Analysis of Meandering Water Rivulets of Finite Amplitude
Publication: Journal of Hydraulic Engineering
Volume 123, Issue 11
Abstract
Water rivulets on inclined smooth plate form a stable meandering pattern under certain conditions. The bend theory for describing the meandering water rivulet includes the effect of the surface-tension force. The governing equations are the St. Venant equations of shallow water as shown in curvilinear coordinates. The resultant bend equation is nonlinear. The linear stability analysis of this equation with minute disturbance was done by the senior author. In that analysis, all the small terms (nonlinear terms) were omitted. The stable meander trajectory formed by streams has finite amplitude as derived from Cartesian sinusoidal patterns. These patterns are very similar in shape to those of meandering rivers. The pattern of meandering rivers can be expressed by sine-generated curves. The meandering river trajectory derived from the first-order sine-generated curve contains periodic deviation characteristics. This deviation is caused by either fattening and/or skewing from the first-order sine-generated curve. The approximate solution for the nonlinear analysis of the bend equation (including the surface-tension force) demonstrated that the deviations could be well formulated by the third-order sine-generated curves. Furthermore, the derived water rivulet forms of finite amplitude were verified by laboratory experimental results.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aggarwal, J. K. (1972). Notes on nonlinear systems. Van Nostrand Reinhold, New York, N.Y.
2.
Brice, J. C.(1974). “Evolution of meander loops.”Geological Soc. of Am. Bull., 85, 581–586.
3.
Carson, M. A., and Lapointo, M. F.(1983). “The inherent asymmetry of river meander plan form.”J. Geol., 91, 41–55.
4.
Davis, T. R. H., and Tinker, C. C.(1984). “Fundamental characteristics of stream meanders.”Geological Soc. of Am. Bull., 95, 505–512.
5.
Furuya, S., and Nagumo, J. (1957). Theory of nonlinear vibrations. Iwanami-shoten, Tokyo, Japan (in Japanese).
6.
Homma, M. (1967). Hydraulics—hydrodynamics for civil engineers. Maruzen, Tokyo, Japan (in Japanese).
7.
Ikeda, S., Parker, G., and Sawai, K.(1981). “Bend theory of river meanders. Part 1. Linear development.”J. Fluid Mech., Cambridge, U.K., 112, 363–377.
8.
Johannesson, H., and Parker, G.(1989). “Linear theory of river meanders.”Am. Geophys. Union Water Resourc. Monograph, 12, 181–213.
9.
Leblond, P. H., and Mysak, L. A. (1978). Waves in the ocean. Elsevier Science Publishing Co., Inc., New York, N.Y.
10.
Mizumura, K.(1993). “Meandering water rivulet.”J. Hydr. Engrg., ASCE, 119(11), 1205–1222.
11.
Parker, G., and Andrews, E.(1986). “On the time development of meander bends.”J. Fluid Mech., 162, 139–156.
12.
Parker, G., Diplas, P., and Akiyama, J.(1983). “Meander bends of high amplitude.”J. Hydr. Engrg., ASCE, 109(10), 1323–1337.
13.
Parker, G., Sawai, K., and Ikeda, S.(1982). “Bend theory of river meanders: Part 2. Nonlinear deformation of finite-amplitude bends.”J. Fluid Mech., 115, 303–314.
14.
Schmuki, P., and Laso, M.(1990). “On the stability of rivulet flow.”J. Fluid Mech., 215, 125–143.
15.
Tanaka, M. (1984). “Turbulent characteristics in meandering wind tunnel,” MS thesis, Saitama Univ., Urawa, Japan (in Japanese).
16.
Tomita, Y. (1980). Rheology. Corona Publishing Co., Ltd., Tokyo, Japan (in Japanese).
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 123 • Issue 11 • November 1997
Pages: 995 - 1003
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Nov 1, 1997
Published in print: Nov 1997
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.