On hydraulic falls of two-layer flow

Abstract-Hydraulic falis and asymptotic mean levels of two-layer flow are determined by means of AfKdV equation in phase coordinate theoretically.By present theory,the hydraulic falls HM_r depend on a characteristic value of the AfKdV equation at the subcritical cutoff points F.It is proved that the differences of the asymptotic mean levels upstream and downstream at the subcritical cutoff points ate equal to 2F.A relation between F and the asymptotic mean levels at the subcritical cutoff points is also found in teens of the solution of the hydraulic falls.Because the AfKdV equation is derived based on the small topography assumption,for semicircular topography the valid region of this theory is α < 0.35,in which α is radius of the semicircular topography.An experiment is carried out to examine the theory of the present paper.From comparisons between the theoretical and experimental results,it is shown that they are in better agreement.Under conditions of different stratified parameters,the hydraulic falls of two-layer flow are predictad theoretically.