Errors of the kinematic wave and diffusion wave approximations are derived for non-uniform, time-independent cases of planar or channel flow under three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation is found to be accurate for KF 2 0≥5, where K is the kinematic wave number and F 0 is the Froudel number. However, in order for the kinematic wave approximation to be sufficiently accurate, KF 2 0 may have to be significantly greater than 5. The accuracy of the diffusion wave approximation is significantly influenced by the downstream boundary condition.
Introduction
In an overland flow a steady state is attained for constant rainfall of sufficiently long duration (greater than or equal to the time of concentration t c), because the depth of flow at the outlet increases until equilibrium is reached. The same is true for flow in a channel subject to constant lateral inflow....
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Govindaraju, R.S., Jones, S.E. and Kavvas, M.L., 1988. On the diffusion wave model for overland flow: 2. Steady state analysis. Water Resources Research, 24(5), 745–754.
Morris, M., 1978. The effect of the small-slope approximation and lower boundary condition on the solutions of the Saint Venant equations. Journal of Hydrology, 40, 31–47.
Parlange, J.Y., Hogarth, W., Sander, G.C. et al., 1989. Comment on ‘On the diffusion wave model for overland flow: 2. Steady state analysis,’ by R.S. Govindaraju, S.E. Jones and M.L. Kavvas. Water Resources Research, 25(8), 1923–1924.
Parlange, J.Y., Hogarth, W., Sander, G. et al., 1990. Asymptotic expansion for steady-state overland flow. Water Resources Research, 26(4), 579–583.
Pearson, C.P., 1989. One-dimensional flow over a plane: criteria for kinematic wave modeling. Journal of Hydrology, 111, 39–48.
Singh, V.P. and Aravamuthan, V., 1992a. Errors in kinematic and diffusion wave approximations for time-independent flows: 1. Cases 1 to 6. Technical Report WRR20, Water Resources Program. Department of Civil Engineering, Louisiana State University, Baton Rouge, LA.
Singh, V.P. and Aravamuthan, V., 1992b. Errors in kinematic and diffusion wave approximations for time-independent flows: 2. Cases 7 to 13. Technical Report WRR21, Water Resources Program, Department of Civil Engineering, Louisiana State University, Baton Rouge, L.A.
Singh. V.P. and Aravamuthan, V., 1992c. Errors in kinematic and diffusion wave approximations for time-independent flows: 3. Cases 14 to 19. Technical Report WRR22, Water Resources Program, Department of Civil Engineering, Louisiana State University, Baton Rouge, LA.
Singh, V.P., Aravamuthan, V. and Joseph, E.S., 1993. Accuracy of hydrodynamic models of flood discharge determinations. Proceedings, International Conference on Environmental Management: Geo-Water and Engineering Aspects, pp. 79–90, Wollongong, Australia.
Cross references
Editor information
Rights and permissions
Copyright information
© 1998 Kluwer Academic Publishers
About this entry
Cite this entry
Herschy, R.W., Herschy, R.W., Singh, V.P., Aravamuthan, V. (1998). Accuracy of hydrodynamic approximations in hydrology: Non-uniform, steady flow. In: Herschy, R.W., Fairbridge, R.W. (eds) Encyclopedia of Hydrology and Water Resources. Encyclopedia of Earth Science. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4497-7_3
Download citation
DOI: https://doi.org/10.1007/978-1-4020-4497-7_3
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-412-74060-2
Online ISBN: 978-1-4020-4497-7
eBook Packages: Springer Book Archive