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SUMMARY:On linear and nonlinear wave-ship interactions - Onno Bokhove (Uni
 versity of Leeds)
DTSTART:20170808T103000Z
DTEND:20170808T113000Z
UID:TALK75771@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Dynamics of buoy and ship motion in linear and nonlinear water
  waves will be considered.&nbsp\;The starting point will be a "pre-Luke" v
 ariational principle (see Cotter & B. [1]&nbsp\;for the case without ship)
  for the combined water-wave motion and the dynamics of a rigid&nbsp\;buoy
 /ship. This principle reduces to Luke&#39\;s variational principle when a 
 scaled density D is set to unity\, in the case&nbsp\;without&nbsp\;buoy/sh
 ip dynamics. The coupling between waves and ship is straightforward: that 
 the shape of the water surface equals the shape of the moving buoy/ship is
  imposed via a Lagrange multiplier. Pre-Luke&#39\;s principle has the adva
 ntage that the boundary conditions on the Lagrange multiplier emerge direc
 tly from the variational principle due to the weak imposition of the densi
 ty constraint\, while in Luke&#39\;s form of the variational principle of 
 the coupled dynamics the boundary condition needs to be imposed on the Lag
 range multiplier. The consequences for a completely space-time variational
 &nbsp\;numerical discretisation will be discussed. Attempts to find an exa
 ct/reduced test solution in the shallow water limit of buoy-fluid motion m
 ay be&nbsp\;considered as well. Movies of a wave-energy device and prelimi
 nary numerical solutions [2\,3\,4] will be used throughout the presentatio
 n.<br><span><br>[1] C. Cotter and O.B. 2010: Water wave model with accurat
 e dispersion and vertical vorticity.&nbsp\;Peregrine Commemorative Issue&n
 bsp\;J. Eng. Maths.&nbsp\;67\, 33-54.<br></span><span><br>[2] Youtube chan
 nel Anna Kalogirou: Movies of simulations and scaled wave-energy device:&n
 bsp\;<a target="_blank" rel="nofollow" href="https://www.youtube.com/user/
 anna9k">https://www.youtube.com/user/anna9k</a><br></span><br>[3]&nbsp\;A.
  Kalogirou and&nbsp\;O.B 2016: Mathematical and numerical modelling of wav
 e impact on wave-energy buoys.&nbsp\;Proc. ASME 2016 35th International Co
 nference on Ocean\, Offshore and Arctic Engineering (OMAE 2016)\, Busan\, 
 South Korea.<br><br>[4] A. Kalogirou\, O.B. and D. Ham 2017: Modelling of&
 nbsp\;nonlinear wave-buoy dynamics using constrained variational methods. 
 Proc. ASME 2017 36th Int. Conf. Ocean\, Offshore and Arctic Engineering (O
 MAE 2017)\, Trondheim\, Norway.
LOCATION:Seminar Room 1\, Newton Institute
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