Abstract
AbstractWe study wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed. For large-amplitude periodic traveling gravity waves that propagate at the water surface in the same direction as the underlying current (downstream waves), we prove explicit uniform bounds for their amplitude. In particular, our estimates show that the maximum amplitude of the waves becomes vanishingly small as the vorticity increases without limit. We also prove that the downstream waves on a global bifurcating branch are never overhanging, and that their mass flux and Bernoulli constant are uniformly bounded.
Funder
Ministerul Educației şi Cercetării Ştiințifice
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference47 articles.
1. Ablowitz, M.J., Fokas, A.S., Satsuma, J., Segur, H.: On the periodic intermediate long wave equation. J. Phys. A 15, 781–786 (1982)
2. Ahlfors, L.V.: Complex Analysis. An Introduction to the Theory of Analytic Functions of One Complex Variable. McGraw-Hill Book Co., New York (1978)
3. Amick, C.J., Fraenkel, L.E., Toland, J.F.: On the Stokes conjecture for the wave of extreme form. Acta Mathematica 148, 193–214 (1982)
4. Buffoni, B., Toland, J.F.: Analytic Theory of Global Bifurcation. Princeton University Press, Princeton and Oxford (2003)
5. Constantin, A.: The trajectories of particles in Stokes waves. Invent. Math. 166, 523–535 (2006)
Cited by
13 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献