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Research Papers: Ocean Engineering

Application of Boundary Element Method for Determination of the Wavemaker Driving Signal

[+] Author and Article Information
Anatoliy Khait

Mem. ASME
School of Mechanical Engineering,
Faculty of Engineering,
Tel Aviv University,
Tel Aviv 6997801, Israel
e-mail: haitanatoliy@gmail.com

Lev Shemer

Mem. ASME
School of Mechanical Engineering,
Faculty of Engineering,
Tel Aviv University,
Tel Aviv 6997801, Israel
e-mail: shemer@eng.tau.ac.il

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the Journal of Offshore Mechanics and Arctic Engineering. Manuscript received August 31, 2018; final manuscript received February 3, 2019; published online March 20, 2019. Assoc. Editor: Felice Arena.

J. Offshore Mech. Arct. Eng 141(6), 061102 (Mar 20, 2019) (10 pages) Paper No: OMAE-18-1136; doi: 10.1115/1.4042942 History: Received August 31, 2018; Accepted February 03, 2019

A method for the generation of steep nonlinear broad-banded wave trains having an arbitrary prescribed shape is developed. It is shown that the second-order contributions to the velocity field are negligible in deep water, while the second-order bound components of the surface elevation are significant. This fact allows improvement of an iterative method of the wavemaker driving signal adjustment that increases the accuracy of excitation of wave train with the prescribed free waves’ spectrum. The decomposition of the complex amplitude spectrum of the surface elevation into free and bound components is based on the approach adopted in the derivation of the Zakharov model. The iterative adjustment of the driving signal is carried out using the numerical wave tank based on the boundary element method. It is demonstrated that accurate wave train excitation is attained for different values of the wave steepness. The method allows decreasing the number of iterations needed for the driving signal adjustment. The surface elevation values measured in the laboratory wave tank agree closely with those obtained in the numerical simulations. The measured and the simulated frequency spectra are in agreement as well.

Copyright © 2019 by ASME
Topics: Waves , Signals
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References

