Upper bound on the slope of a steady water wave
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| Description: |
Strauss, W
Thursday 10th August 2017 - 11:30 to 12:30 |
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| Created: | 2017-08-11 09:37 |
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| Collection: | Nonlinear Water Waves |
| Publisher: | Isaac Newton Institute |
| Copyright: | Strauss, W |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | 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. |
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