Stochastic Theory for Irregular Stream Modeling. Part I: Flow Resistance
Publication: Journal of Hydraulic Engineering
Volume 118, Issue 8
Abstract
A stochastic theory is developed for predicting flow resistance in natural rivers. Irregularly varying river width and bed elevation are represented as one‐dimensional spatial random fields. Large‐scale random flow acceleration and deceleration in response to boundary variations are described by the stochastic differential flow equation. Analytical stochastic flow solutions are developed for the case when boundary variations are small and statistically homogeneous. In particular, closed‐form expressions for the effective flow resistance coefficient and flow variance are obtained. The results indicate that flow resistance in natural rivers is strongly influenced by cross‐sectional nonuniformity and mean flow condition, in addition to relative boundary roughness and mean cross‐sectional shape. The results also show that effective resistance is always greater than uniform resistance in a corresponding mean straight channel. This difference increases as the mean Froude number increases for a given mean bed slope or as mean bed slope decreases for a given mean Froude number. Part II of this paper will be published in the future.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Alam, M. Z., and Kennedy, J. F. (1969). “Friction factors for flow in sand‐bed channels.” J. Hydr. Div., ASCE, 95(6), 1973–1992.
2.
Bathurst, J. C. (1985). “Flow resistance estimation in mountain rivers.” J. Hydr. Engrg., ASCE, 111(4), 625–643.
3.
Burkham, D. E., and Dawdy, D. R. (1976). “Resistance equation for alluvial channel flow.” J. Hydr. Div., ASCE, 102(10), 1479–1489.
4.
Chiu, C. L., and Lee, T. S. (1971). “Stochastic simulation in study of transport processes in irregular natural streams.” Stochastic hydraulics, C. L. Chiu, ed., School of Engrg. Publication Series No. 4, University of Pittsburgh, Pittsburgh, Pa., 95–107.
5.
Einstein, H. A., and Barbarossa, N. L. (1952). “River channel roughness.” Trans. ASCE, 117, 1121–1146.
6.
Engelund, F. (1966). “Hydraulic resistance of alluvial streams.” J. Hydr. Div., ASCE, 92(2), 315–326.
7.
Hey, R. D. (1988). “Bar form resistance in gravel‐bed rivers.” J. Hydr. Engrg., ASCE, 114(12), 1498–1508.
8.
Rouse, H. (1965). “Critical analysis of open channel resistance.” J. Hydr. Div., ASCE, 91(4), 315–326.
9.
Leopold, L. B., Bagnold, R. A., Wolman, M. G., and Lucien, M. B. (1960). “Flow resistance in sinuous or irregular channels.” Professional Paper 282‐D, U.S. Geological Survey, Washington, D.C., 111–134.
10.
Leopold, L. B., and Wolman, M. G. (1957). “River channel patterns: braided, meandering and straight.” Professional Paper 282‐B, U.S. Geological Survey, Washington, D.C., 39–73.
11.
Li, S. G., and McLaughlin, D. B. (1991). “A nonstationary spectral method for solving stochastic groundwater problems: Unconditional analysis.” Water Resour. Res., 27(7), 1589–1608.
12.
Miller, B. A., and Wenzel, H. G. (1985). “Analysis and simulation of low flow hydraulics.” J. Hydr. Engrg., ASCE, 111(12), 1429–1446.
13.
Parker, G., and Peterson, A. W. (1980). “Bar resistance of gravel‐bed streams.” J. Hydr. Div., ASCE, 106(10), 1559–1575.
14.
Priestley, M. B. (1981). Spectral analysis and time series, vol. 2: Multivariate series, prediction and control, part B. Academic Press, New York, N.Y.
15.
Prestegaard, K. L. (1983). “Bar resistance in gravel‐bed streams at bankful stage.” Water Resour. Res., 19(2), 472–476.
16.
Salomonson, V. V., and Rango, A. (1979). Water resources in remote sensing and geology. B. S. Siegal and A. R. Gillepsie, eds., John Wiley & Sons, New York, N.Y., 607–633.
17.
Shen, H. W., Fehlman, H. M., and Mendoza, C. (1990). “Bed form resistance in open channels.” J. Hydr. Engrg., ASCE, 116(6), 1559–1575.
Information & Authors
Information
Published In
Copyright
Copyright © 1992 ASCE.
History
Published online: Aug 1, 1992
Published in print: Aug 1992
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.