Free-Surface Stability Criterion as Affected by Velocity Distribution
This article has a reply.
VIEW THE REPLYPublication: Journal of Hydraulic Engineering
Volume 121, Issue 10
Abstract
This paper examines how the velocity distribution of flow in open channels affects the kinematic and dynamic wave velocities, from which the various forms of the Vedernikov number ( V ) can be formulated. When V > 1, disturbances created in open-channel flow will amplify in the form of roll waves; when V < 1, some (though not all) disturbances will attenuate. The specific state of flow at V = 1 represents a limiting case of neutral stability. A study of the Vedernikov stability criterion ( V ⪋ 1) reveals that it can be readily deduced within the framework of the kinematic and dynamic wave theories by comparing the kinematic wave velocity to the corresponding dynamic wave velocity. This in effect recasts V as the ratio of the kinematic and dynamic wave velocities. This ratio further proves equivalent to F /Fs, the ratio of the Froude number ( F ) to the stability limit for the Froude number ( Fs ). Thus, distinguishing among theoretical Fs -values for laminar and turbulent flows with various velocity distributions enables one to evaluate the role that the velocity distribution plays in the formulation of the Vedernikov stability criterion.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abbott, M. B. (1979). Computational hydraulics, elements of the theory of free surface flow . Pitman Publishing Ltd., London, England.
2.
Chen, C. L. (1989). “Power law of flow resistance in open channels: Manning's formula revisited.”Proc., Int. Conf. on Channel Flow and Catchment Runoff: Centennial of Manning's Formula and Kuichling's Rational Formula, Univ. of Virginia, Charlottesville, Va., 817–848.
3.
Chen, C. L. (1991a). “Power law of flow resistance in open channels: Manning's formula revisited.”Channel Flow Resistance: Centennial of Manning's Formula, B. C. Yen, ed., Water Resour. Publ., Littleton, Colo., 206–240.
4.
Chen, C. L.(1991b). “Unified theory on power laws for flow resistance.”J. Hydr. Engrg., ASCE, 117(3), 371–389.
5.
Chen, C. L.(1992). “Momentum and energy coefficients based on power-law velocity profile.”J. Hydr. Engrg., ASCE, 118(11), 1571–1584.
6.
Chen, C. L.(1993). “Unique laminar-flow stability limit based on shallow-water theory.”J. Hydr. Engrg., ASCE, 119(7), 816–829.
7.
Chow, V. T. (1959). Open-channel hydraulics . McGraw-Hill Book Co., Inc., New York, N.Y.
8.
Craya, A. (1952). “The criterion for the possibility of roll-wave formation.”Proc., NBS Semicentennial Symp. on Gravity Waves, U.S. Nat. Bureau of Standards Circular 521, Nat. Inst. of Standards and Technol., Gaithersburg, Md., 141–173.
9.
Dingman, S. L. (1984). Fluvial hydrology . W. H. Freeman and Co., New York, N.Y.
10.
Dracos, T. A., and Glenne, B.(1967). “Stability criteria for open-channel flow.”J. Hydr. Div., ASCE, 93(6), 79–101.
11.
Dressler, R. F.(1949). “Mathematical solutions of the problems of roll waves in inclined open channels.”Communications on Pure and Appl. Mathematics, 2(2/3), 149–194.
12.
Dressler, R. F. (1952). “Stability of uniform flow and roll-wave formation.”Proc., NBS Semicentennial Symp. on Gravity Waves, U.S. Nat. Bureau of Standards Circular 521, Nat. Inst. of Standards and Technol., Gaithersburg, Md., 237–241.
13.
Dressler, R. F., and Pohle, F. V.(1953). “Resistance effects on hydraulic instability.”Communications on Pure and Appl. Mathematics, 6(1), 93–96.
14.
Engelund, F.(1965). “A note on the Vedernikov's criterion.”La Houille Blanche, Paris, France, 20(8), 801–802.
15.
Escoffier, F. F.(1950). “A graphical method for investigating the stability of flow in open channels or in closed conduits flowing partly full.”Trans. Am. Geophys. Union, 31(4), 583–586.
16.
Escoffier, F. F.(1961). “Discussion of `Roll waves and slug flows in inclined open channel,' by P. G. Mayer.”ASCE Trans., 126, 535–541.
17.
Escoffier, F. F., and Boyd, M. B.(1962). “Stability aspects of flow in open channels.”J. Hydr. Div., ASCE, 88(6), 145–166.
18.
Ishihara, T., Iwagaki, Y., and Ishihara, Y.(1952). “On the rollwave-trains appearing in the water flow on a steep slope surface.”Memoirs of the Fac. of Engrg., Kyoto Univ., Japan, 14(2), 83–91.
19.
Ishihara, T., Iwagaki, Y., and Iwasa, Y. (1954). “Theory of the roll-wave trains in laminar water flow on a steep slope surface—studies on the thin sheet flow, 5th report.”Trans., Japanese Soc. of Civ. Engrg., Tokyo, Japan, 19, 46–57 (in Japanese).
20.
