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Generalized vortex methods for free-surface flow problems

Published online by Cambridge University Press:  20 April 2006

Gregory R. Baker ,
Daniel I. Meiron  and
Steven A. Orszag
Gregory R. Baker
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139 Present address: Department of Mathematics, University of Arizona, Tucson.
Daniel I. Meiron
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139
Steven A. Orszag
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139
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Abstract

The motion of free surfaces in incompressible, irrotational, inviscid layered flows is studied by evolution equations for the position of the free surfaces and appropriate dipole (vortex) and source strengths. The resulting Fredholm integral equations of the second kind may be solved efficiently in both storage and work by iteration in both two and three dimensions. Applications to breaking water waves over finite-bottom topography and interacting triads of surface and interfacial waves are given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 123 , October 1982 , pp. 477 - 501
Copyright
© 1982 Cambridge University Press

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References

Baker, G. R. 1980 J. Fluid Mech. 100, 209.
Baker, G. R., Meiron, D. I. & Orszag, S. A. 1980 Phys. Fluids 23, 1485.
Baker, G. R., Meiron, D. I. & Orszag, S. A. 1982 In preparation.
Ball, F. K. 1964 J. Fluid Mech. 19, 465.
Bergman, S. & Schiffer, M. 1953 Kernel Functions and Elliptic Differential Equations in Mathematical Physics, p. 334. Academic.
Chan, R. K. & Street, R. L. 1970 Tech. Rep. no. 135, Dept Civil Engng, Stanford University.
Chen, B. & Saffman, P. G. 1979 Stud. Appl. Math. 60, 183.
Craik, A. D. D. & Adam, J. A. 1979 J. Fluid Mech. 92, 15.
Hasselman, K. 1966 Rev. Geophys. 4, 801.
Holyer, J. 1979 J. Fluid Mech. 93, 433.
Kellogg, O. D. 1953 Foundations of Potential Theory. Dover.
Kenyon, K. 1966 Ph.D. thesis University of California, San Diego.
Longuet-Higgins, M. S. 1981 Proc. R. Soc. Lond. A 376, 377.
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 Proc. R. Soc. Lond. A 350, 1.
Peregrine, D. H., Cokelet, E. D. & McIver, P. 1980 In Proc. 17th Conf. on Coastal Engng.
Schiffer, M. 1959 Pacific J. Math. 9, 211.
Vanden-Broek, J. M. 1980 Phys. Fluids 23, 1723.
Verdon, C. P., McCrory, R. L., Morse, R. L., Baker, G. R., Meiron, D. I. & Orszag, S. A. 1982 Nonlinear effects of multi-frequency hydrodynamic instabilities on ablatively accelerating thin shells. Phys. Fluids (to be published).
Vinje, T. & Brevig, P. 1981 Adv. Water Resources 4, 77.
Watson, K. M., West, N. J. & Cohen, B. I. 1976 J. Fluid Mech. 77, 185.