• Water for future
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• v.27 no.4
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• pp.123-133
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• 1994

The kinematic and diffusion models using simplified momentum equations of the full dynamic equation have been frequently used for numerical flow simulations, because they have several computational advantages compared to the full dynamic model. In this paper, the more generally acceptable application ranges of the kinematic and diffusion finite difference models were investigated based on three major parameters, which are channel bed slopes So, dimensionless depth increasing numbers Gw at upstream boundary and Froude numbers Fr. The applicable ranges were obtained by comparing the relative magnitudes of the local acceleration, convective acceleration, pressure, gravity and friction terms in the full dynamic equation. In the simulations, a Courant number of 0.5 was used and the channel bed slopes were changed from 0.00001 to 0.05. Also, Froude numbers of 0.1, 0.5 and 0.9 were employed. In this paper, it is indicated that the applicable ranges of kinematic models are increased with increasing of Froude numbers. However, the applicable ranges of diffusion models are decreased with increasing of Froude numbers. Finally, 9 figures were proposed as a guideline in the application of kinematic and diffusion finite difference models based upon the allowable deviation compared to the full dynamic model. With applying the proposed criteria, it is expected that the flow simulations in the channels, streams or rivers are more efficiently achieved.

• Journal of Korea Water Resources Association
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• v.44 no.6
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• pp.449-459
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• 2011

By examining the experimental results, the critical mean velocity which initiates the movement of riprap is increased with the riprap size in mean diameter, the mean diameter over water depth (d/h), Froude number (Fr), and turbulent shear velocity over critical mean velocity (u*/${\nu}$) which have great correlations among them so these parameters are adopted governing hydraulic stability for riprap. The hydraulic stability equation for riprap is developed by regression analysis. The developed equation is expanded from 0.36~0.73 m/s of experimental range to 0~5.0 m/s for the application in engineering discipline. So many useful relations among those parameters including critical mean velocity are derived by expanding to high Reynolds regions. Mean diameter calculation results by expanding to high Reynolds regions coincide with the calculations of ASCE and USBR at the range of 0~3.0 m/s and the calculation result of ASCE at the range of 3.0~5.0 m/s. The results by developed formulae coincide well with the formulae of ASCE in general and also the results by recently developed existing formulae of hydraulic stability for riprap. Thus, the developed equation has the high applicability in engineering discipline to evaluate the hydraulic stability for riprap.