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Group dynamics and wave resonances in a narrow gap: modes and reduced group velocity

  • Wenhua Zhao (a1), P. H. Taylor (a1), H. A. Wolgamot (a1), B. Molin (a2) and R. Eatock Taylor (a3)...


The spatial and temporal structure of the resonant fluid response in a narrow gap (the so-called gap resonance) between two identical fixed boxes is investigated experimentally. Transient wave groups are used to excite the gap resonance from different wave approach directions. This shows a strong beating pattern and a very long duration, reflecting that gap resonance is a multi-mode resonant and weakly damped phenomenon. For head sea excitation the linear transfer function of the $m=2$ gap mode is as significant as that of the $m=1$ mode. Gap resonance can be driven through different mechanisms, e.g. linear excitation and a nonlinear frequency-doubling process. Significant wave group structure is shown in the gap, and the group structure is more distinct in the case with frequency doubling, i.e. long wave, excitation. Then it is clearer visually that the groups originate at the end of the gap, propagate along the gap and are then partially reflected from the other end. The groups within the gap are very clear because the group velocity is close to constant for the first few gap resonance modes, and much smaller than that for free waves on the open sea. In contrast, the phase speed of waves in the gap is larger than that for free waves outside. Only in the limit of short waves do the group velocity and phase speed of the gap modes tend to those of deep-water free waves. The group and phase speeds from these experiments match well the theoretical forms given by Molin et al. (Appl. Ocean Res., vol. 24 (5), 2002, pp. 247–260), albeit for a slightly different box cross-sectional shape.


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Chen, X. B. 2005 Hydrodynamic analysis for offshore LNG terminals. In Proceedings of the 2nd International Workshop on Applied Offshore Hydrodynamics, Rio de Janeiro.
Eatock Taylor, R., Sun, L. & Taylor, P. H. 2008 Gap resonances in focused wave groups. In 23rd International Workshop on Water Waves and Floating Bodies, April 13–16, Jeju, Korea,
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.
Feng, X. & Bai, W. 2015 Wave resonances in a narrow gap between two barges using fully nonlinear numerical simulation. Appl. Ocean Res. 50, 119129.
Feng, X., Bai, W., Chen, X. B., Qian, L. & Ma, Z. H. 2017 Numerical investigation of viscous effects on the gap resonance between side-by-side barges. Ocean Engng 145, 4458.
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.
Huijsmans, R. H. M., Pinkster, J. A. & De Wilde, J. J. 2001 Diffraction and radiation of waves around side-by-side moored vessels. In The Eleventh International Offshore and Polar Engineering Conference. International Society of Offshore and Polar Engineers.
Jonathan, P. & Taylor, P. H. 1997 On irregular, nonlinear waves in a spread sea. J. Offshore Mech. Arctic Engng 119 (1), 3741.
Kristiansen, T. & Faltinsen, O. M. 2008 Application of a vortex tracking method to the piston-like behaviour in a semi-entrained vertical gap. Appl. Ocean Res. 30 (1), 116.
Molin, B. 2001 On the piston and sloshing modes in moonpools. J. Fluid Mech. 430, 2750.
Molin, B., Remy, F., Camhi, A. & Ledoux, A. 2009 Experimental and numerical study of the gap resonances in-between two rectangular barges. In Proceedings of the 13th Congress of the International Maritime Association of the Mediterranean (IMAM 2009), October 12–15, Istanbul, Turkey.
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), 247260.
Newman, J. N. 1977 Marine Hydrodynamics. Massachusetts Institute of Technology Press.
Newman, J. N. 2001 Wave effects on multiple bodies. In Hydrodynamics in Ship and Ocean Engineering (ed. Kashiwagi, M.), pp. 326. RIAM, Kyushu University.
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), 954978.
Wang, H., Wolgamot, H. A., Draper, S., Zhao, W., Taylor, P. H. & Cheng, L. 2019 Resolving wave and laminar boundary layer scales for gap resonance problems. J. Fluid Mech. 866, 759775.
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, 99110.
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, 905939.
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Group dynamics and wave resonances in a narrow gap: modes and reduced group velocity

  • Wenhua Zhao (a1), P. H. Taylor (a1), H. A. Wolgamot (a1), B. Molin (a2) and R. Eatock Taylor (a3)...


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