2016
DOI: 10.1017/jfm.2016.201
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The motion of a freely floating cylinder in the presence of a wall and the approximation of resonances

Abstract: A linear theory, based on wide-spacing and high-frequency approximations, is developed to describe resonant behaviour in two-dimensional water-wave problems involving a freely floating half-immersed cylinder in the presence of a vertical rigid wall. The theory is not able to describe the lowest-frequency resonance, but otherwise yields explicit approximations for the locations of resonances in the complex plane and for their corresponding residues. Two problems are investigated in detail: the time-domain motio… Show more

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Cited by 15 publications
(8 citation statements)
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“…Thus, a completely reflecting boundary of infinite extent was assumed, which although leads to positive in terms of power absorption effects [14], it does not represent adequately the real physical problem. Finally, two-dimensional approximations have been developed in [15] for describing the resonant behavior of a single, free-floating, semi-immersed cylinder in the presence of a vertical rigid wall.…”
Section: Introductionmentioning
confidence: 99%
“…Thus, a completely reflecting boundary of infinite extent was assumed, which although leads to positive in terms of power absorption effects [14], it does not represent adequately the real physical problem. Finally, two-dimensional approximations have been developed in [15] for describing the resonant behavior of a single, free-floating, semi-immersed cylinder in the presence of a vertical rigid wall.…”
Section: Introductionmentioning
confidence: 99%
“…Despite the effect of wave reflections, they can be beneficial for wave energy converters, by increasing their motions, and as a result, their power absorption, which may result in stability and structural issues in the floating structures that are placed nearshore. Indicative theoretical and experimental studies concerning the effect of a vertical wall on the hydrodynamic characteristics of an array of five floating cylindrical bodies are studied in References [33,34], whereas, in Reference [35], the resonances of a freely floating half immersed cylinder in front of a vertical rigid breakwater have been investigated. Additionally, in References [36][37][38][39][40][41], the corresponding wave diffraction problem, as well as the motionand pressure-radiation problems of a single truncated cylinder and of an oscillating water column wave energy converter (WEC), placed in front of a vertical wall, was examined.…”
Section: Body-breakwater Simulation Methodsmentioning
confidence: 99%
“…Thus, both r and p 3 are functions of the real frequency parameter κ = Ka and, for the present purposes, each may be extended analytically into a suitable complex neighbourhood of the real axis (see [14, section 4]). Results will be obtained using the standard wide-spacing approximation ( = 0); the term in 2 is included above to shed light on the magnitude of the first neglected term and will not be be included explicitly from now on (for the case of a half-immersed circular cylinder next to a wall, the effects of this term are discussed in detail in [22]). The overall aim is to obtain approximations to the locations of resonances using high-frequency approximations to the hydrodynamic coefficients that are valid for Ka 1.…”
Section: Locations Of the Complex Resonancesmentioning
confidence: 99%