FOCUSED WAVE GENERATION IN LABORATORY FLUMES OVER UNEVEN BOTTOM
AbstractA proper design of offshore and coastal structures requires further knowledge about extreme wave events. Such waves are highly nonlinear and may occur unexpectedly due to diverse reasons. One of these reasons is wave-wave interaction and the wave focusing technique represents one option to generate extreme wave events in the laboratory. The underlying mechanism is the superimposition and phasing of wave components at a predefined location. To date, most of the existing methods to propagate target wave profile backwards to the position of the wave generator apply linear wave theory. The problem is that the generated waves with different frequencies generate new components which do not satisfy the linear dispersion relation. As a result, small changes in the wave board control signal generally induce large and random shifts in the resulting focused wave. This means that iterations are necessary to get the required wave profile at the correct position in the flume. In this study, a Self Correcting Method (SCM) is applied to optimize the control signal of the wave maker in a Numerical Wave Tank (NWT). The nonlinearities are included in the control signal and accurate wave focusing is obtained irrespective of the prevailing seabed topography (horizontal or sloping) and type of structure (reflective or absorbing). The performance of the proposed SCM is numerically investigated for a wide variety of scenarios and validated by scale model tests in the Large Wave Flume (Großer Wellen Kanal, GWK), Hannover, Germany. The strengths and limitations of the proposed SCM are discussed, including the potential for further developments.
Baldock, T.E., Swan, C., Taylor, P.H., 1996. A laboratory study of nonlinear surface waves on water. Phil. Trans. R. Soc. Lond. A 354, 649.
Baldock, T.E., Swan, C., 1996. Extreme waves in shallow and intermediate water depths. Coast. Eng. 27, 21-46.
Borthwick, A.G.L., Hunt, A.C., Feng, T., Taylor, P.H., Stansby, P.K., 2006. Flow kinematics of focused wave groups on a plane beach in the U.K. Coastal Research Facility. Coast. Eng. 53, 1033-1044.
Buldakov, E., 2013. Tsunami generation by paddle motion and its interaction with a beach: Lagrangian modelling and experiment. Coast. Eng. 80, 83-94.
Chaplin, J., 1996. On frequency-focusing unidirectional waves. International Journal of Offshore and Polar Engineering 6, 131.
Clauss, G.F., Klein, M., 2011. The New Year Wave in a seakeeping basin: Generation, propagation, kinematics and dynamics. Ocean Eng. 38, 1624-1639.
Clauss, G.F., 2002. Dramas of the sea: episodic waves and their impact on offshore structures. Appl. Ocean Res. 24, 147-161.
Daemrich, K.F., Eggert, W.D., Kohlhase, S., 1980. Investigations on irregular waves in hydraulic models. Proceedings of the 17th International Conference on Coastal Engineering .
Daemrich, K.F., Gotschenberg, A., 1988. Wave generation and analysis in channels of the SFB 205. Proceedings of the 2nd international symposium on wave research and coastal engineering .
Do, T., Lleonart, G., Rouillard, V., 2004. Spectral Technique for Generating Gaussian Wave Packets. J. Waterway, Port, Coastal, Ocean Eng. 130, 104-108.
Ducrozet, G., Bonnefoy, F., Le Touzé, D., Ferrant, P., 2012. A modified High-Order Spectral method for wavemaker modeling in a numerical wave tank. European Journal of Mechanics - B/Fluids 34, 19-34.
Fernandez, H., Schimmels, S., Sriram, V., 2013. Focused wave generation by means of a self correcting method. Proc. of the 22nd International Offshore and Polar Engineering Conference .
Fernández, H., Sriram, V., Schimmels, S., Oumeraci, H., 2014. Extreme wave generation using self correcting method - Revisited. Coast. Eng. 93, 15-31.
Funke, E.R., Mansard, E.P.D., 1988. A program for the synthesis of episodic waves. . LTR-HY-65.
Hildebrant, A., Sriram, V., Schlurmann, T., 2013. Simulation of Focusing Waves and Local Line Forces due to Wave Impacts on a Tripod Structure . Proc. of the 22nd International Offshore and Polar Engineering Conference .
Hofland, B., Kaminski, M.L., Wolters, G., 2010. Large scale wave impacts on a vertical wall. Proceedings of the 32th International Conference on Coastal Engineering .
Liu, Z., Zhang, N., Yu, Y., 2011. An efficient focusing model for generation of freak waves. Acta Oceanologica Sinica 30, 19-26.
Ma, Y., Dong, G., Liu, S., Zang, J., Li, J., Sun, Y., 2010. Laboratory Study of Unidirectional Focusing Waves in Intermediate Depth Water. J. Eng. Mech. 136, 78-90.
Osborne, A.R., Onorato, M., Serio, M., 2000. The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains. Physics Letters A 275, 386-393.
Rapp, R.J., Melville, W.K., 1990. Laboratory measurements of deep-water breaking waves. Phil. Trans.
R. Soc. Lond. A 331, 735.
Roux de Reilhac, P., Bonnefoy, F., Rousset, J.M., Ferrant, P., 2011. Improved transient water wave technique for the experimental estimation of ship responses. J. Fluids Struct. 27, 456-466.
Schäffer H.A., 1996. Second order wavemaker theory for irregular waves. Ocean Engineering 23, 47.
Schmittner, C., Kosleck, S., Henning, J., 2009. A phase-amplitude iteration scheme for the optimization of deterministic wave sequences. . Proceedings of the 28th International Conference on Offshore Mechanics and Artic Engineering .
Shemer, L., Goulitski, K., Kit, E., 2007. Evolution of wide-spectrum unidirectional wave groups in a tank: an experimental and numerical study. European Journal of Mechanics - B/Fluids 26, 193-219.
Sriram, V., Sannasiraj, S.A., Sundar, V., 2006. Numerical simulation of 2D nonlinear waves using Finite Element with Cubic Spline Approximation. Journal of Fluid and Structures 22, 663.
Sriram, V., Schlurmann, T., Schimmels, S., 2013. Focused Wave Evolution in Intermediate Water Depth Using First and Second Order Wave Maker Theory . Proc. of the 22nd International Offshore and Polar Engineering Conference .
Stansberg, C., 2002. Nonlinear Amplitude Dispersion Effects in Extreme Deep-Water Random Waves. Ocean Wave Measurement and Analysis .
Westphalen, J., Greaves, D.M., Williams, C.J.K., Hunt-Raby, A.C., Zang, J., 2012. Focused waves and wave-structure interaction in a numerical wave tank. Ocean Eng. 45, 9-21.