order. The flat form approximation greatly reduces lengthy calculations of the high-order transfer functions.

JFM classification

Waves/Free-surface Flows: Wave-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 926 , 10 November 2021 , A3
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Chau, F.P. & Eatock Taylor, R. 1992 Second-order wave diffraction by a vertical cylinder. J. Fluid Mech. 240, 571–599.CrossRefGoogle Scholar
Chen, X.B. 2005 Hydrodynamic analysis for offshore LNG terminals. In Proceedings of the 2nd International Workshop on Applied Offshore Hydrodynamics, Rio de Janeiro.Google Scholar
Craxton, R. 1981 High efficiency frequency tripling schemes for high-power Nd: glass lasers. IEEE J. Quantum Electron. 17 (9), 1771–1782.CrossRefGoogle Scholar
Faltinsen, O.M. & Timokha, A.N. 2015 On damping of two-dimensional piston-mode sloshing in a rectangular moonpool under forced heave motions. J. Fluid Mech. 772, R1.CrossRefGoogle Scholar
Feng, X. & Bai, W. 2015 Wave resonances in a narrow gap between two barges using fully nonlinear numerical simulation. Appl. Ocean Res. 50, 119–129.CrossRefGoogle Scholar
Fitzgerald, C.J., Taylor, P.H., Eatock Taylor, R., Grice, J. & Zang, J. 2014 Phase manipulation and the harmonic components of ringing forces on a surface-piercing column. Proc. R. Soc. Lond. A 470 (2168), 20130847.Google Scholar
Grice, J.R., Taylor, P.H., Eatock Taylor, R., Zang, J. & Walker, D.A.G. 2015 Extreme wave elevations beneath offshore platforms, second order trapping, and the near flat form of the quadratic transfer functions. Comput. Fluids 119, 13–25.CrossRefGoogle Scholar
Jonathan, P. & Taylor, P.H. 1997 On irregular, nonlinear waves in a spread sea. J. Offshore Mech. Arctic Engng 119 (1), 37–41.CrossRefGoogle Scholar
Kim, M.H. & Yue, D.K.P. 1990 The complete second-order diffraction solution for an axisymmetric body. Part 2. Bichromatic incident waves and body motions. J. Fluid Mech. 211, 557–593.Google Scholar
Malenica, Š., Eatock Taylor, R. & Huang, J.B. 1999 Second-order water wave diffraction by an array of vertical cylinders. J. Fluid Mech. 390, 349–373.CrossRefGoogle Scholar
Molin, B. 1979 Second-order diffraction loads upon three-dimensional bodies. Appl. Ocean Res. 1 (4), 197–202.CrossRefGoogle Scholar
Molin, B. 2001 On the piston and sloshing modes in moonpools. J. Fluid Mech. 430, 27–50.CrossRefGoogle Scholar
Molin, B., Remy, F., Kimmoun, O. & Stassen, Y. 2002 Experimental study of the wave propagation and decay in a channel through a rigid ice-sheet. Appl. Ocean Res. 24 (5), 247–260.CrossRefGoogle Scholar
Newman, J.N. 1974 Second-order, slowly-varying forces on vessels in irregular waves. In Proceedings of International Symposium on Dynamics of Marine Vehicles and Structures in Waves, London (ed. Bishop, R.E.D. & Price, W.G.), pp. 182–186.Google Scholar
Santo, H., Taylor, P.H., Carpintero Moreno, E., Stansby, P., Eatock Taylor, R., Sun, L. & Zang, J. 2017 Extreme motion and response statistics for survival of the three-float wave energy converter M4 in intermediate water depth. J. Fluid Mech. 813, 175–204.CrossRefGoogle Scholar
Sun, L., Eatock Taylor, R. & Taylor, P.H. 2010 First-and second-order analysis of resonant waves between adjacent barges. J. Fluids Struct. 26 (6), 954–978.Google Scholar
Sun, L., Eatock Taylor, R. & Taylor, P.H. 2015 Wave driven free surface motion in the gap between a tanker and an FLNG barge. Appl. Ocean Res. 51, 331–349.CrossRefGoogle Scholar
Taylor, P.H., Zang, J., Walker, A.G. & Eatock Taylor, R. 2007 Second order near-trapping for multi-column structures and near-flat QTFs. In 22nd International Workshop on Water Waves and Floating Bodies. April 15–18, Plitvice, Croatia, http://www.iwwwfb.org/Abstracts/iwwwfb22/iwwwfb22_48.pdf.Google Scholar
Tromans, P.S., Anaturk, A.R. & Hagemeijer, P. 1991 A new model for the kinematics of large ocean waves – application as a design wave. In 1st International Offshore and Polar Engineering Conference. 11–16 August, Edinburgh, UK.Google Scholar
Walker, D.A.G., Taylor, P.H. & Eatock Taylor, R. 2004 The shape of large surface waves on the open sea and the Draupner New Year wave. Appl. Ocean Res. 26 (3–4), 73–83.CrossRefGoogle Scholar
Zhao, W., Milne, I.A., Efthymiou, M., Wolgamot, H.A., Draper, S., Taylor, P.H. & Eatock Taylor, R. 2018 Current practice and research directions in hydrodynamics for FLNG side-by-side offloading. Ocean Engng 158, 99–110.CrossRefGoogle Scholar
Zhao, W., Taylor, P.H., Wolgamot, H.A. & Eatock Taylor, R. 2019 Amplification of random wave run-up on the front face of a box driven by tertiary wave interactions. J. Fluid Mech. 869, 706–725.CrossRefGoogle Scholar
Zhao, W., Taylor, P.H., Wolgamot, H.A., Molin, B. & Eatock Taylor, R. 2020 Group dynamics and wave resonances in a narrow gap: modes and reduced group velocity. J. Fluid Mech. 883, A22.CrossRefGoogle Scholar
Zhao, W., Wolgamot, H.A., Taylor, P.H. & Eatock Taylor, R. 2017 Gap resonance and higher harmonics driven by focused transient wave groups. J. Fluid Mech. 812, 905–939.CrossRefGoogle Scholar