ALGEBRAIC FUNCTIONS FOR TURBULENT KINETIC ENERGY AND DISSIPATION RATE IN OPEN CHANNEL FLOWS

摘要

The work reported herein deals with the derivation of algebraic forms of the vertical variation of the turbulent kinetic energy and its dissipation rate for fully developed, steady flows in open channels of large aspect ratio. The equations of momentum, turbulent energy and its dissipation rate are being used, after neglecting the terms describing advective and diffusive transport. Assuming, initially, a linear relationship for the vertical variation of turbulent kinetic energy, an analytical relationship for the dissipation rate is obtained as well as an improved relation for the kinetic energy variation. The two coefficients of the initial relationship are computed utilizing the assumption of local equilibrium of turbulent energy production and dissipation near the wall and by substituting the final analytical relationships into the dissipation equation and subsequent optimization. The results compare well with both experimental and numerical data or other algebraic model computations available in the literature. The proposed algebraic model may be used as a turbulence closure model for solving the continuity and momentum transport equations in open channels with large aspect ratio.