Near critical free surface flow past an obstacle
Author:
Susan L. Cole
Journal:
Quart. Appl. Math. 41 (1983), 301-309
MSC:
Primary 76B15
DOI:
https://doi.org/10.1090/qam/721420
MathSciNet review:
721420
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Abstract: This paper describes the nonlinear effects produced by arbitrarily small bumps in two-dimensional free surface flows with Fraude numbers close to 1$^{+}$ . These effects are determined by asymptotically matching (approximate) solutions to the ideal flow equations.
Kelvin, On stationary waves in flowing water, Mathematical and Physical Papers, Vol. IV, Cambridge Press, 270–302, 1910
- Julian D. Cole, Limit process expansions and approximate equations, Singular perturbations and asymptotics (Proc. Adv. Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1980) Publ. Math. Res. Center Univ. Wisconsin, vol. 45, Academic Press, New York-London, 1980, pp. 19–40. MR 606034
N. N. Mosieev, On the Non-uniqueness of the Possible Forms of Steady Flows of a Heavy Fluid for Froude Numbers Close to 1, P.M.M. 21 860–864 (1957)
- I. G. Filippov, Solution of the problem of the motion of a vortex under the surface of a fluid, for Froude numbers near unity, J. Appl. Math. Mech. 24 (1960), 698–716. MR 0128208, DOI https://doi.org/10.1016/0021-8928%2860%2990176-3
Kelvin, On stationary waves in flowing water, Mathematical and Physical Papers, Vol. IV, Cambridge Press, 270–302, 1910
J. D. Cole, Limit process expansions and approximate equations, Singular Perturbations and Asymptotics, R. E. Meyer, S. Parter, ed., Academic Press, 35–39 1980
N. N. Mosieev, On the Non-uniqueness of the Possible Forms of Steady Flows of a Heavy Fluid for Froude Numbers Close to 1, P.M.M. 21 860–864 (1957)
I. G. Fillipov, Solution of the Problem of the Motion of a Vortex Under the Surface of a Fluid, for Froude Numbers Near Unity, P.M.M. 24, 478–490 (1960)
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Article copyright:
© Copyright 1983
American Mathematical Society