Hydraulic condition for undular-jump formations

This paper presents the upper limit of the inflow Froude number for undular-jump formations in smooth rectangular channels. It has been found that the formation of undular jumps depends not only on the inflow Froude number but on the boundary-layer development at the toe of the jump under conditions in which the effects of the aspect ratio and the Reynolds number on the flow condition are negligible. The velocity of the first wave crest immediately before the breaking is at a maximum near the water surface and becomes a critical velocity. For the undular jumps with the developing inflow, the upper limit of the Froude number F-1limit has been shown experimentally as F-1limit = 1.3-2.3. For the fully developed inflow, F-1limit = 1.7 has also been obtained, and it shows the same value as described in many textbooks. The upper limit of the inflow Froude number for undular-jump formations has been derived by taking account of the boundary-layer development and considering the how along the water surface immediately before the breaking. The predicted values agree with experimental results.