Subcritical free-surface flow caused by a line source in a fluid of finite depth

1992 ◽  
Vol 26 (4) ◽  
pp. 455-466 ◽  
Author(s):  
G. C. Hocking ◽  
L. K. Forbes
Keyword(s):  
Free Surface ◽  
Line Source ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Surface Flow

scholarly journals Flow from a source above a sloping base

2020 ◽  
Vol 61 ◽  
pp. C75-C88
Author(s):  
Shaymaa Mukhlif Shraida ◽  
Graeme Hocking
Keyword(s):  
Free Surface ◽  
Flow Rate ◽  
Water Waves ◽  
Line Source ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Theoretical Research ◽  
Line Sink

We consider the outflow of water from the peak of a triangular ridge into a channel of finite depth. Solutions are computed for different flow rates and bottom angles. A numerical method is used to compute the flow from the source for small values of flow rate and it is found that there is a maximum flow rate beyond which steady solutions do not seem to exist. Limiting flows are computed for each geometrical configuration. One application of this work is as a model of saline water being returned to the ocean after desalination. References Craya, A. ''Theoretical research on the flow of nonhomogeneous fluids''. La Houille Blanche, (1):22–55, 1949. doi:10.1051/lhb/1949017 Dun, C. R. and Hocking, G. C. ''Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary''. J. Eng. Math. 29:1–10, 1995. doi:10.1007/bf00046379 Hocking, G. ''Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom''. ANZIAM J. 26:470–486, 1985. doi:10.1017/s0334270000004665 Hocking, G. C. and Forbes, L. K. ''Subcritical free-surface flow caused by a line source in a fluid of finite depth''. J. Eng. Math. 26:455-466, 1992. doi:10.1007/bf00042763 Hocking, G. C. ''Supercritical withdrawal from a two-layer fluid through a line sink", J. Fluid Mech. 297:37–47, 1995. doi:10.1017/s0022112095002990 Hocking, G. C., Nguyen, H. H. N., Forbes, L. K. and Stokes,T. E. ''The effect of surface tension on free surface flow induced by a point sink''. ANZIAM J., 57:417–428, 2016. doi:10.1017/S1446181116000018 Landrini, M. and Tyvand, P. A. ''Generation of water waves and bores by impulsive bottom flux'', J. Eng. Math. 39(1–4):131-170, 2001. doi:10.1023/A:1004857624937 Lustri, C. J., McCue, S. W. and Chapman, S. J. ''Exponential asymptotics of free surface flow due to a line source''. IMA J. Appl. Math., 78(4):697–713, 2013. doi:10.1093/imamat/hxt016 Stokes, T. E., Hocking, G. C. and Forbes, L.K. ''Unsteady free surface flow induced by a line sink in a fluid of finite depth'', Comp. Fluids, 37(3):236–249, 2008. doi:10.1016/j.compfluid.2007.06.002 Tuck, E. O. and Vanden-Broeck, J.-M. ''A cusp-like free-surface flow due to a submerged source or sink''. ANZIAM J. 25:443–450, 1984. doi:10.1017/s0334270000004197 Vanden-Broeck, J.-M., Schwartz, L. W. and Tuck, E. O. ''Divergent low-Froude-number series expansion of nonlinear free-surface flow problems". Proc. Roy. Soc. A., 361(1705):207–224, 1978. doi:10.1098/rspa.1978.0099 Vanden-Broeck, J.-M. and Keller, J. B. ''Free surface flow due to a sink'', J. Fluid Mech, 175:109–117, 1987. doi:10.1017/s0022112087000314 Yih, C.-S. Stratified flows. Academic Press, New York, 1980. doi:10.1016/B978-0-12-771050-1.X5001-3

scholarly journals Two infinite-Froude-number cusped free-surface flows due to a submerged line source or sink

1986 ◽  
Vol 28 (2) ◽  
pp. 260-270 ◽  
Author(s):  
I. L. Collings
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Ideal Fluid ◽  
Line Source ◽  
Steady Motion ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Flows ◽  
Flow Problems

