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Conservation relations for two-dimensional wave-current interactions

Presented by: 
Gareth Thomas University College Cork
Monday 7th August 2017 - 11:30 to 12:30
INI Seminar Room 1
For a uniform current interacting with a monochromatic wavetrain in water of locally constant depth, the resulting wavefield will be irrotational. The conservation relations required to link the slowly-varying properties of the wavefield to the local properties, such as those induced by a change in water depth, can be obtained by an appropriate method such as a variational approach of Whitham. There are relatively few difficulties for linear waves but the problem is much more difficult for nonlinear waves and this requires a careful description of the reference frame and the free surface datum level. In this approach the Bernoulli constants, sometimes referred to as the secondary triad, play an important role. When the current is rotational, difficulties arise even for linear waves on a current possessing uniform vorticity. The talk will identify and describe these difficulties in the rotational case, for both linear and nonlinear waves, but will not promise to provide a definitive formulation.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons