Second Research Meeting 2025

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The second meeting will be held on Friday 13 June 2025 at the University of Exeter. If you would like to attend the meeting, please register by sending an email to h.alemi-ardakani@exeter.ac.uk

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University of Exeter

 New advances in mathematical modelling and numerical analysis in ocean wave energy.  

 

This meeting will be devoted to new mathematical models and numerical algorithms for nonlinear water waves and wave-structure interactions. Topics will include: New geometric formulations for highly-coupled nonlinear systems in ocean wave energy. New structure-preserving and conservative algorithms for long-time computational modelling of water waves and wave-structure + flexible membrane interactions and boundary coupling. New advances in Computational Fluid Dynamics (CFD) and machine learning methods for wave-structure interactions and ocean wave energy.

 

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Theme: New advances in mathematical modelling and numerical analysis in ocean wave energy

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Date: Friday 13 June 2025, 10:30 – 16:30

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Venue: Room 203, Harrison Building, University of Exeter, Streatham Campus, Exeter EX4 4QF

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Timetable

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10:30–11:00 Arrival and Coffee

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11:00–11:40 Onno Bokhove (University of Leeds)

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Power optimisation of a heaving buoy in a wave-enhancing contraction (+)

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11:40–12:20 Richard Porter (University of Bristol)

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Metamaterials in the design of ocean wave energy converters

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12:20–13:00  Kang Ren (University of Southampton)

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Liquid Motion in Cylindrical Containers with Elastic Covers under External
Excitation

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13:00–14:00 Lunch and discussion

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14:00–14:40 Matt Turner (University of Surrey)

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Wave breaking due to a sharp-crested superharmonic instability

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14:40–15:20 Simone Michele (University of Rome Tor Vergata & University
of Plymouth)

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Theoretical and Experimental Analysis of Flexible Disks and Rigid Rectan-
gular Compound Plates

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15:20–15:40 Coffee break

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15:40–16:20 Hamid Alemi Ardakani (University of Exeter)

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A fourth-order Poisson-bracket solver for shallow-water sloshing in the FlexS-
losh WEC with inflow-outflow boundary conditions

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16:20–16:30 Conclusion and discussion

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Titles and Abstracts

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Onno Bokhove (University of Leeds)

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Power optimisation of a heaving buoy in a wave-enhancing contraction (+)​

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Onno Bokhove, School of Mathematics and Leeds Institute for Fluid Dynamics (LIFD), Leeds, UK with:
Peter Grieve, Jongrae Kim, Jaemin Lee, Omar Naar, Harvey Thompson School of Mechanical Engineering, University of Leeds

 

Power optimisation of a heaving-buoy wave-energy device will be considered for a device placed in a wave-amplitude enhancing (V-shaped) contraction. I will present our variational, mathematical and numerical, (non)linear wave-to-wire model [1,2]. It consists of three coupled components: (i) hydrodynamics, (ii) buoy motion and (iii) power generation. It is ideally placed in a breakwater or in an array of contractions moored at sea. I will partition and analyse our model in: (ii-iii) a buoy-generator sub-model [3] and (i-ii) a hydrodynamic wave and buoy sub-model. The (ii-iii) buoy-generator model will either be driven by a specified hydrodynamic force or via a moving hanging point. We have extended the buoy-generator sub-model (ii-iii): (a) to an N -induction-coil model rectified in parallel, enhancing power output relative to a single coil of similar length; (b) with nonlinear simulations of the ODEs of the buoy-generator model (both for ideal rectifiers and via Matlab’s Simulink); (c) by adaption of a Shockley power-using load to a similar Butler-Volmer battery model; and, (d) via experimental validation of the dry model hanging from a moving point. Furthermore, I will describe progress on our (incomplete) wave-buoy sub-model (i-ii), including: the numerical potential-flow model with reduced/optimized vertical resolution and how it is coupled to the buoy motion. We are exploring a novel inequality-constraint (variational and numerical) technique to couple nonlinear wave hydrodynamics and buoy motion. Finally, time and progress permitting, I will show our preliminary laboratory results of another elastomer-wave energy device placed in or near the beach’ surf-zone!

 

[1] Bokhove, O., Kalogirou, A, Zweers W. 2019: From bore-soliton-splash to a new wave-to-wire wave-energy model. Water Waves 1, 217-258. 10.1007/s42286-019-00022-9.

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[2] Bokhove O., Anna Kalogirou, A., Henry, D., Thomas, G. 2020: A novel rogue-wave-energy device with wave amplification and induction actuator. Int. Marine Energy J. 30, 37-43.

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[3] Bokhove, O., Bolton, J. and Thompson, H. 2024: Geometric power optimisation of a rogue-wave energy device in a (breakwater) contraction. 8th IEEE Conf. on Control Technology and Applications, 21-23 Aug 2024, Newcastle Upon Tyne, UK.

