Numerical wave tank computations of nonlinear motions of two-dimensional arbitrarily shaped free floating bodies

Time domain simulations of nonlinear motions of two-dimensional floating bodies in waves are presented. The so called `body exact' approach is adopted in a numerical wave tank. A new scheme for pressure evaluation on the wetted hull is developed and systematically used with good results in terms of accuracy and stability. Strongly flared geometries are successfully handled even at very large amplitude motions. The validation of the code is carried out according to the 20th ITTC Seakeeping Committee recommendations through internal checks of consistency and through comparisons with available experimental data.     

Direct time domain analysis of floating structures with linear and nonlinear mooring stiffness in a 3D numerical wave tank

In this paper, motion response of a moored floating structure interacting with a large amplitude and steep incident wave field is studied using a coupled time domain solution scheme. Solution of the hydrodynamic boundary value problem is achieved using a three-dimensional numerical wave tank (3D NWT) approach based upon a form of Mixed-Eulerian–Lagrangian (MEL) scheme. In the developed method, nonlinearity arising due to incident wave as well as nonlinear hydrostatics is completely captured while the hydrodynamic interactions of radiation and diffraction are determined at every time step based on certain simplifying approximations. Mooring lines are modelled as linear as well as nonlinear springs. The horizontal tension for each individual mooring line is obtained from the nonlinear load-excursion plot of the lines computed using catenary theory, from which the linear and nonlinear line stiffness are determined. Motions of three realistic floating structures with different mooring systems are analyzed considering various combinations of linear and approximate nonlinear hydrodynamic load computations and linear/nonlinear mooring line stiffness. Results are discussed to bring out the influence and need for consideration of nonlinearities in the hydrodynamics and hydrostatics as well as the nonlinear modelling of the line stiffness.     

Application of a nonlinear frequency domain wave–current interaction model to shallow water recurrence effects in random waves

The effect of ambient currents on nearshore nonlinear wave–wave energy transfer in random waves is studied with the use of a nonlinear frequency domain wave–current interaction model. We focus on the phenomenon of wave recurrence as a classical nonlinear phenomenon whose characteristics are well established for systems truncated to small numbers of frequency modes. The model used for this study is first extended to enhance accuracy; comparisons of permanent form solutions to analytical forms confirm the model accuracy. Application of the model to a highly truncated system confirmed the model’s consistency with published results for both positive (following) and negative (adverse) currents. Propagation of random wave spectra over a flat bottom was performed with the model, with the intent of determining the prevalence of recurrence between the spectral peak and its harmonics. For spectra of moderate Ursell number, it was found that positive currents extended the length scale of recurrence relative to the case with no currents; conversely, negative currents reduced the recurrence lengths. However, beyond a propagation distance of ≈40 wavelengths of the spectral peak, recurrence becomes almost completely damped as the spectra becomes broad and the spectral energies equilibrate. For spectra of high Ursell number, in contrast, recurrence is almost immediately damped, suggesting that the nonlinearity is sufficient to allow immediate spectral broadening and equilibration and overwhelming any preferential interactions among the spectral peak and its harmonics, regardless of current magnitude or direction.     

Hybrid three-dimensional finite-difference and finite-element analysis of seismic wave induced fluid–structure interaction of a vertical cylinder

The two-dimensional finite-difference scheme has been extended to three dimensions to solve nonlinear hydrodynamic pressures and structural responses of a deformable, vertical and circular surface-piercing offshore cylinder during earthquakes. A complete three-dimensional analysis has been made with both the three-dimensional equations of motion and the simultaneous action of three components of ground acceleration included in the analysis. Not only the magnitude but also the direction of the acting ground motion can be varied with time. The dynamic response of a cylinder is approximated by the displacements in the fundamental modes of vibration. A comparison of the dynamic displacement of the cylinder with and without surrounding sea water has been made. The flexibility of the offshore cylinder can significantly increase the hydrodynamic pressures acting on cylinder faces, that is, the fluid-structure interaction is necessary in offshore cylinder analysis. Although the hydrodynamic pressure induced by the vertical ground acceleration of the El Centro 1979 earthquake is significant, the calculated structural dynamic response of a cylinder is very small and the corresponding resultant hydrodynamic force is almost nil. The hydrodynamic force induced by two-horizontal ground acceleration is about the same as that by three simultaneous components of ground acceleration. For a solid and stubbier circular cylinder, the vertical component of ground acceleration may be neglected.     

Nonlinear wave profiles of wave–wave interaction in a finite water depth by fixed point approach

In this paper, a superposition of two periodic wave profiles in a finite water depth was investigated. This paper is focused on the improvement of a wave profile on the linear superposition of two waves. This improvement was realized by introducing an iterative method, which was based on a fixed point approach. Application of the fixed point approach to the wave superposition made it possible to obtain a wave profile of wave–wave interaction. The improved result of the wave profile was in good agreement with that of the nonlinear perturbation solution of the second order. It was interesting that the improved result revealed the higher-order nonlinear frequencies for two interacting Stokes waves while Dalzell's solution by a perturbation method could not predict them.