A Lagrangian for water waves

Physics of Fluids

Volumn 8, Issue 2, 1996, Pages 416-420

  Balk, A M ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MODELLING-MATHEMATICAL; UNSTEADY; WATER WAVES;

EID: 0029675640     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.868795     Document Type: Article

References (12)

1. G. G. Stokes, "On the theory of oscillatory waves," Trans. Cambridge Philos. Soc. 8, 441 (1847).
2. G. G. Stokes, "Supplement to a paper on the theory of oscillatory waves," Mathematical and Physical Papers (Cambridge University Press, Cambridge, 1880), Vol. 1, pp, 225-228.
3. M. S. Longuet-Higgins, "Some new relations between Stokes's coefficients in the theory of gravity waves," J. Inst. Math. Appl. 22, 261 (1978).
4. P. G. Saffman, "Long wavelength bifurcation of gravity waves on deep water," J. Fluid Mech. 101, 567 (1980).
5. J. A. Zufiria, "Non-symmetric gravity waves on water of infinite depth," J. Fluid Mech. 181, 17 (1987).
6. V. E. Zakharov, "Stability of periodic waves of finite amplitude on the surface of deep fluid," J. Appl. Mech. Tech. Phys. 2, 190 (1968).
7. The function L in the variational principle considered in the text [G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1973) [see formula (13.17)] is not strictly a Lagrangian, as it is not expressed in terms of generalized coordinates, it does not define the canonical Lagrange equations, and the Legendre transform is not applicable.
8. M. S. Longuet-Higgins, "Bifurcation in gravity waves," J. Fluid Mech 151, 457 (1985).
9. D. I. Meiron, S. A. Orszag, and M. Israeli, "Applications of numerical conformal mapping," J. Comput. Phys. 40, 345 (1981).
10. J. A. Simmen and P. G. Saffman, "Steady deep water waves on a linear shear current," Stud. Appl. Math. 73, 35 (1985).
11. A. I. Dyachenko, E. A. Kuznetsov, M. D. Spector, and V. E. Zakharov "Canonical formalism and conformal mapping for the free-surface hydrodynamics," to appear in Phys. Lett. A.
12. A. I. Dyachenko, Y. V. Lvov, and V. E. Zakharov, "Five-wave interaction on the surface of deep fluid," Physica D 87, 233 (1995).