Paper:

# Tsunami Bore Impingement onto a Vertical Column

## Halldor Arnason^{*}, Catherine Petroff^{**}, and Harry Yeh^{***}

^{*}Verkis Consulting, Armuli 4, 108 Reykjavik, Iceland

^{**}LP4 Associates LLC, P.O. Box 1331, Mercer Island, WA, 98040, USA

^{***}School of Civil & Construction Engineering, Oregon State University 220 Owen Hall, Corvallis, OR 97331-3212, USA

In a laboratory wave tank, bores were generated by dam-break: by lifting a gate that initially separated quiescent shallow water from a volume of impounded water. The study was motivated by the problem of tsunami-structure interaction and sought to further the understanding of interactions between the bore-like flow of a broken tsunami wave and structures of different cross sections. Experiments were designed to observe the structure’s effect on the bore as well as the bore’s effect on the structure. This comprehensive study used highly repeatable experiments to measure water-surface variations, velocity flow fields, and forces exerted by bores on vertically erected columns. The temporal and spatial variations of the water-surface elevations were quantified with a Laser-Induced Fluorescence (LIF) technique; velocity flow fields were recorded with a combination of Laser Doppler Velocimeter (LDV) and Digital Particle Image Velocimetry (DPIV); forces on the columns were measured with a miniature load-cell transducer. The laboratory data obtained in the study are available for validating numerical models that predict forces on structures in unsteady flows.

*J. Disaster Res.*, Vol.4, No.6, pp. 391-403, 2009.

- [1] S. Hibberd and D. H. Peregrine, “Surf and run-up on a beach: a uniform bore,” J Fluid Mech Vol.95, pp. 323-45, 1979.
- [2] J. F. Lander, L. S. Whiteside, P. A. Lockridge et al., “Two Decades of Global Tsunamis, 1982-2002,” Science of Tsunami Hazards, the International Journal of the Tsunami Society, Honolulu, Hawaii, USA, Vol.21, No.1, pp. 3-82, 2003.
- [3] A. Ritter, “Die Fortpflanzung der Wasserwellen (The propagation of water waves),” Z Ver Dtsch Ing Vol.36, No.33, pp. 947-954, 1892.
- [4] F. Alcrudo, “A State of The Art Review on Mathematical Modelling of Flood Propagation,” Presented at First IMPACT project workshop. Wallingford, UK. p. 22,

http://www.samui.co.uk/impact—project/cd/Papers/Screen/008_s_02-05-16_IMPACT_Alcrudo.pdf ,

