Gyarmati Principle and Open‐Channel Velocity Distribution

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.