Applied Ocean Research 63 (2017) 229–241 Contents lists available at ScienceDirect Applied Ocean Research journal homepage: www.elsevier.com/locate/apor Wave runup on a surging vertical cylinder in regular waves Wei Jian a , Deping Cao a , Edmond Yatman Lo b,∗ , Zhenhua Huang c , Xiaobo Chen d , Zhiping Cheng e , Hai Gu e , Binbin Li d a Maritime Institute, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore b School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore c Department of Ocean and Resources Engineering, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, HI 96822-2303, USA d Deepwater Technology Research Centre, Bureau Veritas Marine Singapore, 20 Science Park Road #03-01, Teletech Park, Singapore Science Park II, 117674, Singapore e Singapore Innovation and Research Centre, American Bureau of Shipping, 438 Alexandra Road #10-00, Alexandra Point, 119958, Singapore a r t i c l e i n f o Article history: Received 3 August 2016 Received in revised form 18 January 2017 Accepted 19 January 2017 Keywords: Wave runup Surging cylinder Regular waves SPH Offshore structures a b s t r a c t The wave runup caused by a vertical cylinder surging in regular waves is studied both experimentally and numerically. The so-called DualSPHysics Smoothed Particle Hydrodynamics (SPH) code is used for the 3-D numerical modelling. A wide range of cylinder sizes and wave conditions is investigated with results comparing favourably between the experimental and SPH model under both fixed and forced- surge conditions. The experimental and SPH results are further used to predict the maximum runup amplification, in particular the ratio of the runup caused by the surging cylinder to that of the fixed, over the phase difference between the incident wave and surge motion. This maximum runup ratio has been analysed for its dependence on factors such as wave steepness, wave scattering and surge amplitude. An empirical equation is proposed for predicting the maximum runup ratio from known incident wave and surge conditions. Comparison with results from linear solvers suggests that the linear solvers under-predict the full nonlinear runup by a factor of 1.3–1.5. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction As oil exploration and exploitation progress into increasingly deeper water, offshore floating structures are subject to more hostile environmental conditions. For such large volume floating structures, the wave runup on the wave-incident side of the sup- porting columns is particularly important for air-gap design and ultimately for the avoidance of impulsive pressure loads on the underside of the deck structure. The present engineering practice for modelling motion responses and the runup of moving columns are based on linear potential theory, assuming the flow is incompressible and irrota- tional. Linear theories have been well developed for the general case for the motion of a floating body with full six degrees of free- dom (e.g., [1–3]). However, they are only valid when the wave ∗ Corresponding author. E-mail addresses: jianwei@ntu.edu.sg (W. Jian), dpcao@ntu.edu.sg (D. Cao), cymlo@ntu.edu.sg (E.Y. Lo), zhenhua@hawaii.edu (Z. Huang), xiao-bo.chen@bureauveritas.com (X. Chen), zhcheng@eagle.org (Z. Cheng), hgu@eagle.org (H. Gu), binbin.li@sg.bureauveritas.com (B. Li). and structure motion amplitudes are small with respect to the wave steepness and typical structure dimension. Significant efforts have been devoted into developing nonlinear potential theories to predict the motion of floating structures in large waves. Most of such models found in literature generally fall into two cat- egories, weakly nonlinear frequency domain methods and fully nonlinear time domain methods. The weakly nonlinear frequency domain method uses a perturbation expansion and approximates the exact boundary conditions at the water and body surfaces by Taylor approximations. Early works by Molin [4] and Lighthill [5] evaluated the second-order diffraction forces on a single or multiple cylinders without explicitly calculating the second-order potential. Numerical methods were subsequently proposed to yield the second-order potential in complete fluid domain ([6,7]). This approach is valid for weakly nonlinear waves and forms the basis of some commercial software packages used in industry (e.g., WAMIT, ANSYS AQWA), which are based on the linear and second- order potential theory, some with nonlinear extensions. The other widely used approach is the fully nonlinear time domain method, first proposed by Longuet-Higgins and Cokelet [8] using a Mixed Eulerian-Lagrangian (MEL) time stepping scheme. It enforces the fully nonlinear boundary conditions on the water and body sur- http://dx.doi.org/10.1016/j.apor.2017.01.016 0141-1187/© 2017 Elsevier Ltd. All rights reserved.