Structure of the turbulent hydraulic jump in a trapezoidal channel

Abstract

The axial flow structure of turbulent hydraulic jump has been analysed and the general equation valid for a channel of arbitrary cross section has been proposed. Based on the Reynolds equations of mean turbulent motion in two dimensional steady incompressible flow subjected to hydrostatic pressure distribution, the integral equations of depth averaged flow over a channel of arbitrary cross sectional area are obtained. An integral method has been developed where inertia, pressure gradient and depth averaged normal Reynolds stress play the dominant role. The closure model for variation of depth averaged normal Reynolds stress has been expressed as product of the constant eddy viscosity and the gradient of the depth averaged axial velocity with respect to axial distance. In the trapezoidal channel the closed form solution for the upper surface profile and axial length of the hydraulic jump have been obtained. The comparison of the theory with experimental data is remarkably good. The theory shows that for F, larger than a fixed value, the surface profile approaches a limiting universal solution provided the variables are appropriately non-dimensionalized. Further, the present predictions on the roller length are also supported by experimental data in rectangular and triangular channels.