Dean, R. G., and Dalrymple, R. A., 1991, Water Wave Mechanics for Engineers and Scientists, World Scientific, Singapore.
Schäffer, H. A., 1996, “Second-Order Wavemaker Theory for Irregular Waves,” Ocean Eng., 23, pp. 47–88. [CrossRef]
Spinneken, J., and Swan, C., 2009, “Second-Order Wave Maker Theory Using Force-Feedback Control. Part I: A New Theory for Regular Wave Generation,” Ocean Eng., 36(8), pp. 539–548. [CrossRef]
Spinneken, J., and Swan, C., 2009, “Second-Order Wave Maker Theory Using Force-Feedback Control. Part II: An Experimental Verification of Regular Wave Generation,” Ocean Eng., 36(8), pp. 549–555. [CrossRef]
Aknin, D., and Spinneken, J., 2017, “A Laboratory Investigation Concerning the Superharmonic Free Wave Suppression in Shallow and Intermediate Water Conditions,” Coastal Eng., 120, pp. 112–132. [CrossRef]
Houtani, H., Waseda, T., Fujimoto, W., Kiyomatsu, K., and Tanizawa, K., 2015, “Freak Wave Generation in a Wave Basin With HOSM-WG Method,” ASME Paper No. OMAE2015-42284.
Houtani, H., Waseda, T., Fujimoto, W., Kiyomatsu, K., and Tanizawa, K., 2018, “Generation of a Spatially Periodic Directional Wave Field in a Rectangular Wave Basin Based on Higher-Order Spectral Simulation,” Ocean Eng., 169, pp. 428–441. [CrossRef]
Chaplin, J. R., 1996, “On Frequency-Focusing Unidirectional Waves,” Int. J. Offshore Polar Eng., 6(2), pp. 131–137. https://www.onepetro.org/journal-paper/ISOPE-96-06-2-131
Lugni, C., 2000, “An Investigation on the Interaction Between Free-Surface Waves and Floating Structure,” Ph.D. thesis, University of Rome, Italy (in Italian).
Shemer, L., Goulitski, K., and Kit, E., 2006, “Steep Waves in Tanks: Experiments and Simulations,” ASME Paper No. OMAE2006-92547.
Shemer, L., Goulitski, K., and Kit, E., 2007, “Evolution of Wide-Spectrum Unidirectional Wave Groups in a Tank: An Experimental and Numerical Study,” Eur. J. Mech. B Fluids, 26(2), pp. 193–219. [CrossRef]
Schmittner, C., Kosleck, S., and Hennig, J., 2009, “A Phase-Amplitude Iteration Scheme for the Optimization of Deterministic Wave Sequences,” ASME Paper No. OMAE2009-80131.
Buldakov, E., Stagonas, D., and Simons, R., 2017, “Extreme Wave Groups in a Wave Flume: Controlled Generation and Breaking Onset,” Coastal Eng., 128, pp. 75–83. [CrossRef]
Mei, C. C., 1989, The Applied Dynamics of Ocean Surface Waves, World Scientific, Singapore.
Zakharov, V. E., 1968, “Stability of Periodic Waves of Finite Amplitude on the Surface of a Deep Fluid,” J. Appl. Mech. Tech. Phys., 9, pp. 190–194. [CrossRef]
Stiassnie, M., and Shemer, L., 1984, “On Modification of Zakharov Equation for Surface Gravity Waves,” J. Fluid Mech., 143, pp. 47–67. [CrossRef]
Stiassnie, M., and Shemer, L., 1987, “Energy Computations for Evolution of Class I and II Instabilities of Stokes Waves,” J. Fluid Mech., 174, pp. 299–312. [CrossRef]
Krasitskii, V. P., 1994, “On the Reduced Equations in the Hamiltonian Theory of Weakly Nonlinear Surface Waves,” J. Fluid Mech., 272, pp. 1–20. [CrossRef]
Grilli, S. T., and Svendsen, I. A., 1990, “Corner Problems and Global Accuracy in the Boundary Element Solution of Nonlinear Wave Flows,” Eng. Anal. Bound. Elem., 7(4), pp. 178–195. [CrossRef]
Grilli, S. T., and Subramanya, R., 1996, “Numerical Modeling of Wave Breaking Induced by Fixed or Moving Boundaries,” Comput. Mech., 17, pp. 374–391. [CrossRef]
Grilli, S. T., Skourup, J., and Svendsen, I. A., 1989, “An Efficient Boundary Element Method for Nonlinear Water Waves,” Eng. Anal. Bound. Elem., 6(2), pp. 97–107. [CrossRef]
Grilli, S. T., and Horrillo, J., 1997, “Numerical Generation and Absorption of Fully Nonlinear Periodic Waves,” J. Eng. Mech., pp. 1060–1069.
Tian, Z., Perlin, M., and Choi, W., 2010, “Energy Dissipation in Two-Dimensional Unsteady Plunging Breakers and an Eddy Viscosity Model,” J. Fluid Mech., 655, pp. 217–257. [CrossRef]

Figures

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Fig. 1

Relative contribution of (a) the second-order bound waves to the surface elevation and (b) the second-order horizontal velocity component, as a function of wave steepness and water depth

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Fig. 2

Normalized velocity fields of (a) the propagating and (b) second-order components of a regular wave at kh = π and ka = 0.3

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Fig. 3

Comparison of the contributions (8) to the vertical motion of the free surface of regular wave with ka = 0.3

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Fig. 4

Schematic of the NWT

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Fig. 5

Assessment of effectiveness of the numerical wave absorption techniques

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Fig. 6

Separation of the spectrum into free and bound components

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Fig. 7

Amplitude and phase adjustment for free components of the surface elevation

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Fig. 8

Adjustment of the numerically simulated and the actual spectra of the wavemaker motion

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Fig. 9

The measured spectrum of free waves after correction of the wavemaker motion

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Fig. 10

Comparison of experimental, numerical, and target wave forms

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Fig. 11

Separation of the surface elevation spectrum into free and bound waves

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Fig. 12

Amplitude and phase adjustment for free components utilizing NWT

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Fig. 13

Experimental spectrum of free waves after correction of the wavemaker motion

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Fig. 14

Comparison of experimental, numerical, and target wave forms

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Fig. 15

Adjustment of (a) amplitudes and (b) phases in the spectra of the wavemaker motion needed for excitation of wave trains with different steepnesses

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