Ishihara, T., Iwagaki, Y., and Iwasa, Y. (1955). “Mechanism of water erosion on land-surfaces and roll-wave trains.”Bull., Engrg. Res. Inst., Kyoto Univ., Japan, 7, 23–28 (in Japanese).
21.
Ishihara, T., Iwagaki, Y., and Iwasa, Y.(1961). “Discussion of `Roll waves and slug flows in inclined open channels,' by P. G. Mayer.”ASCE Trans., 126, 548–563.
22.
Iwagaki, Y., and Iwasa, Y. (1955). “On the hydraulic characteristics of the roll-wave trains—studies on the thin sheet flow, 7th report.”Proc., Japanese Soc. of Civ. Engrg., Tokyo, Japan, 40(1), 5–12 (in Japanese).
23.
Iwasa, Y.(1954). “The criterion for instability of steady uniform flows in open channels.”Memoirs of the Fac. of Engrg., Kyoto Univ., Japan, 16(4), 264–275.
24.
Jeffreys, H.(1925). “The flow of water in an inclined channel of rectangular section.”Philosophical Mag. and J. Sci., London, England, 49(6), 793–807.
25.
Julien, P. Y., and Hartley, D. M.(1986). “Formation of roll waves in laminar sheet flow.”J. Hydr. Res., 24(1), 5–17.
26.
Keulegan, G. H., and Patterson, G. W.(1940). “A criterion for instability of flow in steep channels.”Trans. Am. Geophys. Union, 21, 594–596.
27.
Koloseus, H. J., and Davidian, J. (1966). “Free-surface instability correlations.”U.S. Geological Survey Water-Supply Paper 1592-C, U.S. Geological Survey.
28.
Liggett, J. A. (1975). “Stability.”Unsteady flow in open channels, K. Mahmood and V. Yevjevich, eds., Water Resour. Publ., Fort Collins, Colo., Vol. I, Chap. 6, 259–282.
29.
Lighthill, M. J., and Whitham, G. B. (1955). “On the kinematic waves—I. flood movement in long rivers.”Proc., Royal Society London, London, England, 229, Ser. A, 281–316.
30.
Montouri, C.(1961a). “Discussion of `Stability aspects of flow in open channels,' by F. F. Escoffier and M. B. Boyd.”J. Hydr. Div., ASCE, 89(4), 264–273.
31.
Montouri, C. (1961b). “La formazione spontanea dei treni d'onde su canali a pendenza molto forte.”Relazioni su ricerche studi promossi dall' ANIDEL. 1–19 (in Italian; translated by J. C. Van Thienhoven, “Spontaneous formation of wave trains in steep channels.” U.S. Army Wtrwy. Experiment Station, Translation No. 65-12, 1965).
32.
Ponce, V. M.(1991). “New perspective on the Vedernikov number.”Water Resour. Res., Am. Geophys. Union, 27(7), 1777–1779.
33.
Ponce, V. M., and Mainser, M. P.(1993). “Verification of theory of roll wave formation.”J. Hydr. Engrg., ASCE, 119(6), 768–773.
34.
Powell, R. W.(1948). “Vedernikov's criterion for ultra-rapid flow.”Trans., Am. Geophys. Union, 29(6), 882–886.
35.
Robertson, J. M., and Rouse, H.(1941). “On the four regimes of open-channel flow.”Civ. Engrg., ASCE, 11(3), 169–171.
36.
Rosso, M., Schiara, M., and Berlamont, J.(1990). “Flow stability and friction factor in rough channels.”J. Hydr. Engrg., ASCE, 116(9), 1109–1118.
37.
Rouse, H.(1965). “Critical analysis of open-channel resistance.”J. Hydr. Div., ASCE, 91(4), 1–25.
38.
Seddon, J. A.(1900). “River hydraulics.”ASCE Trans., 43, 179–243.
39.
Stoker, J. J. (1957). Water waves, the mathematical theory with applications . Interscience Publishers, Inc., New York, N.Y.
40.
Thomas, H. A. (1940). “The propagation of waves in steep prismatic conduits.”Proc., Hydr. Conf., Univ. of Iowa, Iowa City, Iowa, 214–229.
41.
Vedernikov, V. V.(1945). “Conditions at the front of a translation wave disturbing a steady motion of a real fluid.”Comptes Rendus (Doklady) de l'Académie des Sciences de l'URSS, 48(4), 239–242.
42.
Vedernikov, V. V.(1946). “Characteristic features of a liquid flow in an open channel.”Comptes Rendus (Doklady) de l'Académie des Sciences de l'URSS, 52(3), 207–210.
43.
Vedernikov, V. V.(1951). “Discussion of `Vedernikov's criterion for ultra-rapid flow,' by R. W. Powell.”Trans. Am. Geophys. Union, 32(4), 603–607.
44.
Whitham, G. B. (1974). Linear and nonlinear waves, John Wiley & Sons, New York, N.Y.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 121 • Issue 10 • October 1995
Pages: 736 - 743
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Oct 1, 1995
Published in print: Oct 1995
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.