Physically Based Hydraulic Jump Model for Depth-Averaged Computations

Consideration of momentum conservation within a hydraulic jump leads to the conclusion that both the momentum correction due to the nonuniform mean velocity profile and the depth-averaged turbulent normal stress are important mechanisms. A model is constructed where the turbulent stresses are approximated with a simplified algebraic stress model. These stresses are shown to depend primarily on the vertical gradient of the longitudinal velocity. An estimate for the jump velocity distribution is then obtained from a moment of momentum equation. A single new term in the St. Venant momentum equation, combining the turbulent stress and velocity distribution effects, in terms of the depth and depth-averaged velocity is proposed. The new jump momentum flux term is nonlinear and diffusive in character. With an appropriate calibration of a single coefficient, the model gives good results for the location, length, and profile of hydraulic jumps ranging in Froude numbers from 2 to 7. The numerical results are obtained from a finite-element model with and without numerical dissipation.