Explore the vast range of titles available.

Motivated by the relevance of so-called nonlinear Froude–Krylov (FK) hydrodynamic effects in the accurate dynamical description of wave energy converters (WECs) under controlled conditions, and the apparent lack of a suitable control framework effectively capable of optimally harvesting ocean wave energy in such circumstances, we present, in this paper, an integrated framework to achieve such a control objective, by means of two main contributions. We first propose a data-based, control-oriented, modelling procedure, able to compute a suitable mathematical representation for nonlinear FK effects, fully compatible with state-of-the-art control procedures. Secondly, we propose a moment-based optimal control solution, capable of transcribing the energy-maximising optimal control problem for WECs subject to nonlinear FK effects, by incorporating the corresponding data-based FK model via moment-based theory, with real-time capabilities. We illustrate the application of the proposed framework, including energy absorption performance, by means of a comprehensive case study, comprising both the data-based modelling, and the optimal moment-based control of a heaving point absorber WEC subject to nonlinear FK forces.

Wave energy converters (WECs) have gained significant attention as a promising renewable energy source. Optimal control strategies, crucial for maximizing energy extraction, have traditionally relied on linear models based on small motion assumptions. However, recent studies indicate that these models do not adequately capture the complex dynamics of WECs, especially when large motions are introduced to enhance power absorption. The nonlinear Froude–Krylov (FK) forces, particularly in heaving-point-absorbers with varying cross-sectional areas, are acknowledged as key contributors to this discrepancy. While high-fidelity computational models are accurate, they are impractical for real-time control applications due to their complexity. This paper presents a parameterized approach for expressing nonlinear FK forces across a wide range of point-absorber buoy shapes inspired by implementing real-time, model-based control laws. The model was validated using measured force data for a stationary spherical buoy subjected to regular waves. The FK model was also compared to a closed-form buoyancy model, demonstrating a significant improvement, particularly with high-frequency waves. Incorporating a scattering model further enhanced force prediction, reducing error across the tested conditions. The outcomes of this work contribute to a more comprehensive understanding of FK forces across a broader range of buoy configurations, simplifying the calculation of the excitation force by adopting a parameterized algebraic model and extending this model to accommodate irregular wave conditions.

Wave energy converters (WECs) inherently require appropriate control system technology to ensure maximum energy absorption from ocean waves, consequently reducing the associated levelised cost of energy and facilitating their successful commercialisation. Regardless of the control strategy, the definition of the control problem itself depends upon the specification of a suitable WEC model. Not only is the structure of the model relevant for the definition of the control problem, but also its associated complexity: given that the control law must be computed in real-time, there is a limit to the computational complexity of the WEC model employed in the control design procedure, while there is also a limit to the (analytical) complexity of mathematical models for which a control solution can be efficiently found. This paper presents a systematic nonlinear model reduction by moment-matching framework for WEC systems, capable of providing control-oriented WEC models tailored for the control application, which inherently preserves steady-state response characteristics. Existence and uniqueness of the associated nonlinear moment for WECs are proved in this paper, for a general class of systems. Given that the definition of nonlinear moments depends upon the solution of a nonlinear partial differential equation, an approximation framework for the computation of the nonlinear moment is proposed, tailored for the WEC application. Finally, the use and capabilities of the framework are illustrated by means of case studies, using different WEC systems, under a variety of wave conditions.

The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\\epsilon \\leq c_0\\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \\rightarrow \\infty $. For times $t \\gtrsim \\mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of \"2.5 dimensional\" streamwise-independent solutions referred to as streaks.

A new validation campaign was conducted at the W2 Harold Alfond Ocean Engineering Laboratory at the University of Maine to investigate the hydrodynamic loading on floating offshore wind substructures, with a focus on the low-frequency contributions that tend to drive extreme and fatigue loading in semisubmersible designs. A component-level approach was taken to examine the hydrodynamic loads on individual parts of the semisubmersible in isolation and then in the presence of other members to assess the change in hydrodynamic loading. A variety of wave conditions were investigated, including bichromatic waves, to provide a direct assessment of difference-frequency wave loading. An assessment of the impact of wave uncertainty on the loading was performed, with the goal of enabling validation with this dataset of numerical models with different levels of fidelity. The dataset is openly available for public use and can be downloaded from the U.S. Department of Energy Data Archive and Portal.

