Abstract
For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of river bed are taken into account. The depth-averaged equations of k-ɛ turbulence model are also obtained. Because it accounts for the three-dimensional effect, this model is named as the complete depthaveraged model.
The boundaries of natural water bodies are usually curved. In this work, the derived equations in Cartesian coordinates are transformed into orthogonal coordinates. The obtained equations can be applied directly to numerical computation of practical problems.
Similar content being viewed by others
References
J. Kuipers and C. B. Vregdenhil, Calculations of two-dimensional horizontal flow, Report S 163, Part I, Delft Hydraulic Laboratory (1973).
A. K., Rastogi and W., Rodi, Predications of heat and mass transfer in open channels, J. Hydr. Div., ASCE, 104, 3 (1978), 397–420.
J. J., McGuirk and W., Rodi, A depth-averaged mathematical model for the near field of side discharge into open channel flows, J. Fluid Mech., 86 (1978), 761–781.
Tsai, Shutang and Wu, Feng, The fundamental equations of two-dimensional layer flows, Applied Mathematics and Mechanics (English Ed.), 7, 9 (1986), 835–840.
The ASCE Task Committee on Turbulence Model in Hydraulic Computations, Turbulence modeling of surface water flow and transport, J. of Hydr. Engrg., ASCE, 114, 9 (1988), 970–1073.
B. E., Launder and D. B., Spakling, The numerical computation of turbulent flows, Comp. Meths. Appl. Mech. Eng., 3 (1974), 269.
Ding Yan, Complete depth-averaged turbulence model and computation for side discharge into an unsteady natural river flow, Ph. D., dissertation, Tsinghua University, Beijing (1993).
S. B., Pope, The calculation of turbulent recirculation flows in general orthogonal coordinates, J. of Computational Physics, 26 (1978), 197.
Author information
Authors and Affiliations
Additional information
Communicated by Bian Yingui
Rights and permissions
About this article
Cite this article
Yan, D., Xueyi, Z., Changzhao, Y. et al. The equations of complete depth-averaged turbulence model in general orthogonal coordinates. Appl Math Mech 17, 53–63 (1996). https://doi.org/10.1007/BF00131295
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00131295