Characteristics of a hydraulic jump in Bingham fluid
  In this paper, we seek an adequate macroscopic model for a hydraulic jump in Bingham fluid. The formulas for conjugate depths, sequent bottom shear stress and critical depth are established. Since no exact analytical solution in closed form is available for conjugate depths, an approximate formula is developed. This formula can provide good results with an error less than 4%. The analytical results have revealed that the critical depth and the ratio of conjugate depths increase until bottom shear stress exceeds a certain value and then decrease afterwards. The bottom shear stress downstream of the jump is smaller than that upstream. The results are verified by experimental data and observations available in the literature. 
Jian-Jun Shu and Jian Guo Zhou
physics.flu-dyn