A SMALL-SCALE FIELD EXPERIMENT FOR THE VALIDATION OF A THEORY ON REFLECTION OF NONLINEAR SHORT-CRESTED WAVE GROUPS

Alessandra Romolo, Felice Arena

Abstract


A closed-form solution of free surface displacement and velocity potential for nonlinear short-crested (3D) wave groups interacting with a reflective sea wall is presented. The theory is applied to investigate the fluctuation wave pressures when an exceptionally high crest or deep trough occurs on the reflective wall. A characteristic behaviour has been observed. Due to non-linearity, on one hand, great reduction of the highest crest and enhancement of the deepest troughs on wave pressures are realized; on the other hand, the profiles show always a strong asymmetry between the absolute maxima and the minima and sometimes the formation of characteristic humped wave pressures corresponding to the impact on the structure of the highest wave crest. All the theoretical results have been validated through a small-scale field experiment carried out at the Natural Ocean Engineering Laboratory (N.O.E.L., www.noel.unirc.it) of Reggio Calabria (Italy).

Keywords


nonlinear sea wave; reflection; short-crested wave groups; wave pressure; sea wall; upright breakwater

References


Boccotti P., 1981. On the Highest Waves in a Stationary Gaussian Process. Trans. National Ligure Academy of Science and Literature, Genoa, 38, 271.

Boccotti, P., 1982. On Ocean Waves with High Crests. Meccanica, 17, 16-19. http://dx.doi.org/10.1007/BF02156003

Boccotti P., 1988. Refraction, Reflection and Diffraction of Irregular Gravity Waves, Excepta of Italian Contribution to the Field of Hydraulic Engineering, 3, 47-89.

Boccotti, P., 1989. On Mechanics of Irregular Gravity Waves. Atti Acc. Naz. Lincei, Memorie, VIII, 19, 111-170.

Boccotti P., Barbaro G. and Mannino L., 1993a. A Field Experiment on the Mechanics of Irregular Gravity Waves. J. Fluid Mech., 252, 173. http://dx.doi.org/10.1017/S0022112093003714

Boccotti P., Barbaro G., Fiamma V. Mannino L. and Rotta A., 1993b. An Experiment at Sea on the Reflection of the Wind Waves, Ocean Engineering, 20, 493. http://dx.doi.org/10.1016/0029-8018(93)90017-C

Boccotti P., 1997. A General Theory of Three-Dimensional Wave Groups. Part I: The Formal Derivation. Part II: Interaction with a Breakwater, Ocean Engineering, 24, 265-300. http://dx.doi.org/10.1016/S0029-8018(96)00013-3

Boccotti P., 2000. Wave Mechanics for Ocean Engineering, Elsevier Science, New York, 496.

Boccotti, P., Arena, F., Fiamma, V., Romolo, A. & Barbaro, G., 2010. A small scale field experiment on wave forces on upright breakwaters, under peer review.

Goda Y., 1967. The Fourth Order Approximation to the Pressure of Standing Waves, Coastal Engineering in Japan, 10, 1-11.

Goda Y., 1999. Random Seas and Design in Maritime Structures, World Scientific. PMCid:1566058

Jeng D. S. 2002. Wave Kinematics of Partial Reflection from a Vertical Wall. Ocean Engineering, 29, 1711. http://dx.doi.org/10.1016/S0029-8018(01)00090-7

Hasselmann K., Barnett T. P., Bouws E., Carlson H., Cartwright D. E., Enke K., Ewing J. A., Gienapp H., Hasselmann D. E., Krusemann P., Meerburg A., Müller P., Olbers D. J., Richter K., Sell W., and Walden H., 1973. Measurements of wind wave growth and swell decay during the Joint North Sea Wave Project JONSWAP, Dtsch. Hydrogr. Z. A8, 1.

Kimmoun O., Branger H. and Kharif C., 1999. On Short-Crested Waves: Experimental and Analytical Investigation. European Journal of Mechanics B. Fluids, 18, 889.

Lin M. C., Liu S. J. and Chuang M. F., 1987. Numerical Analysis of the Short-Crested Water Wave Properties. J. Soc. Naval Arch. Marine Eng, ROC 6, 1, 269.

