Monopiles are commonly adopted in marine structures and subject to combined loading from waves and currents. The nature of superposition of wave and current loads needs to be known during the design stage. In the present paper, combined hydrodynamic loading induced by nonlinear waves and uniform currents on a cylinder is experimentally investigated. The current is represented by towing the cylinder along the flume. By this, nonlinear wave–current interactions are excluded physically, but the loading of a proportional current following or opposing a wave group is captured and analyzed. It is argued that towing makes provision for analyzing the nature of superposition of wave and current loads using Morison theory (which is not applicable to true combined wave–current fields) and also facilitates experimentation of a wide range of nonlinear wave and uniform current loading combinations onto the structure. Accordingly, regular, steep non-breaking and breaking focused waves interacting with the cylinder towed along and in opposition to the wave-field at different speeds have been investigated. The non-breaking wave–structure interactions have been analyzed within the framework of Morison theory using Fully Nonlinear Potential Theory (FNPT) based kinematics. Breaking wave–cylinder interactions have been analyzed through a spectral approach. The experiments demonstrate that wave and locally-acting current loads on the structure can be linearly superimposed, irrespective of the nature of waves and towing speed. Hence, provided wave–current interactions are excluded, steep breaking wave and uniform current loads can be linearly superimposed, despite focused wave generation itself being inherently nonlinear.

The paper presents coupling between a mesh-based finite-element model for Boussinesq equations (FEBOUSS Agarwal et al., 2022) with a meshless local Petrov–Galerkin model for the Navier–Stokes equations (MLPG_R Agarwal et al., 2021) in 3D. Boussinesq equation models are widely used for simulating wave-propagation over large domains with uneven topography using a 2D surface mesh. Mesh-less models inherently capture large free-surface deformations and have shown promise in simulating wave-structure interaction, run-up and breaking phenomenon. The hybrid approach in this paper assumes a 3D MLPG_R sub-domain surrounded by the 2D mesh of FEBOUSS. The coupling interface in MLPG_R consists of relaxation zones that can be placed along multiple boundaries of the sub-domain for exchanging particle velocity from FEBOUSS. This hybrid model is therefore capable of simulating directional waves, that has not been reported previously.
The paper first presents the procedure for calculating the depth-resolved velocities in 3D from the Boussinesq model. The resultant velocities are compared against theory, experiments and other models. The following sections present the coupling algorithm along a single and multiple coupling interfaces in MLPG_R. Validation results for this hybrid model are provided using surface elevation and velocity measurements for regular waves, including directional cases. In general, the results from the hybrid model are reported to have marginal over-prediction of peaks compared to purely MLPG_R simulation. Finally, the interaction of a vertical cylinder with direction regular wave is simulated using the 3D hybrid model.

In this paper, the comparative study carried out for focused wave interaction with a moving cylinder in ISOPE-2020 is reported. The fixed cylinder cases are reported in the companion paper as Part A (Sriram, Agarwal, Yan et al., 2021). The paper discusses qualitative and quantitative comparison between four different numerical solvers that participated in this comparative study. This is a challenging problem, as the cylinder moves over 40 m and interacts with the focusing waves. The performance of various solvers is compared for two different moving cylinder speeds. Both weakly coupled models and full Navier–Stokes (NS) solvers with different strategies for modeling the cylinder motion were adopted by the participants. In particular, different methods available for numerically simulating the forward speed problem emerge from this paper. The qualitative comparison based on the wave probe and pressure probe time histories between laminar and turbulent solvers is presented. Furthermore, the quantitative error analysis for individual solvers shows deviations up to 30% for moving wave probes and 50% for pressure time history. The reliability of each method is discussed based on all the wave probe and pressure probe discrepancies against experiments. The deviations for higher speed shown by all solvers indicate that further improvements in the modeling capabilities are required.

