On the existence of extreme waves and the Stokes conjecture with vorticity

When?

Friday 8 May 2009, 4:00pm

Where?

Room 22AA04

Open to:

Staff, Students

Speaker:

Eugen Varvaruca (Imperial College)

We present some recent results on singular solutions of the problem of travelling gravity surface water waves on flows with vorticity. We show that, for any nonpositive vorticity function, a sequence of large-amplitude regular waves converges to a nontrivial extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a symmetric corner of 120 degrees or a horizontal tangent at any isolated stagnation point. Moreover, the profile necessarily has a symmetric corner of 120 degrees if the vorticity is nonnegative near the free surface.