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SUMMARY:Conservation relations for two-dimensional wave-current interactio
 ns - Gareth Thomas (University College Cork)
DTSTART:20170807T103000Z
DTEND:20170807T113000Z
UID:TALK74631@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:For a uniform current interacting with a monochromatic wavetra
 in in water of locally constant depth\, the resulting wavefield will be ir
 rotational.  The conservation relations required to link the slowly-varyin
 g properties of the wavefield to the local properties\, such as those indu
 ced by a change in water depth\, can be obtained by an appropriate method 
 such as a variational approach of Whitham. There are relatively few diffic
 ulties for linear waves but the problem is much more difficult for nonline
 ar waves and this requires a careful description of the reference frame an
 d the free surface datum level. In this approach the Bernoulli constants\,
  sometimes referred to as the secondary triad\, play an important role. Wh
 en the current is rotational\, difficulties arise even for linear waves on
  a current possessing uniform vorticity. The talk will identify and descri
 be these difficulties in the rotational case\, for both linear and nonline
 ar waves\, but will not promise to provide a definitive formulation.
LOCATION:Seminar Room 1\, Newton Institute
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