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Title:  Excitation of trapped water waves by the forced motion of structures 
Authors:  McIver, P. McIver, M. Zhang, J. 
Issue Date:  2003 
Publisher:  © Cambridge University Press 
Citation:  MCIVER, MCIVER and ZHANG, 2003. Excitation of trapped water waves by the forced motion of structures. Journal of Fluid Mechanics, 494, pp. 141–162. 
Abstract:  A numerical and analytical investigation is made into the response of a fluid when a
twodimensional structure is forced to move in a prescribed fashion. The structure is
constructed in such a way that it supports a trapped mode at one particular frequency.
The fluid motion is assumed to be small and the timedomain equations for linear
waterwave theory are solved numerically. In addition, the asymptotic behaviour
of the resulting velocity potential is determined analytically from the relationship
between the time and frequencydomain solutions. The trapping structure has two
distinct surfacepiercing elements and the trapped mode exhibits a vertical ‘pumping’
motion of the fluid between the elements. When the structure is forced to oscillate
at the trappedmode frequency an oscillation which grows in time but decays in
space is observed. An oscillatory forcing at a frequency different from that of the
trapped mode produces bounded oscillations at both the forcing and the trappedmode
frequency. A transient forcing also gives rise to a localized oscillation at the
trappedmode frequency which does not decay with time. Where possible, comparisons
are made between the numerical and asymptotic solutions and good agreement is
observed. The calculations described above are contrasted with the results from a
similar forcing of a pair of semicircular cylinders which intersect the free surface at
the same points as the trapping structure. For this second geometry no localized or
unbounded oscillations are observed. The trapping structure is then given a sequence
of perturbations which transform it into the two semicircular cylinders and the timedomain
equations solved for a transient forcing of each structural geometry in the
sequence. For small perturbations of the trapping structure, localized oscillations
are produced which have a frequency close to that of the trapped mode but with
amplitude that decays slowly with time. Estimates of the frequency and the rate of
decay of the oscillation are made from the timedomain calculations. These values
correspond to the real and imaginary parts of a pole in the complex force coefficient
associated with a frequencydomain potential. An estimate of the position of this pole
is obtained from calculations of the added mass and damping for the structure and
shows good agreement with the timedomain results. Further timedomain calculations
for a different trapping structure with more widely spaced elements show a number
of interesting features. In particular, a transient forcing leads to persistent oscillations
at two distinct frequencies, suggesting that there is either a second trapped mode,
or a very lightly damped neartrapped mode. In addition a highly damped pumping
mode is identified. 
Description:  This article was published in the journal, Journal of Fluid Mechanics [© Cambridge University Press] and is available at: http://journals.cambridge.org/action/displayJournal?jid=FLM. 
URI:  https://dspace.lboro.ac.uk/2134/2219 
ISSN:  14697645 
Appears in Collections:  Published Articles (Maths)

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