theoretical criterion for stability of free hydraulic jump on adverse stilling basins

hydraulic jump on adverse stilling basin is an unstable phenomenon which causes some complexities in controlling of the   jump. this paper considers the stability of free hydraulic jump on adverse stilling basins from a theoretical point of view. a minimum value of upstream froude number is needed to produce the free hydraulic jump on adverse stilling basins which was presented by a theoretical equation. also, the effects of an end sill and divergence in section on the minimum froude number were investigated. moreover, it is required that the bed has a minimum friction for making the jump stable which is obtained as a function of upstream froude number and bed slope. this condition was compared with the criterion proposed by previous researchers and showed the considerable deviations at larger bed slopes. the result showed that it is impossible to establish the hydraulic jump on concrete adverse stilling basins without any appurtenances. however, diverging in section can improve the stability of hydraulic jump on adverse stilling basins.