Representative models of the nonlinear behavior of floating platforms are essential for their successful design, especially in the emerging field of wave energy conversion where nonlinear dynamics can have substantially detrimental effects on the converter efficiency. The spar buoy, commonly used for deep-water drilling, oil and natural gas extraction and storage, as well as offshore wind and wave energy generation, is known to be prone to experience parametric resonance. In the vast majority of cases, parametric resonance is studied by means of simplified analytical models, considering only two degrees of freedom (DoFs) of archetypical geometries, while neglecting collateral complexity of ancillary systems. On the contrary, this paper implements a representative 7-DoF nonlinear hydrodynamic model of the full complexity of a realistic spar buoy wave energy converter, which is used to verify the likelihood of parametric instability, quantify the severity of the parametrically excited response and evaluate its consequences on power conversion efficiency. It is found that the numerical model agrees with expected conditions for parametric instability from simplified analytical models. The model is then used as a design tool to determine the best ballast configuration, limiting detrimental effects of parametric resonance while maximizing power conversion efficiency.

A theoretical framework to study linear and nonlinear Richtmyer-Meshkov instability (RMI) is presented. This instability typically develops when an incident shock crosses a corrugated material interface separating two fluids with different thermodynamic properties. Because the contact surface is rippled, the transmitted and reflected wavefronts are also corrugated, and some circulation is generated at the material boundary. The velocity circulation is progressively modified by the sound wave field radiated by the wavefronts, and ripple growth at the contact surface reaches a constant asymptotic normal velocity when the shocks/rarefactions are distant enough. The instability growth is driven by two effects: an initial deposition of velocity circulation at the material interface by the corrugated shock fronts and its subsequent variation in time due to the sonic field of pressure perturbations radiated by the deformed shocks. First, an exact analytical model to determine the asymptotic linear growth rate is presented and its dependence on the governing parameters is briefly discussed. Instabilities referred to as RM-like, driven by localized non-uniform vorticity, also exist; they are either initially deposited or supplied by external sources. Ablative RMI and its stabilization mechanisms are discussed as an example. When the ripple amplitude increases and becomes comparable to the perturbation wavelength, the instability enters the nonlinear phase and the perturbation velocity starts to decrease. An analytical model to describe this second stage of instability evolution is presented within the limit of incompressible and irrotational fluids, based on the dynamics of the contact surface circulation. RMI in solids and liquids is also presented via molecular dynamics simulations for planar and cylindrical geometries, where we show the generation of vorticity even in viscid materials.

In this paper, we present numerical modelling for the investigation of dynamic responses of a floating offshore wind turbine subject to focused waves. The modelling was carried out using a Computational Fluid Dynamics (CFD) tool. We started with the generation of a focused wave in a numerical wave tank based on a first-order irregular wave theory, then validated the developed numerical method for wave-structure interaction via a study of floating production storage and offloading (FPSO) to focused wave. Subsequently, we investigated the wave-/wind-structure interaction of a fixed semi-submersible platform, a floating semi-submersible platform and a parked National Renewable Energy Laboratory (NREL) 5 MW floating offshore wind turbine. To understand the nonlinear effect, which usually occurs under severe sea states, we carried out a systematic study of the motion responses, hydrodynamic and mooring tension loads of floating offshore wind turbine (FOWT) over a range of wave steepness, and compared the results obtained from two potential flow theory tools with each other, i.e., Électricité de France (EDF) in-house code and NREL Fatigue, Aerodynamics, Structures, and Turbulence (FAST). We found that the nonlinearity of the hydrodynamic loading and motion responses increase with wave steepness, revealed by higher-order frequency response, leading to the appearance of discrepancies among different tools.

Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.

In extreme marine environments, the interaction between offshore wind turbine pile foundations (OWTPFs) is critical, and the associated hydrodynamic loads are complex. This study focused on fixed OWTPFs and used computational fluid dynamics (CFD) to numerically simulate the flow field around pile foundations under the combined action of focusing waves and current. The objective was to investigate the influence of different focusing wave and current parameters on the hydrodynamic properties of the pile foundations. The findings indicate the following: (1) When the wave and current directions are opposite, the maximum wave force on the pile foundations is greater than when they are aligned. (2) Large-amplitude focusing waves around pile foundations generate secondary loads, which are nonlinear and lead to a rapid increase in the wave force. These secondary loads are short-lived and particularly prominent near the front row of pile foundations. (3) The influence of the group pile effect diminishes under high-amplitude waves, where the wave component dominates the generation of the dimensionless wave force, and the impact of the current on this force decreases.