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SUMMARY:Variational Water Waves: on Continuum and Discrete Modelling\, and
  Experimental Validation - Bokhove\, O (University of Leeds)
DTSTART:20140808T090000Z
DTEND:20140808T113000Z
UID:TALK53679@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:1. Some variational mechanics will be introduced first before 
 embarking on formulating continuum models for water waves in fluids. A for
 ced-dissipative nonlinear oscillator will be used as an example\, inspired
  by wave motion in a laboratory Hele-Shaw cell for (breaking) water waves 
 and beach morphodynamics. Subsequently\, variational principles for 3D wat
 er waves by Miles and Luke will be derived using constraints. 2. The simpl
 er\, depth-averaged\, spatially 2D\, shallow water analogue of Miles' vari
 ational principle will be discretized in space and subsequently in time\, 
 using space and time finite elements\, to yield a compatible geometric alg
 ebraic variational principle. Likewise\, Miles variational principle will 
 be discretized in space and subsequently in time\, using space and time fi
 nite elements\, to yield a compatible geometric algebraic variational prin
 ciple. The latter interim variational principle with continuous time will 
 be essential to find the time discretization\, ensuring that there is an u
 nderlying discrete boundary element structure and that the mesh movement i
 s soundly integrated in the variational structure to ensure numerical stab
 ility. The simple oscillator will serve as an illustrative example for the
  discontinuous Galerkin finite element time discretization developed. The 
 similarities between these discrete 2D shallow water and 3D water wave mod
 els at the fre e surface will be discussed. 3. The resulting discretizatio
 ns will be validated against wave tank data from the Maritime Research Ins
 titute Netherlands (MARIN) and in-house Hele-Shaw wave tank experiments (s
 hown live). 4. Time permitting\, extensions of the above results will be d
 iscussed. These concern water wave models with a vertical component of vor
 ticity\, experiments of a bore-soliton rogue wave\, modelling of breaking 
 waves\, or a wave-energy device using geometric rogue-wave focussing.\n\n\
 n
LOCATION:CMS\, RM9
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