Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

On the Structure of Waves Radiated by a Submerged Cylinder
Undergoing Large-Amplitude Heave Motions
Raphaël Alwan1 , Boyin Ding1 , David M. Skene1 , Zhaobin Li2 and Luke G. Bennetts121
University of Adelaide, Adelaide, South Australia, Australia
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, ChinaABSTRACT

et al. (2014) used LPF theory to model the hydrodynamic behaviour of asubmerged heaving cylinder and found broadly similar behaviours to Yeung (1981). Sabuncu and Calisal (1981) showed that, for a surface piercing circular cylinder undergoing a forced oscillatory motion (i.e. heave,
pitch and sway), there exist a difference between the hydrodynamics coefficients predicted by LPF theory and those derived from experimental
data. They suggested that the discrepancy is related to viscosity, which
is neglected by LPF theory.
For better capture of the hydrodynamics at more extreme cases, i.e. larger
oscillation amplitudes and oscillation frequencies, non-linear boundary
conditions should be taken into considerations. Isaacson et al. (1993)
used a boundary element method to solve the second order time domain
potential flow theory. They treated the problem of a heaving and that ofa surging surface piercing circular cylinder. Results were obtained for
dimensionless wave number ka = 1.6, water depth h/a = 1.5, cylinderdraft dc /a = 0.5 and heave amplitude Ah /a = 0.1. They showed that theradiated wave is axisymmetric and that the first and second order waves
propagate away from the cylinder. The wave run-up (i.e. wave elevation measured on the surface of the cylinder) calculated by the second
order potential flow theory has steeper crests and flatter troughs. In addition, it was illustrated that, unlike the first order force, the second orderheave force increases while increasing the excitation frequency. Similarly, Gören (1996), used a frequency domain approach to solve a similar
problem. Results agreed with the findings of Isaacson et al. (1993).
The fully nonlinear potential flow theory of a heave cylinder was treatedby Bai and Taylor (2006) and Zhou et al. (2014). Bai and Taylor (2006)
studied the heave forced motion of a surface piercing cylinder (as well
as a surge forcing). Similar to Isaacson et al. (1993) and Gören (1996),
in the case of a heaving cylinder, they showed that increasing the excitation frequency decreases the total vertical force and increases runup wave
amplitude. In addition, it was shown that while the heave force can beevaluated using the linear theory, the runup wave elevation was more sensitive to non-linearities. Similar results were shown by Zhou et al. (2014)
for the case of a heaving flared cylinder. Hu et al. (2002) used the finite
element method to solve the fully non-linear potential flow theory of amoving surface piercing cylinder, where the cylinder undergoes a forced
surge motion. The results show that for small dimensionless surge amplitudes (i.e. ratio of the surge amplitude to the water depth of 0.01), thenon-linear solution agrees with the linear solution. However, this is not
the case for larger dimensionless surge amplitudes. In this case, it was
shown that even at low surge frequencies, non-linear phenomena, represented by higher harmonic wave amplitudes, are captured.

The problem of non-linear radiated waves generated by a submerged circular cylinder undergoing a forced heaving oscillation is studied. TheLinear Potential Flow (LPF) theory approximation is used as a reference
to the solution. A Computational Fluid Dynamics (CFD) commercialsoftware FLOW-3D® is used to simulate Euler approximation of Navier–Stokes equations and generate radiated water wave data. Results showthat non-linear radiated waves are not proportional to the heave amplitude and that the geometric decay follows a similar trend as linear waves.
Moreover, for large heave amplitudes, in the vicinity of the cylinder, theradiated waves are horizontally asymmetric, and converge to their symmetric structure when propagating away.

KEY WORDS: Linear potential flow theory; Euler approximation;
Navier–Stokes equations; nonlinear radiated waves.

INTRODUCTION
The investigation is motivated by the large amplitude, resonant motionsof wave energy converters (WECs). Recent literature on modelling ofWEC hydrodynamics shows that non-linear models are required for accurate predictions of WEC motions during the resonant phase, and, thus,
their energy absorption and performance (Schubert et al. , 2020). However, the properties of the wave field during the resonant phase is a knowledge gap that will affect the performance of WEC arrays. According
to linear potential flow (LPF) theory, which will be used as a referencein this study, the wave field surrounding a WEC consists of diffracted
waves and radiated waves (Linton and McIver, 2001). In this paper, wewill study the radiated waves created by a submerged cylinder undergoing large amplitude forced motions, where, for simplicity, the cylinder isrestricted to heave oscillation.
The classical problem of a heaving surface piercing cylinder was treatedby Yeung (1981), using the analytical solution of LPF theory. The formulation of the linear problem states that the radiated velocity potential, hence the radiated water waves, are proportional to the heave amplitude, and that away from the body the generated wave amplitude decays
proportionally to the square root of the distance from the cylinder (alsoknown as the geometric decay). Yeung (1981), studied the behaviour ofthe hydrodynamic coefficients (added mass and hydrodynamic damping)as the geometry and heave frequency of the cylinder changes. He found,for example, that at high frequencies the damping coefficient tends tozero and the added mass tends to a non-zero asymptotic value. Jiang

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