Higher-harmonic wave forces and ringing of vertical cylinders

Grue, John; Huseby, Morten

doi:10.1016/s0141-1187(02)00048-2

Cited by 76 publications

(80 citation statements)

References 6 publications

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“…Such a procedure represents a first step also in the more general (and broadbanded) case. We have in our laboratory measured the nonlinear dispersion relation in focusing wave groups finding that the measurements of wave period and wave length fit with nonlinear theory of slowly varying wave trains [26,27].…”

Section: Velocity Profile On Nondimensional Formmentioning

confidence: 81%

Kinematics of extreme waves in deep water

Grue

Clamond

Huseby

et al. 2003

Applied Ocean Research

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The velocity profiles under crest of a total of 62 different steep wave events in deep water are measured in laboratory using particle image velocimetry. The waves take place in the leading unsteady part of a wave train, focusing wave fields and random wave series. Complementary fully nonlinear theoretical/numerical wave computations are performed. The experimental velocities have been put on a nondimensional form in the following way: from the wave record (at a fixed point) the (local) trough-to-trough period, T TT and the maximal elevation above mean water level, h m of an individual steep wave event are identified. The local wavenumber, k and an estimate of the wave slope, e are evaluated from v 2 =ðgkÞ ¼ 1 þ e 2 ; kh m ¼ e þ 1 2 e 2 þ 1 2 e 3 ; where v ¼ 2p=T TT and g denotes the acceleration of gravity. A reference fluid velocity, e ffiffiffiffi g=k p is then defined. Deep water waves with a fluid velocity up to 75% of the estimated wave speed are measured. The corresponding kh m is 0.62. A strong collapse of the nondimensional experimental velocity profiles is found. This is also true with the fully nonlinear computations of transient waves. There is excellent agreement between the present measurements and previously published Laser Doppler Anemometry data. A surprising result, obtained by comparison, is that the nondimensional experimental velocities fit with the exponential profile, i.e. e ky ; y the vertical coordinate, with y ¼ 0 in the mean water level.

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Section: Velocity Profile On Nondimensional Formmentioning

confidence: 81%

Kinematics of extreme waves in deep water

Grue

Clamond

Huseby

et al. 2003

Applied Ocean Research

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“…Additionally, some later waves in addition to the main packet are observed in the third-order force (more obvious in figure 9a). This slight mismatch could be due to several factors, such as the third-harmonic term that arises from the u|u| term in Morison drag, a contribution from nonlinear free-surface ringing forces in potential flow (Faltinsen, Newman & Vinje 1996;Chaplin et al 1997), and the secondary load cycle due to short and steep waves around the surface of the cylinder (Grue & Huseby 2002). The analysis of (Fitzgerald et al 2014) suggests that even for fully nonlinear potential flow the third harmonic is in a real sense 'different' from the others, with extra nonlinear dynamics occurring, supportive of the FNV analysis of (Faltinsen et al 1996).…”

Section: Spectral Decompositionmentioning

confidence: 99%

“…The high-frequency forces include nonlinear force components up to at least the fifth harmonic of the incoming waves. Grue, Bjørshol & Strand (1993), Chaplin, Rainey & Yemm (1997) and Grue & Huseby (2002) investigated the ringing response of vertical cylinders in laboratory experiments, and found that a secondary load cycle might have an important effect on the ringing response. A Fourier series expansion in force history suggests that there is a relationship between the occurrence of the secondary load cycle and the appearance of a pronounced higher harmonic force.…”

Section: Introductionmentioning

confidence: 99%

An experimental decomposition of nonlinear forces on a surface-piercing column: Stokes-type expansions of the force harmonics

et al. 2018

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Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the 'phase-inversion' method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the nth-harmonic force scales with the nth power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the † Email addresses for correspondence: lifen.chen@uwa.edu.au, chenlifen239@163.com, J.Zang@bath.ac.uk Nonlinear forces on a column 43 high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.

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“…This resonant excitation can occur even when the high-frequency incident wave and local diffracted wave components are small relative to the total wave field. The excitation of sharp transient structural response by the higher-order harmonics (typically the component at the third-order sum frequency) is referred to as 'ringing' and has been demonstrated experimentally by among others [1,2]. Both studies involved vertical circular cylinders.…”

Section: Introductionmentioning

confidence: 99%

Phase manipulation and the harmonic components of ringing forces on a surface-piercing column

Fitzgerald

Taylor

et al. 2014

Proc. R. Soc. A.

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A general phase-based harmonic separation method for the hydrodynamic loading on a fixed structure in water waves of moderate steepness is proposed. An existing method demonstrated in the experimental study described by Zang et al. (Zang et al. 2010 In Proc. Third Int. Conf. on Appl. of Phys. Modelling to Port and Coastal Protection. pp. 1-7.) achieves the separation of a total diffraction force into odd and even harmonics by controlling the phase of incident focused waves. Underlying this method is the assumption that the hydrodynamic force in focused waves possesses a Stokes-like structure. Under the same assumption, it is shown here how the harmonic separation method can be generalized, so that the first four sum harmonics can be separated by phase control and linear combinations of the resultant time-histories. The effectiveness of the method is demonstrated by comparisons of the Fourier transforms of the combined time-histories containing the harmonics of interest. The local wave elevations around the focus time are also visualized for the first three harmonics in order to reveal the local dynamics driving components within the wave force time-history.

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Higher-harmonic wave forces and ringing of vertical cylinders

Cited by 76 publications

References 6 publications

Kinematics of extreme waves in deep water

Kinematics of extreme waves in deep water

An experimental decomposition of nonlinear forces on a surface-piercing column: Stokes-type expansions of the force harmonics

Phase manipulation and the harmonic components of ringing forces on a surface-piercing column

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