Numerical investigation of vorticity and bubble clustering in an air entraining hydraulic jump

A high resolution computational fluid dynamics model is used to simulate a steady air entraining laboratory scale hydraulic jump. A detailed examination of shear layer instabilities reveals the dynamic relationship between spanwise vortices, free surface fluctuations, and air-water spatial patterns. Spanwise vortices generated at the toe roll-up under a variable depth roller, creating large free surface fluctuations through high velocity water ejections in the roller. The mean shear layer elevation and free surface elevations periodically alternate between positive and negative correlation throughout the roller, driven by dynamic vortex transport. Vortices descending towards the lower wall create an upwelling of non-bubbly fluid into the shear layer that contributes to regions of decreased bubble concentration between vortices. The position of a strong shear layer at the location of maximum air entrainment, directly above the jump toe, leads to highly aerated vortices that influence bubble behavior. Bubbles breakup quickly after entrainment at the toe and bubble clusters are observed most frequently below and at the end of the roller where bubble breakup and energy dissipation are diminished. The dominant separation angle of clustered bubbles is independent of downstream distance and aligns closely with the direction of initial shear, suggesting bubble clustering is a remnant of bubble breakup.