281 Advances in Renewable Energies Offshore – Guedes Soares (Ed.) © 2019 Taylor & Francis Group, London, ISBN 978-1-138-58535-5 Wave diffraction by a floating fixed truncated vertical cylinder based on Boussinesq equations S.C. Mohapatra, H. Islam & C. Guedes Soares Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal ABSTRACT: Mathematical modelling of wave diffraction by a floating fixed truncated vertical cylinder is formulated based on Boussinesq-type equations in the application range of weakly dispersive Boussinesq model. The nonlinear Boussinesq equations with depth parameters, which indicate the specific elevations in exterior region are obtained based on an expansion of velocity potentials as a power series in the dispersive effect. Using Bessel functions in the velocity potentials, the mathematical problem is handled for second-order wave amplitudes using perturbation technique and structural boundary conditions. To check the fidelity of the analytical model, the initial results of second-order super-harmonic wave amplitude around the vertical cylinder are compared with CFD simulations and CFD results are compared against Experimental Fluid Data (EFD) for normalized wave height. For CFD simulations, the open source CFD toolkit, OpenFOAM, is used. The initial comparison shows a good level of agreement among analytical, CFD and EFD models. Therefore, recently, some researchers are target- ing the implementation of Boussinesq-type model to study WECs associated with floating vertical cylinder. In the literature, few studies can be found on the analytical study of nonlinear wave diffraction by a vertical cylinder based on Boussinesq approach in shallow water has received limited attention. For instance, Yu (1987) employed Bessel coordinate transformation to study the wave forces on mul- tiple cylinders in shallow water based on cnoidal and solitary wave theory approach. Basmat & Zie- gler (1998) obtained the analytical solutions using Fourier transformation technique based on higher- order Boussinesq equations of wave diffraction by a rigid vertical circular cylinder to investigate the wave loading on the cylinder. Kang et al. (2015) studied the wave forces and free surface displace- ment around a fixed floating truncated vertical cyl- inder based on three-dimensional numerical model and the results are compared with experimental and analytical results in deep water. On the other hand, recent efforts have been made to formulate and provide some analytical solutions of the problems associated with wave interaction with floating structures based on Boussinesq-type equations. Mohapatra & Guedes Soares (2015b) studied the wave forces acting on the floating structure based on linearized Boussin- esq equations using eigenmode expansion method. Lannes (2017) provided some analytical solutions 1 INTRODUCTION Over the decades, there has been considerable progress on the linear analytical hydrodynamic models associated with fluid-structure interactions for the assessment of motions, loads, power pro- duction, and hence the wave energy sector relies heavily on the use of these models. On the other hand, limited work has been done on nonlinear analytical models associated with wave interaction with floating structures for the wave load analysis based on Boussinesq-type equations, and there is much room for progress. Boussinesq-type equations allow the use of non- linear hydrodynamics and can also realise a large number of irregular sea states needed for valida- tion, optimization and fatigue predictions. Hence, study of wave-structure interaction and wave- induced forces associated with non-linear effect on floating structures based on analytical models using Boussinesq equations is of recent interest due to its wide applicability in the field of ocean and coastal engineering. In order to design floating wave energy con- verters (WECs), accurate prediction of the wave induced loads on the floating structure is neces- sary. Especially, the incoming wave height or wave amplitude considered during design is substantial. So, the nonlinear wave effects cannot be ignored, thus, the linear potential theory may not predict realistic values for wave amplitude and wave forces.