Free streamline flow over curved topography
Authors:
A. C. King and M. I. G. Bloor
Journal:
Quart. Appl. Math. 48 (1990), 281-293
MSC:
Primary 76B10
DOI:
https://doi.org/10.1090/qam/1052137
MathSciNet review:
MR1052137
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Abstract: The determination of the free streamline of a jet of ideal fluid flowing past a wall of arbitrary shape is considered. A transformation technique is used to formulate the fluid mechanics problem by relating the deflection of the free surface to the angle made by the wall to the undisturbed jet which is found as a solution of a nonlinear integral equation. Linearized solutions, based upon small elevations or depressions in the wall, and nonlinear numerical solutions to this equation are presented for a variety of wall shapes. Some inadequacies of both this linear theory and shallow water theory are found.
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F. Dias, A. R. Ekrat, and L. N. Trefethen, Ideal Jet Flow in Two Dimensions, J. Fluid Mech. 185, 275 (1987)
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A. C. King and M. I. G. Bloor, Free surface flow over a step, J. Fluid Mech. 182, 193 (1987)
- A. C. King and M. I. G. Bloor, A note on the free surface induced by a submerged source at infinite Froude number, J. Austral. Math. Soc. Ser. B 30 (1988), no. 2, 147–156. MR 965408, DOI https://doi.org/10.1017/S0334270000006123
R. F. Dressler, A new approach to flows over a curved bed, J. Hydraulic Res. 16, 205 (1978)
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H. Helmholtz, Uber diskontinvierliche Flüssigkeitsstrahlen, Mber. Akad. Wiss. Berlin, 215 (1868)
G. Kirchhoff, Zur Theorie Freier Flüssigkeitsstrahlen, J. reine angew Math. 70, 289 (1869)
R. von Mises, Selected Papers of Richard von Mises, Amer. Math. Soc., 1963
G. Birkhoff and E. H. Zarantonello, Jets, Wakes and Cavities, Academic Press, New York, 1957
D. Gilbarg, Jets and Cavities, Handbuch der Physik, Vol. 9, Springer, 1960, p. 311
M. I. Gurevich, Theory of Jets in an Ideal Fluid, Academic Press, New York, 1965
L. N. Trefethen, Numerical computation of the Schwarz-Christoffel transformation, SIAM J. Sci. Stat. Comp. 1, 82 (1980)
F. Dias, A. R. Ekrat, and L. N. Trefethen, Ideal Jet Flow in Two Dimensions, J. Fluid Mech. 185, 275 (1987)
T. Levi-Civita, Scie e leggi de resistenza, Rend. Circ. Mat. Palermo 18, 1 (1907)
H. Villat, Sur la résistance des fluides, Ann. Sci. Ec. Norm. Sup. 28, 203 (1911)
N. A. Nekrasov, Sur la mouvement discontinu à deux dimensions de fluid autour d’un obstacle en forme d’arc de cercle, Publ. Inst. Polytech. Ivanovo-Voszniesiensk 32 (1922)
S. Brodetsky, Discontinuous fluid motion past circular and elliptic cylinders, Proc. Roy. Soc. A 102, 361 (1923)
M. I. G. Bloor, Large amplitude surface waves, Pt. 1, J. Fluid Mech. 84, 167 (1978)
A. C. King and M. I. G. Bloor, Free surface flow over a step, J. Fluid Mech. 182, 193 (1987)
A. C. King and M. I. G. Bloor, Cusped free surface flow due to a submerged source, J. Aus. Math. Soc. B 30, 147 (1988)
R. F. Dressler, A new approach to flows over a curved bed, J. Hydraulic Res. 16, 205 (1978)
P. Rabinowitz, Numerical Methods for Nonlinear Algebraic Equations, Gordon & Breach, 1970
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© Copyright 1990
American Mathematical Society