Preprint: https://eartharxiv.org/repository/view/7260/

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Richard Porter (University of Bristol)

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Metamaterials in the design of ocean wave energy converters

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In this talk I will review some recent work which incorporates small scale structures into the design of wave energy converters as a means of increasing the capacity for generating power. The term metamaterial is borrowed from other areas of physics and used generically to describe sub wavelength structures that can produce exotic effects on the underlying wave field. It will be shown both theoretically and numerically how circular devices are capable of producing power which far exceeds the theoretical limits of the equivalent traditional device operating in normal solid body motion.

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Kang Ren (University of Southampton)

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Liquid Motion in Cylindrical Containers with Elastic Covers under External
Excitation

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The coupled motion of liquid with an elastic plate or membrane cover in a cylindrical container under external excitation is investigated. Unlike self-oscillation problem at a natural frequency, the problem is fully transient, and it is first converted from the time domain to the s-domain through the Laplace transform. For each given s, velocity potential for the fluid flow and cover deflection are obtained through the Bessel-Fourier series. The solution in the time domain is then obtained through the inverse Laplace transform with respect to s. When doing so analytically, it is necessary to find singularities of the integrand in the entire complex plane s. It is shown that these singularities are only on the imaginary axis, corresponding precisely to the natural frequencies of the system and the excitation frequencies. This allows that the final solution to be obtained explicitly, which gives insight how the motion behaves. Extensive results are presented for the time history of the cover deflection and the energy components under various external excitation, including tank motion and external pressure on the cover. The frequency components of the solutions are analysed both at resonance and off-resonance. The energy transfer into the system from external forcings and its redistribution during vibration within the system are analysed.

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Matt Turner (University of Surrey)

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Wave breaking due to a sharp-crested superharmonic instability

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In order to understand the wave energy potential of our oceans we must also understand the wave breaking properties they have too. In this talk we examine the mechanism for the emergence of breaking water waves in deep water, based on the superharmonic instability of periodic two-dimensional Stokes waves. We test  real-world perturbations such as dissipation, approximation error, changes in depth, nonzero air density, fluctuations in wave and frame speed. An implicit perturbation is added to a large-amplitude unstable Stokes wave, which is then taken as initial data in a direct numerical solution of the Navier-Stokes equations, using the Basilisk numerical software package. We identify a dipole shape in the filtered wave that correlates with the superharmonic unstable mode. Our findings show that the inclusion of real-world effects has little qualitative effect, when they are kept small, on the emergence of breaking. We finish by discussing how this idea can be extended to three-dimensions to analyse wave breaking in short-crested waves.

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Simone Michele (University of Rome Tor Vergata & University
of Plymouth)

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Theoretical and Experimental Analysis of Flexible Disks and Rigid Rectangular Compound Plates

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We first present results from physical model tests conducted in the COAST Laboratory at the University of Plymouth, investigating the hydrodynamics of a flexible floating disk. Response amplitude operators are determined for both incident monochromatic and irregular wave trains. Free-surface displacements are measured, and the plate motion is recorded using a QUALISYS® motion tracking system. Various basin depths, plate thicknesses, and wave amplitudes are considered. We report synchronous and subharmonic nonlinear responses for monochromatic waves, and displacement spectra for irregular waves. The measured wave hydrodynamics and disk hydroelastic responses show good agreement with theoretical predictions based on potential flow theory.

 

Then, we present a theoretical model for analysing the hydrodynamics of three-dimensional, rigid, floating, compound rectangular plates in the open sea. The hydrodynamic problem is solved using Green’s theorem and a free-surface Green’s function. Plate motion is predicted by decomposing it into rigid-body natural modes. We first analyse a single rectangular plate and validate our model against experimental results obtained from physical model tests in the COAST Laboratory. The theory is then extended to wave energy converters (WECs), complex geometries, and arrays of plates. We examine how platform geometry, incident wave direction, and power take-off coefficients affect the platform's response and the corresponding absorbed energy.

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Hamid Alemi Ardakani (University of Exeter)

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A fourth-order Poisson-bracket solver for shallow-water sloshing in the FlexSlosh WEC with inflow-outflow boundary conditions

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The second-order mass-, energy-, and potential-enstrophy-conserving discretisation introduced by Arakawa & Lamb (1981) for the shallow-water equations with periodic boundary conditions, and extended by Salmon (2004) in the context of Hamiltonian Poisson-bracket discretisation, is further extended to a fourth-order discretisation in the potential-vorticity dependent component of the Poisson-bracket, for the problem of nonlinear shallow-water sloshing over a corrugated bottom surface in a rectangular rigid basin, with non-symmetric porous side walls and coupled no-flow and non-periodic influx-efflux boundary conditions, undergoing a prescribed coupled surge-sway motion. Adaptation to a finite domain with non-periodic inflow-outflow boundary conditions requires a new approach to the boundary conditions at porous solid boundaries in the context of the fourth-order discretisation on the Arakawa C grid. The scheme is implemented, shown to preserve the total mass, energy, and potential enstrophy over long-time integration. This higher-order C-bracket sloshing integrator provides a robust, stable, fast and precise building block for long-time computational modelling of floating ocean wave energy extractors with flexible components.

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For any enquiries, please contact Hamid Alemi Ardakani.