Geometric orbits of surface waves from a circular hydraulic jump

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 6, 1997, Pages 7048-7062

  Hansen, S H ^a   Horluck S ^a   Zauner, D ^a   Dimon, P ^a   Ellegaard, C ^a   Creagh, S C ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

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[No Author keywords available]

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EID: 4244175619     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.7048     Document Type: Article

References (24)

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15. See, for example, J D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Chap. 7.
16. This derivation follows that given for deep-water gravity waves in L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1987), p. 94.
17. This result was obtained in somewhat different form by other authors. See J N. Hunt, Houille Blanche19, 685 (1964);
18. L. Montefusco, Acc. Naz. Lincei, Rend. Accad. Sc. Fis. Mat. Nat. Naples Ser. VIII46, 704 (1969);
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20. P H. LeBlond and F. Mainardi, Acta Mechanica68, 203 (1987).
21. J. Lighthill, Waves in Fluids (Cambridge University Press, Cambridge, 1993), p. 231.
22. A similar expression was obtained earlier by K. M. van Vliet, A. van der Ziel and R R. Schmidt, J. Appl. Phys.51, 2947 (1980).
23. This statement implicitly makes certain assumptions concerning the conservative properties of the system. For example, if L is the operator for the diffusion equation, then it implies that the field φ is not strictly conserved. [See, for example, T. Hwa and M. Kardar, Phys. Rev. Lett.62, 1813 (1989).] For surface waves, however, the situation is more complicated, and although there is certainly a conservation law for the surface displacement of an incompressible fluid, this statement may still be valid.
24. See, for example, P M. Morse and H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).