2002. - [5] J. J. Stoker, “Water Waves; The Mathematical Theory with Applications,” Interscience Publishers, New York, 1957.
- [6] F. M. Henderson, “Open Channel Flow,” Macmillan Publishing Co., New York, New York, pp522, 1966.
- [7] G. B. Whitham, “Linear and Nonlinear Waves,” a Wiley-Interscience Pub., New York, pp636, 1974.
- [8] L. K. Forbes and L. W. Schwartz, “Supercritical Flow Past Blunt Bodies in Shallow Water,” Z Angew Math Phys Vol.32, No.3, pp. 314-28, 1981.
- [9] G. Yu, E. J. Avital, and J. J. R. Williams, “Large Eddy Simulation of Flow Past Free Surface Piercing Circular Cylinders,” J Fluids Eng Trans ASME Vol.130, No.10, pp. 1013041-1013049, 2008.
- [10] M. Tseng, C. Yen, and C. C. S. Song, “Computation of Three-Dimensional Flow Around Square and Circular Piers,” Int J Numer Methods Fluids Vol.34, No.3, pp. 207-227, 2000.
- [11] C. Dalton and W. Zheng, “ Numerical Solutions of a Viscous Uniform Approach Flow Past Square and Diamond Cylinders,” J Fluids Struct Vol.18, Nos.3-4, pp. 455-465, 2003.
- [12] A. Sohankar, “Flow Over a Bluff Body from Moderate to High Reynolds Numbers Using Large Eddy Simulation,” Comput Fluids Vol.35, No.10, pp. 1154-68, 2006.
- [13] P. K. Mohapatra and M. H. Chaudhry, “Numerical Solution of Boussinesq Equations to Simulate Dam-Break Flows,” J Hydraul Eng Vol.130, No.2, pp. 156-159, 2004.
- [14] F. Federico and A. Amoruso, “Impact Between Fluids and Solids. Comparison Between Analytical and FEA Results,” Int J Impact Eng Vol.36, No.1, pp. 154-164, 2009.
- [15] H. Yeh, A. Ghazali, and I. Marton, “Experimental Study of Bore Run-Up,” J Fluid Mech Vol.206, pp. 563-578, 1989.
- [16] H. G. Hornung, C. Willert, and S. Turner, “The Flow Field Downstream of a Hydraulic Jump,” J Fluid Mech Vol.287, pp. 299-316, 1995.
- [17] I. A. Svendsen, J. Veeramony, and J. Bakunin, “The Flow in Weak Turbulent Hydraulic Jumps,” J Fluid Mech Vol.418, pp. 25-57, 2000.
- [18] G. Lauber and W. H. Hager, “Experiments to Dambreak Wave: Horizontal Channel,” J Hydraul Res/Rech Hydraul Vol.36, No.3, pp. 291-307, 1998.
- [19] C. Koch and H. Chanson, “Turbulent Mixing Beneath an Undular Bore Front,” J Coast Res Vol.24, No.4, pp. 999-1007, 2008.
- [20] B. Dargahi, “Turbulent Flow Field Around a Circular Cylinder,” Exp Fluids Vol.8, Nos.1-2, pp. 1-12, 1989.
- [21] M. A. F. Sadeque, N. Rajaratnam, and M. R. Loewen, “Flow Around Cylinders in Open Channels,” J Eng Mech Vol.134, No.1, pp. 60-71, 2008.
- [22] R. Reinauer and W. H. Hager, “Supercritical Flow Behind Chute Piers,” J Hydraul Eng Vol.120, No.11, pp. 1292-1308, 1994.
- [23] R. H. Cross, “Tsunami Surge Forces,” ASCE Proc, J Waterw Harb Div Vol.93, pp. 201-231, 1967.
- [24] Y. Fukui, M. Nakamura, and H. Shiraishi, “Hydraulic Study on Tsunami,” Coast Eng Jpn Vol.6, pp. 67-82, 1963.
- [25] S. Nakamura and Y. Tsuchiya, “On Shock Pressure of Surge on a Wall,” Bull. Disaster Prevention Res. Inst., Kyoto Univ., Vol.23, Parts 3-4, No.12, pp. 47-58, 1973.
- [26] R. Asakura, K. Iwase, T. Ikeya, M. Takao, T. Kaneto, N. Fujii, and M. Ohmori, “The Tsunami Wave Force Acting on Land Structures,” Proceedings of the 28th International Conference on Coastal Engineering. Cardiff, Wales, pp. 1191-1202, 2002.
- [27] J. D. Ramsden, “Tsunamis: Forces on a Vertical Wall Caused by Long Waves, Bores, and Surges on a Dry Bed,” PhD Thesis, Calif Inst Tech, 1993.
- [28] J. D. Ramsden and F. Raichlen, “Forces on Vertical Wall Caused by Incident Bores,” J Waterway Port Coast Ocean Eng Vol.116, No.5, pp. 592-613, 1990.
- [29] J. S. McNown and G. H. Keulegan, “Vortex Formation and Resistance in Periodic Motion,” Proc ASCE J Eng Mech Div Vol.85, pp. 1-6, 1956.
- [30] V. I. Bukreev and V. V. Zykov, “Bore impact on a vertical plate,” J Appl Mech Tech Phys Vol.49, No.6, pp. 926-933, 2008.
- [31] J. Wienke and H. Oumeraci, “Breaking Wave Impact Force on a Vertical and Inclined Slender Pile - Theoretical and Large-Scale Model Investigations,” Coast Eng Vol.52, No.5, pp. 435-462, 2005.
- [32] S. Gardarsson, “Shallow-Water Sloshing,” PhD Thesis, Univ of Wash, 1997.
- [33] H. Arnason, “Interactions between an incident bore and a free-standing coastal structure,” PhD Thesis, Univ Wash., 2005.
- [34] D. M. Causon, D. M. Ingram, and C. G. Mingham, “Calculation of Shallow Water Flows Using a Cartesian Cut Cell Approach,” Adv Water Resour Vol.23, No.5, pp. 545-562, 2000.
- [35] H. Yeh, “Design Tsunami Forces for Onshore Structures,” J Disaster Res Vol.2, No.6, pp. 531-536, 2007.
- [36] S. K. Chakrabarti, K. K. Debus, J. Berkoe, and B. Rosendall, “CFD Analysis of Current-Induced Loads on Large Caisson at Supercritical Reynolds Number,” J. Offshore Mech. Arctic Engr. Vol.127, No.111, pp. 104-111, 2005.