The Undular Hydraulic Jump: On a numerical method for the computation of flows with curved streamlines

From the theory composed of the method of characteristics and the set of all possible continuous ancillary conditions a closed theory is formed by introducing step functions together with overall mass and momentum conservation equations. However, this representation cannot be called realistic when the jump has the form of the undular hydraulic jump. The objective of the present study may novw be stated as follows: 1. to provide a closed and realistic theory which is able to describe the short wave radiation behind the hydraulic jump; 2. to investigate the reality of the usual "closure" of the quasi-linear wave theory, by proceeding to the next approxilnation that is provided by 1. As these aims are to be attained using a digital machine, they imply the construction of a closed and realistic numerical theory that will provide "contradictory" results under those conditions that provide instability in the hydraulic jump, manifest as some breaking-down of the short wave motion into turbulent motion.