Forced Hydraulic Jumps Described by Classic Hydraulic Equations Reproducing Cusp Catastrophe Features

Abstract

The information content of the classic equations describing the problem of forced hydraulic jumps in open channels is the subject of this paper. The forcing refers to designed structural composites to transform incoming supercritical flows into outgoing subcritical flows through hydraulic jumps. The complete flow history through such systems is described by two stable flow profiles, which are interlocked and one can jump to the other. The interlocked profiles underpin a hydraulic effect known as hysteresis with the prime feature of the dependence of flows on their past history. The paper develops an algorithm by using classic hydraulic equations alone to identify hysteresis by building on tacit knowledge already published. The algorithm reproduces the effects of catastrophe theory and shows that hysteresis has predictable configurations. It is validated for geometries with step-rises by using published experimental data; as well as a flume with abrupt contractions by authors’ experimental data.