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SUMMARY:On Time Integration and the Use of Clebsch Variables in Shallow Wa
 ter Equations - Bokhove\, O (University of Leeds)
DTSTART:20131206T110000Z
DTEND:20131206T114500Z
UID:TALK49233@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Two topics will be covered in this lecture. The shallow water 
 equations will be used as a test bed to introduce the ideas. \n\n(i) For f
 orced variational systems such as the potential flow shallow water wave eq
 uations\, variational and symplectic time integrators will be extended usi
 ng a new finite element approach. Here\, a standard variational finite ele
 ment discretization will be applied in space. \n\n(ii) The shallow water e
 quations formulated in terms of Clebsch variables will be discussed. The a
 dvantage of Clebsch variables is that they lead to canonical Hamilton's eq
 uations for shallow water dynamics\, in the Eulerian framework. A disadvan
 tage is that the the system\, is less compactly expressed in comparison to
  the usual formulation in terms of the velocity and fluid depth. I will ma
 ke a link between a symmetry in the Hamiltonian and the associated mass we
 ighted potential vorticity conservation law\, also within the Eulerian fra
 mework. This will be done in two dimensions (2D) and in a quasi-2D symmetr
 ic form. \n\n
LOCATION:Seminar Room 1\, Newton Institute
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