## Abstract

Depth-averaged models such as non-linear shallow water (NLSW) and Boussinesq based codes usually use the quadratic friction law with Manning's coefficient to describe the surface roughness of the bottom. Large roughness elements such as buildings and tree vegetation, which are too small to be resolved by the grid of the bottom topography, are mainly considered by using purely empirical Manning coefficients. This approach, however, is not physically sound and may thus result in very large uncertainties in inundation modeling. A more physically-based approach is to determine prediction formulae for the hydraulic resistance of large roughness elements, considering for example different shapes, sizes and arrangements which can then be directly implemented in such models. Such prediction formulae can be determined on the basis of systematic simulations using a validated 3D numerical model. To better understand complex flow phenomena involved in tsunami inundation, three vertical emerged cylinders have been arranged in four different configurations with four different distances between each other and subject to a solitary wave and to a bore. A validated three-dimensional two-phase Reynolds-averaged Navier-Stokes (RANS) model and the Volume of Fluid (VOF) method (OpenFOAM) has been used to assess flow velocities and water levels near the cylinders and the inline forces acting on the cylinders. The effects of side-by-side, tandem and two staggered arrangements as well as the effect of the distances between them on the flow induced by a solitary wave and a bore are discussed. The study led to an improved understanding in the near field of cylinders, which forms the basis for further studies related to larger groups of cylinders and other shapes.## References

Árnason, H., 2004. Interactions between an Incident Bore and a Free-Standing Coastal Structure, Ph.D. thesis, University of Washington, USA.

Árnason, H., Yeh, H. and Petroff, C. 2005. Interactions between an Incident Bore and a Vertical Column, http://people.oregonstate.edu/~yehh/tsunamiforces/, last accessed: June 13, 2014.

Augustin, L.N., Irish, J.L. and Lynett P.J. 2009. Laboratory and numerical studies of wave damping by emergent and near-emergent wetland vegetation, Coastal Engineering, 56, 332-340.

Bonakdar, L. 2012, personal communication, 19/10/2013 18:32 CET.

Bonakdar, L. and Oumeraci, H. 2014. Small and large scale experimental investigations of wave loads on a slender pile withinclosely spaced neighbouring piles, Proceedings of 33rd International Conference on Ocean, Offshore and Arctic Engineering, San Francisco, California.

CFD-Wiki. 2012. Turbulence free stream boundary conditions, http://www.cfd-online.com/Wiki/Turbulence_free-stream_boundary_conditions, last accessed: 27 February 2014.

Choi, J. and Yoon, S.B. 2009. Numerical simulations using momentum source wave-maker applied RANS equation model, Coastal Engineering, 56, 1043-1060.

Chow, V. 1959. Open Channel Hydraulics, McGraw Hill, New York.

Dean, R.G. and Dalrymple, R.A. 1991. Water Wave Mechanics for Engineers and Scientists, Advanced Series on Ocean Engineering, World Scientific, Singapore.

Gayer, G., Leschka, S., Noehren, I., Larsen, O. and Guenther, H. 2010. Tsunami inundation modelling based on detailed roughness maps of densely populated areas, Natural Hazards & Earth System Science, 10, 1679-1687.

Goseberg, N. 2011. The Run-up of Long Waves-Laboratory-scaled Geophysical Reproduction and Onshore Interaction with Macro-Roughness Elements. PhD Thesis, Universität Hannover, Germany.

Harada, K. and Imamura, F. 2000. Experimental study on the resistance by mangrove under the unsteady flow, Proceedings of the 1st Congress of APACE, pp. 975-984.

Hori, E. 1959. Experiments on Flow around Pair of Parallel Circular Cylinders, Proceedings of 9th Japan National Congress for Applied Mechanics, Tokyo, pp. 231-234.

Husrin, S., Strusinska, A. and Oumeraci, H. 2012. Experimental study on tsunami attenuation by mangrove forest. Earth Planets Space, 64, 973-989.

