Asymptotic expansion for steady state overland flow

Parlance, J.-Y.; Hogarth, W. L.; Sander, G. C.; Rose, C. W.; Haverkamp, R.; Surin, A. M.; Brutsaert, Wilfried

doi:10.1029/wr026i004p00579

Cited by 9 publications

(4 citation statements)

References 6 publications

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“…For steady state one-dimensional flow over a plane he derived a new criterion as K ½ 3 C 5/Fo 2 where K is the kinematic wave number and Fo is the Froude number corresponding to normal flow. Parlange et al (1990) investigated errors in the KW and DW approximations by comparing their predictions with the numerical solution of the SV equations under steady state conditions. They suggested splitting the solution in two regions, one near the downstream end of the plane and the other covering most of the plane.…”

Section: Comparison Of Kinematic Wave Theory With Diffusion Wave and mentioning

confidence: 99%

Is hydrology kinematic?

Singh

2002

Hydrological Processes

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Abstract:A wide range of phenomena, natural as well as man-made, in physical, chemical and biological hydrology exhibit characteristics similar to those of kinematic waves. The question we ask is: can these phenomena be described using the theory of kinematic waves? Since the range of phenomena is wide, another question we ask is: how prevalent are kinematic waves? If they are widely pervasive, does that mean hydrology is kinematic or close to it? This paper addresses these issues, which are perceived to be fundamental to advancing the state-of-the-art of water science and engineering.

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Section: Comparison Of Kinematic Wave Theory With Diffusion Wave and mentioning

confidence: 99%

Is hydrology kinematic?

Singh

2002

Hydrological Processes

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“…Singh and Aravamuthan (1993) presented a comprehensive treatment of such flows using both the KW and DW approximations. Parlange et al (1990) investigated errors in both the KW and DW approximations by comparing their results with the numerical solution of the St. Venant equations under steady state conditions. Singh and Aravamuthan (1995) derived errors of these approximations under one upstream and two downstream boundary conditions: (1) zero flux at the upstream boundary, (2) critical flow depth at the downstream boundary, and (3) zero depth gradient at the downstream boundary.…”

Section: Introductionmentioning

confidence: 99%

Errors of kinematic wave and diffusion wave approximations for time-independent flows with infiltration and momentum exchange included

2005

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Abstract:Error equations for kinematic wave and diffusion wave approximations were derived for time-independent flows on infiltrating planes and channels under one upstream boundary and two downstream boundary conditions: zero flow at the upstream boundary, and critical flow depth and zero depth gradient at the downstream boundary. These equations specify error in the flow hydrograph as a function of space. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors below 2% for values of KF (e.g. KF ½ 7Ð5), where K is the kinematic wave number and F is the Froude number. Even for small values of KF (e.g. KF D 2Ð5), the errors were typically less than 3%. The accuracy of the diffusive approximation was greatly influenced by the downstream boundary condition. For critical flow depth downstream boundary condition, the error of the kinematic wave approximation was found to be less than 10% for KF ½ 7Ð5 and greater than 20% for smaller values of KF. This error increased with strong downstream boundary control. The analytical solution of the diffusion wave approximation is adequate only for small values of K.

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“…Singh and Aravamuthan (1993) presented a comprehensive treatment of such¯ows using both KW and DW approximations. Parlange et al (1990) were probably the ®rst to undertake an investigation of errors in the KW and DW approximations by comparing their predictions with the numerical solution of the St Venant (SV) equations under steady-state conditions. Singh and Aravamuthan (1995) derived errors in these approximations under one upstream and two downstream boundary conditions: (1) zero¯ux at the upstream boundary; (2) critical ow depth at the downstream boundary condition; and (3) zero depth gradient at the downstream boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Accuracy of the kinematic wave and diffusion wave approximations for time-independent flows with infiltration included

Singh

Aravamuthan

1998

Hydrol. Process.

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Abstract:Errors in the kinematic wave and diusion wave approximation for time-independent (or steady-state) cases of channel¯ow with in®ltration were derived for three types of boundary conditions: zero¯ow at the upstream end, and critical¯ow depth and zero depth gradient at the downstream end. The diusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1 . 4% for KF 2 0 5 7 . 5, and up to 14% for KF 2 0 4 0 . 75 for the upstream boundary condition of zero discharge and ®nite depth, where K is the kinematic wave number and F 0 is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF 2 0 (41). The accuracy of these approximations was signi®cantly in¯uenced by the downstream boundary, both in terms of the magnitude of the error and the segment of the channel reach for which these approximations would be applicable. #

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Asymptotic expansion for steady state overland flow

Cited by 9 publications

References 6 publications

Is hydrology kinematic?

Is hydrology kinematic?

Errors of kinematic wave and diffusion wave approximations for time-independent flows with infiltration and momentum exchange included

Accuracy of the kinematic wave and diffusion wave approximations for time-independent flows with infiltration included

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