AbstractSolutions are found to two cusp-like free-surface flow problems involving the steady motion of an ideal fluid under the infinite-Froude-number approximation. The flow in each case is due to a submerged line source or sink, in the presence of a solid horizontal base.

scholarly journals The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth

2017 ◽  
Vol 156 ◽  
pp. 526-533
Author(s):  
G.C. Hocking ◽  
H.H.N. Nguyen ◽  
T.E. Stokes ◽  
L.K. Forbes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Surface Flow ◽  
Effect Of Surface

scholarly journals An open-channel flow meeting a barrier and forming one or two jets

2000 ◽  
Vol 41 (4) ◽  
pp. 458-472 ◽  
Author(s):  
L. H. Wiryanto ◽  
E. O. Tuck
Keyword(s):  
Free Surface ◽  
Open Channel ◽  
Vertical Wall ◽  
Open Channel Flow ◽  
Free Surface Flow ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Surface Flow ◽  
Parameter Measuring ◽  
Two Jets

AbstractA steady two-dimensional free-surface flow in a channel of finite depth is considered. The channel ends abruptly with a barrier in the form of a vertical wall of finite height. Hence the stream, which is uniform far upstream, is forced to go upward and then falls under the effect of gravity. A configuration is examined where the rising stream splits into two jets, one falling backward and the other forward over the wall, in a fountain-like manner. The backward-going jet is assumed to be removed without disturbing the incident stream. This problem is solved numerically by an integral-equation method. Solutions are obtained for various values of a parameter measuring the fraction of the total incoming flux that goes into the forward jet. The limit where this fraction is one is also examined, the water then all passing over the wall, with a 120° corner stagnation point on the upper free surface.

scholarly journals Exponential asymptotics of free surface flow due to a line source

2013 ◽  
Vol 78 (4) ◽  
pp. 697-713 ◽  
Author(s):  
C. J. Lustri ◽  
S. W. McCue ◽  
S. J. Chapman
Keyword(s):  
Free Surface ◽  
Line Source ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Exponential Asymptotics

The time-dependent free surface flow induced by a submerged line source or sink

1995 ◽  
Vol 284 ◽  
pp. 225-237 ◽  
Author(s):  
E. M. Sozer ◽  
M. D. Greenberg
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Stagnation Point ◽  
Line Source ◽  
Flow Direction ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Time Dependent ◽  
Infinite Depth ◽  
Source And Sink

The unsteady nonlinear potential flow induced by a submerged line source or sink is studied by a vortex sheet method, both to trace the free surface evolution and to explore the possible existence of steady-state solutions. Only steady-state flows have been considered by other investigators, and these flows have been insensitive to whether they are generated by a source or sink, except with respect to the flow direction along the streamlines. The time-dependent solution permits an assessment of the stability of previously found steady solutions, and also reveals differences between source and sink flows: for the infinite-depth case, steady stagnation-point-type solutions are found both for source flows and sink flows, above the critical value reported by other investigators; finally, it is shown that streamline patterns of steady stagnation-point flows are identical for source and sink flows only in the limiting case of infinite depth.

Unsteady free surface flow induced by a line sink in a fluid of finite depth

2008 ◽  
Vol 37 (3) ◽  
pp. 236-249 ◽  
Author(s):  
T.E. Stokes ◽  
G.C. Hocking ◽  
L.K. Forbes
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Surface Flow ◽  
Line Sink

scholarly journals A cusp-like free-surface flow due to a submerged source or sink

1984 ◽  
Vol 25 (4) ◽  
pp. 443-450 ◽  
Author(s):  
E. O. Tuck ◽  
J.-M. Vanden Broeck
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Line Source ◽  
Free Surface Flow ◽  
Surface Flow

AbstractA solution is found for a line source or sink beneath a free surface, at a unique squared Froude number of 12.622.

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