Workshop: On the vorticity threshold for water waves with a non-favorable constant vorticity, Evgeniy Lokharu

Date: 2023-09-15

Time: 10:30 - 11:20


Evgeniy Lokharu, Lund University


In this talk we will discuss effects of a strong non-favorable constant vorticity on the global dynamics of Stokes waves. We will prove that for constant vorticities above some threshold value the horizontal velocity on the surface is always separated from zero by a constant depending only on the vorticity. In particular this forbids formation of extreme and overhanging waves before a critical layer appears inside the fluid, first at the bottom right below the crest. This also shows that the slopes of unidirectional solutions are uniformly bounded by a constant close to the unity, provided the vorticity is large enough and is non-favorable. Our analytic results agree with the numerical analysis by Ko and Strauss.

This is a joint work with Miles Wheeler from Bath University, UK.