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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Variational Water Waves: on Continuum and Discrete
Modelling\, and Experimental Validation - Bokhove
\, O (University of Leeds)
DTSTART;TZID=Europe/London:20140808T100000
DTEND;TZID=Europe/London:20140808T123000
UID:TALK53679AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53679
DESCRIPTION:1. Some variational mechanics will be introduced f
irst before embarking on formulating continuum mod
els for water waves in fluids. A forced-dissipativ
e nonlinear oscillator will be used as an example\
, inspired by wave motion in a laboratory Hele-Sha
w cell for (breaking) water waves and beach morpho
dynamics. Subsequently\, variational principles fo
r 3D water waves by Miles and Luke will be derived
using constraints. 2. The simpler\, depth-average
d\, spatially 2D\, shallow water analogue of Miles
' variational principle will be discretized in spa
ce and subsequently in time\, using space and time
finite elements\, to yield a compatible geometric
algebraic variational principle. Likewise\, Miles
variational principle will be discretized in spac
e and subsequently in time\, using space and time
finite elements\, to yield a compatible geometric
algebraic variational principle. The latter interi
m variational principle with continuous time will
be essential to find the time discretization\, ens
uring that there is an underlying discrete boundar
y element structure and that the mesh movement is
soundly integrated in the variational structure to
ensure numerical stability. The simple oscillator
will serve as an illustrative example for the dis
continuous Galerkin finite element time discretiza
tion developed. The similarities between these dis
crete 2D shallow water and 3D water wave models at
the fre e surface will be discussed. 3. The resul
ting discretizations will be validated against wav
e tank data from the Maritime Research Institute N
etherlands (MARIN) and in-house Hele-Shaw wave tan
k experiments (shown live). 4. Time permitting\, e
xtensions of the above results will be discussed.
These concern water wave models with a vertical co
mponent of vorticity\, experiments of a bore-solit
on rogue wave\, modelling of breaking waves\, or a
wave-energy device using geometric rogue-wave foc
ussing.\n\n\n
LOCATION:CMS\, RM9
CONTACT:Mustapha Amrani
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