Longuet-Higgins M. S. and Dommermuth D. G., 2001. On the Breaking of Standing Waves by Falling Jets. Phys. Fluids, 13, 1652. http://dx.doi.org/10.1063/1.1369141

Longuet-Higgins M. S. and Dommermuth D. G., 2001. Vertical Jets from Standing Waves. II. Proc. R. Soc. Lond., 457, 2137. http://dx.doi.org/10.1098/rspa.2001.0832

Longuet-Higgins M. S. and Drazen D. A., 2002. On Steep Gravity Waves Meeting a Vertical Wall: a Triple Instability. J. Fluid Mech., 466, 305. http://dx.doi.org/10.1017/S0022112002001246

Marchant T. R. & Roberts A. J. 1987. Properties of short-crested waves in water of finite depth. J. Aust. Math. Soc. B, 29, 103. http://dx.doi.org/10.1017/S0334270000005658

Mercer G. N. and Roberts A. J., 1992. Standing Waves in Deep Water: Their Stability and Extreme Form. Phys. Fluids, 4, 259. http://dx.doi.org/10.1063/1.858354

Mercer G. N. and Roberts A. J., 1994. The Form of Standing Waves on Finite Depth Water. Wave Motion, 19, 233. http://dx.doi.org/10.1016/0165-2125(94)90056-6

Mitsuyasu, H., Tasai, F., Suara, T., 1975. Observation of directional spectrum of ocean waves using a clover-leaf buoy. Journal of Physical Oceanography 5, 750–760. http://dx.doi.org/10.1175/1520-0485(1975)005<0750:OOTDSO>2.0.CO;2

Peregrine D. H., 2003. Water-wave impact on walls. Annual Review of Fluid Mechanics, 35, 23-43. doi: 1. 1146/annurev.fluid.35.101101.161153

Prabhakar V. and Sundar V., 2001. Standing Wave Pressures on Walls. Ocean Engineering, 28, 439. http://dx.doi.org/10.1016/S0029-8018(00)00016-0

Roberts A. J. 1983a. A stable and accurate numerical method to calculate the motion of a sharp interface between fluids. IMA J. Appl. Math., 31, 13. http://dx.doi.org/10.1093/imamat/31.1.13

Roberts A. J. 1983b. Highly nonlinear short-crested water waves. J. Fluid Mech. 135, 301. http://dx.doi.org/10.1017/S0022112083003092

Roberts A. J. and Schwartz L. W., 1983. The Calculation of Nonlinear Short-Crested Gravity Waves. Phys. Fluids. 26, 9, 2388.

Romolo A., 2007. Mechanics of Nonlinear Random Sea Waves interacting with a Reflective Upright Breakwater. Formal Derivation and Validation' (in English), PhD Thesis on Ocean Engineering at 'Mediterranea' University of Reggio Calabria, n. OE3 - SSD: ICAR/02, 1-291.

Romolo A., Arena F, 2007. Non-linear extreme random forces on a vertical wall given by very high sea wave groups, 5th Coastal Structures International Conference (cst07), 2-4, Luglio, 2007, 5th Coastal Structures International

Conference (CSt07) - ASCE., Volume name: Functional Design, Venezia, Italia, Vol. 1, 2009, pp. 895-906.

Romolo, A. & Arena, F. 2008a. Mechanics of nonlinear random wave groups interacting with a vertical wall, Physics of Romolo A., Arena F. 2008b. Three-dimensional Nonlinear Wave Groups interacting with an Upright Breakwater. Proc. 31st International Conference on Coastal Engineering (ICCE 2008) - ASCE. Hamburg, Germany, Aug. 31 – Sept. 5, 2008.

Fluids. Vol. 20, Issue 3, paper 036604, pp. 1-16. DOI: 10.1063/1.2890474. http://dx.doi.org/10.1063/1.2890474

Saintflou G. 1928. Essai sur les digues maritimes verticales. Annual Ponts et Chaussees, 98 (1), 5-48.

Schultz W. W., Vanden-Broeck J.-M., Jiang L. and Perlin M., 1998. Highly Nonlinear Standing Water Waves with Small Capillary effect. J. Fluid Mech., 369, 253.

Svendsen I. A. & Jonsson I. G. 1976. Hydrodynamics of Coastal Regions. Den Private Ingeniorfond-Technical University of Denmark, DK-2800, Lyngby.

Tadjbakhsh I. & Keller J. B. 1960. Standing Surface Waves of Finite Amplitude, J. Fluid Mech. 8, 442. http://dx.doi.org/10.1017/S0022112060000724

Tsai C. P., Jeng D.S. and Hsu J. R. C., 1994. Computations of the almost Highest Short-Crested Waves in Deep Water.


Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.