A complex-analytic approach to kinetic energy properties of irrotational flows

Constantin, O.; Persson, A.-M.

doi:10.1090/proc/15936

A complex-analytic approach to kinetic energy properties of irrotational flows
HTML articles powered by AMS MathViewer

by O. Constantin and A.-M. Persson PDF

Proc. Amer. Math. Soc. 150 (2022), 2647-2653 Request permission

Abstract:

Using methods from complex analysis we obtain some qualitative results for the kinetic energy of two-dimensional irrotational water flows (monotonicity of horizontal averages with depth, location of the extrema).

References

A. Aleman and A. Constantin, On the decrease of kinetic energy with depth in wave-current interactions, Math. Ann. 378 (2020), no. 3-4, 853–872. MR 4163514, DOI 10.1007/s00208-019-01910-8
C. J. Amick and J. F. Toland, On periodic water-waves and their convergence to solitary waves in the long-wave limit, Philos. Trans. Roy. Soc. London Ser. A 303 (1981), no. 1481, 633–669. MR 647410, DOI 10.1098/rsta.1981.0231
Biswajit Basu, A flow force reformulation for steady irrotational water waves, J. Differential Equations 268 (2020), no. 12, 7417–7452. MR 4079002, DOI 10.1016/j.jde.2019.11.057
Boris Buffoni and John Toland, Analytic theory of global bifurcation, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, 2003. An introduction. MR 1956130, DOI 10.1515/9781400884339
Didier Clamond, Note on the velocity and related fields of steady irrotational two-dimensional surface gravity waves, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 370 (2012), no. 1964, 1572–1586. MR 2902474, DOI 10.1098/rsta.2011.0470
Walter Craig, Philippe Guyenne, and Henrik Kalisch, Hamiltonian long-wave expansions for free surfaces and interfaces, Comm. Pure Appl. Math. 58 (2005), no. 12, 1587–1641. MR 2177163, DOI 10.1002/cpa.20098
Walter Craig and Peter Sternberg, Symmetry of free-surface flows, Arch. Rational Mech. Anal. 118 (1992), no. 1, 1–36. MR 1151925, DOI 10.1007/BF00375690
W. Craig and C. Sulem, Numerical simulation of gravity waves, J. Comput. Phys. 108 (1993), no. 1, 73–83. MR 1239970, DOI 10.1006/jcph.1993.1164
Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
R. S. Johnson, A modern introduction to the mathematical theory of water waves, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1997. MR 1629555, DOI 10.1017/CBO9780511624056
Serge Lang, Complex analysis, 4th ed., Graduate Texts in Mathematics, vol. 103, Springer-Verlag, New York, 1999. MR 1659317, DOI 10.1007/978-1-4757-3083-8
M. S. Longuet-Higgins, On the decrease of velocity with depth in an irrotational water wave, Proc. Cambridge Philos. Soc. 49 (1953), 552–560. MR 57093, DOI 10.1017/S030500410002870X
A. Nachbin and R. Ribeiro-Junior, Capturing the flow beneath water waves, Philos. Trans. Roy. Soc. A 376 (2018), no. 2111, 20170098, 17. MR 3744206, DOI 10.1098/rsta.2017.0098
Donald Sarason, The $H^{p}$ spaces of an annulus, Mem. Amer. Math. Soc. 56 (1965), 78. MR 188824
Walter A. Strauss, Steady water waves, Bull. Amer. Math. Soc. (N.S.) 47 (2010), no. 4, 671–694. MR 2721042, DOI 10.1090/S0273-0979-2010-01302-1
J. F. Toland, Stokes waves, Topol. Methods Nonlinear Anal. 7 (1996), no. 1, 1–48. MR 1422004, DOI 10.12775/TMNA.1996.001