In this paper, a new set of experiments on the focused wave (using the second-order wavemaker theory) and current interactions with cylinders is being carried out. To represent a uniform current in laboratory, a cylinder is towed with a velocity opposite to the wave propagation directions. This paper discusses the experimental setup and test cases that were released for the comparative study at the ISOPE-2020 meeting. To obtain good correlation with different runs, the repeatability of the experiments is confirmed by comparing the surface elevation measurements at the fixed wave gauge location near the wave paddle, and an uncertainty analysis was carried out. The details on different test cases with varying frequency bandwidths of the focusing waves, speeds of the cylinder, and the locations of focusing are reported in this paper. Furthermore, a comparison of the dynamic pressure on the cylinder is reported between experiments with focusing waves with but without the towing condition. The present experimental campaign can be used as a validation case for state-of-theart numerical models.

This paper presents new developments in meshless local Petrov–Galerkin with Rankine source (MLPG_R) particle based method for studying interaction of waves with fixed structures in a numerical wave-tank. A new 3D formulation of the Lagrangian flow problem for incompressible fluid with optimised solution strategy is presented. The pressure Poisson equation is solved in local weak-form with integration done semi-analytically using a new symmetric expression. The wave-generation is done using one-way coupling with a 2D fully-nonlinear potential theory based finite-element model. Further a simple identification method for free-surface particles is proposed, which is shown to work well in vicinity of the structure. The solid-wall boundary condition is treated using ghost and mirror particles for accurate calculation of gradients. The waterline on domain boundary faces is treated using a tangentially moving side-wall approach which makes this particle based scheme capable of capturing small amplitude waves and focusing waves. The paper briefly presents experimental setup used for studying the interaction of a fixed emergent cylinder with uni-directional regular and focusing waves in 3D. The numerical model is validated against results from this experiment. An analysis is conducted on parameters related to local integration domain, wave-making coupling algorithm, particle distribution and time-step. This work highlights the use of hybrid approach for efficient and accurate simulation of waves-structure interaction.

In this paper, a new set of experiments on the focused wave (using the 2nd order wavemaker theory) and current interactions with cylinder is being carried out. In order to represent a uniform current in laboratory, cylinder is towed with a velocity opposite to the wave propagation directions. This paper discusses about the experimental setup and test cases that was released for the comparative study in the ISOPE 2020. In order to obtain good correlation with different runs, the repeatability of the experiments is confirmed by comparing the surface elevation measurements at the fixed wave gauge location near the wave paddle and uncertainty analysis was carried out. Different test cases with varying frequency bandwidth of the focusing waves, speed of the cylinder and the locations of focusing are investigated and will be reported in this paper. Further, a comparison for the dynamic pressure on cylinder is reported between experiments with wave and wave with uniform current.

This paper presents a 2D/3D hybrid numerical model for studying the interaction of non-breaking waves with cylindrical structure. The work combines the strengths of mesh-based and particle-based methods, where the wave propagation is solved using 2D mesh-based potential theory model and the interaction with the structure is solved using 3D particle-based Navier-Stokes model. The paper presents the formulation of the two models and the weak-coupling methodology, along with recent improvements in the 3D MLPG_R (Mesh-less Petrov-Galerkin based on Rankine source solution) particle based method. The numerical results from interaction of fixed cylinder with solitary and focussed waves are compared with experimental data. The work demonstrates a significant reduction in simulation time for wave-structure interaction problems achieved using this hybrid approach without compromising on accuracy.

The paper presents a numerical model of the two-dimensional enhanced Boussinesq equations to simulate wave transformations in the near-shore region. The finite element-based discretisation over unstructured mesh with triangular elements uses mixed linear and quadratic shape functions. The domain integrals are calculated analytically. The model is extended to study flow through porous structures using Darcy velocity, with the energy dissipation within the porous medium modelled through additional laminar and turbulent resistance terms. A single set of empirical constants gives accurate prediction for various stone sizes and porosity. This paper reports the model development and its validation using existing experimental studies. Application of the model is demonstrated by studying the interaction between ship-generated waves in a narrow channel and the porous walls of the channel.