Jacobsen, N.G., Furmann, D.R. and Fredsoe, J. 2012. A wave generation toolbox for the Open-Source CFD Library: OpenFOAM. Int. J. Numerl. Meth. Fluids, 70(9), 1073-1088.

Jakeman. 2010, J.D., Nielsen, O.M., can Putten, K., Mleczko, R., Burbidge, D. and Horspool, N. 2010. Towards spatially distributed quantitative assessment for tsunami inundation models. Ocean Dyn., 60, 1115-1138.

Kaiser, G., Scheele, L., Kortenhaus, A., Løvolt, F., Roemer, H. and Leschka, S. 2011. The influence of land cover roughness on the resultof high resolution tsunami inundation modeling. Nat. Hazards Earth Syst. Sci., 11, 2521-2540.

Latief, H. 2000. Study on tsunamis and their mitigation by using a green belt in Indonesia. Ph.D. thesis, Tohoku University, Sendai, Japan

Leschka, S. and Oumeraci, H. [2011] "3D numerical simulations of the effect of large roughness elements on the propagation of solitary waves,†6th Annual Int. Workshop and Expo on Sumatra Tsunami Disaster and Recovery 2011 in Conjunction with 4th South China Sea Tsunami Workshop, Banda Aceh, Indonesia, available at http://www.dhi-ntu.com.sg/-/media/publications/news/2013/04/leschkaoumeraci_2011-effectoflargerougnesselementsonthepropagationofsolitarywaves.pdf (accessed on September 24, 2014)

Leschka, S., Oumeraci, H. and Larsen, O. 2014. Hydrodynamic Forces on a Group of Three Emerged Cylinders by Solitary Waves and Bores: Effect of Cylinder Arrangements and Distances. Journal of Earthquake and Tsunami, 8 (3), 144005 (36 pages).

Matsutomi, H., Ohnuma, K., Suzuki, A. and Imai, K. 2006. Governing equations for inundated flow in vegetated areas and similarity laws for tree trunks. Proceedings of 30th Int. Conf. Coastal Engineering, San Diego, California.

Olsson, E. and Kreiss, G. 2005. A conservative level set method for two phase flow. J. Comput. Phys., 210, 225-246.

Olsson, E., Kreiss, G. and Zahedi, S. 2007. A conservative level set method for two phase flow II. J. Comput. Phys., 225, 785-807.

Satake, K., Bourgeois, J., Abe, Ku., Abe, Ka., Tsuji, Y., Imamura, F., Iito, Y., Katao, H., Noguera, E. and Estrada, F. 1993. Tsunami field survey of the 1992 Nicaragua Earthquake. EOS Trans. Am. Geophys. Union, 74 (13), 145-160.

Strusinska, A. 2010. Hydraulic Performance of an Impermeable Submerged Structure for Tsunami Damping. Ph.D. thesis, TU Braunschweig, Germany.

Suzuki, T. and Arikawa, T. 2010. Numerical analysis of bulk drag coefficients in dense vegetation by immerse boundary method. Proceedings of 32 Int. Conf. Coastal Engineering, Shanghai, China.

Synolakis, C. E., Imamura, F., Tsuji, Y., Matsutomi, H., Tinti, S., Cook, B., Chandra, Y. P. and Usman, M. 1995. Damage conditions of East Java Tsunami of 1994 analyzed. EOS Trans. Am. Geophys. Union, 76 (26), 257-264.

Yeh, H., Imamura, F., Synolakis, C., Tsuji, Y., Liu, P. L.-F. and Shaozhong, S. 1993. The Flores Island Tsunami. EOS Trans. Am. Geophys. Union, 74 (33), 369, 371-373.

Yeh, H. 2014. Personal communication, April 1, 2014 06:20 CET.

Yuan, Z. and Huang, Z. 2009. Solitary wave forces on an array of closely spaced circular cylinders. Proceedings of 5th Int. Conf. Asian and Pacific Coasts, Vol. 1, Singapore, pp. 136-142.

Zdravkovich, M. M. 1977. Review-review of flow interference between two circular cylinders in various arrangements. J. Fluids Eng., 99 (4), 618-633.