Extension of the averaging theory for circular hydraulic jumps to account for surface tension effects

The circular hydraulic jump (CHJ), a seemingly discontinuous change of flow height and velocity, occurs in the film flow developing on a flat plate vertically impinged by a liquid jet. It can be interpreted as a transition region connecting a supercritical to a subcritical region. In the supercritical region, waves do not move fast enough to travel upstream, whereas in the subcritical region, they can propagate upstream. In the jump region, different flow structures occur, which can be used to classify CHJs. Models based on boundary layer (BL) theory and the method introduced by Karman and Pohlhausen have shown to be capable of capturing a certain class of CHJs. Here, a previously developed averaging theory based on BL theory, is further extended to account for surface tension effects on the jump. Detailed comparisons to more expensive numerical models are carried out to evaluate the accuracy of the extended model and gain new insights into the physics of CHJs. Including surface tension decreases the curvature of the film surface in the jump region, and consequently, leads to a weaker jump and a less pronounced or even vanishing recirculation region. The jump position decreases slightly.