Gyarmati Principle and Open‐Channel Velocity Distribution
Publication: Journal of Hydraulic Engineering
Volume 113, Issue 5
Abstract
The relationship between the mixing‐length theory and the nonlinear theory is analyzed. The equation of motion for open‐channel flows can be obtained by the Gyarmati integral, which includes the linear and nonlinear terms of dissipation potential. The velocity distribution for laminar and turbulent flows in an open channel can be deduced by this integral. The relationship between the theory of minimum energy dissipation rate and the Gyarmati principle is analyzed. It shows that the constitutive structure of the mixing‐length model is valid in principle from the thermodynamic point of view. For the simple case of quasi‐uniform river flow, the Gyarmati integral of maximization should be reduced to the theory of minimum energy dissipation rate.
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References
1.
Boussinesq, T. V., “Essai sur la theorie des eaux courantes,” Mem. Pres. Acad. Sci., XXIII, 46, Paris, France, 1877.
2.
Chang, H. H., “Geometry of Rivers in Regime,” Journal of the Hydraulics Division, ASCE, Vol. 105, No. 6, 1979, pp. 691–706.
3.
Chang, H. H., “Minimum Stream Power and River Channel Patterns,” Journal of Hydrology, Vol. 41, 1979, pp. 303–327.
4.
Van Driest, E. R., “On the Turbulent Flow Near a Wall,” J. Aero. Sci., Vol. 23, 1956, p. 1007.
5.
Gyarmati, I., Non‐Equilibrium Thermodynamics, Springer‐Verlag, Berlin, 1970.
6.
Gyarmati, I., “On the Governing Principle of Dissipative Processes and its Extension to Non‐Linear Problems,” Ann. Phys. 7, Bd. 23, 1968.
7.
von Karman, T., “Mechanische Ähnlichkeit und Turbulenz,” Nachr. Ges. Wiss. Göttingen, Math. Phys. Klasse, 58, 1932.
8.
Li, J. C. M., “Thermodynamics for Non‐Equilibrium Systems, The Principle of Macroscopic Separability and the Thermodynamic Potential,” Journal of Applied Physics, Vol. 33, 1962, p. 616.
9.
Malkus, W. V. R., “Outline of a Theory of Turbulent Shear Flow,” Journal of Fluid Mechanics, Vol. 2, 1956, p. 521.
10.
Nikuradse, I., “Gesetzmässigkeiten der turbulenten Strömung in glatten Rohren,” Forschungs‐Arb. Ing.‐Wesen, No. 356, 1932.
11.
Prandtl, L., “Über die ausgebildete Turbulenz,” ZAMM, s. 136, 1932.
12.
Song, C. S. C., and Yang, C. T., “Velocity Profiles and Minimum Stream Power,” Journal of the Hydraulics Division, ASCE, Vol. 105, No. 8, 1979, pp. 981–998.
13.
Taylor, G. I., “The Transport of Vorticity and Heat through Fluids in Turbulent Motion,” Proceedings of the Royal Society, Series A, Vol. 135, 1932, p. 685.
14.
Yang, C. T., and Song, C. S. C., “Theory of Minimum Energy and Energy Dissipation Rate,” Encyclopedia of Fluid Mechanics, Vol. 1, Chap. 11, N. P. Cheremisinoff, Ed., Gulf Publishing Co., 1986.
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Published In
Journal of Hydraulic Engineering
Volume 113 • Issue 5 • May 1987
Pages: 563 - 572
Copyright
Copyright © 1987 ASCE.
History
Published online: May 1, 1987
Published in print: May 1987
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