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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Upper bound on the slope of a steady water wave

## Upper bound on the slope of a steady water waveAdd to your list(s) Download to your calendar using vCal - Walter Strauss (Brown University)
- Thursday 10 August 2017, 11:30-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact INI IT. NWWW01 - Nonlinear water waves Consider the angle of inclination of the profile of a steady 2D (inviscid, symmetric, periodic or solitary) water wave subject to gravity. Although the angle may surpass 30 degrees for some irrotational waves close to the extreme Stokes wave, Amick proved in 1987 that the angle must be less than 31.15 degrees if the wave is irrotational. However, for any wave that is not irrotational, the question of whether there is any bound on the angle has been completely open. An example is the extreme Gerstner wave, which has adverse vorticity and vertical cusps. Moreover, numerical calculations show that waves of finite depth with adverse vorticity can overturn, so the angle can be 90 degrees. On the other hand, Miles Wheeler and I prove that there is an upper bound of 45 degrees for a large class of waves with favorable vorticity and finite depth. Seung Wook So and I prove a similar bound for waves with small adverse vorticity. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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