Numerical simulation of a turbulent hydraulic jump: Characterization of the free interface and large bubble structure

Bubble generation is a ubiquitous and complex phenomenon occurring as a result of non-linear behavior of the free surfaces. Plunging breakers, spilling breakers and plunging jets are just a few scenarios where bubble generation occurs. Due to its complexity and our lack of complete understanding of this phenomenon, the models developed in the literature are far from being predictive (Moraga et al. 2008) (Ma et al. 2011). In addition to macro-bubble generation another mechanism has been discovered by Sigler & Mesler (1990), which generates micro bubbles, bubbles which are generated as a result of impact of two interfaces. A thin air film is trapped in a gap between the surfaces at impact. This thin film becomes unstable and fragments into tens to hundreds of micro bubbles (Thoroddsen et al. 2012). The sizes of these bubbles are in the range of tens to hundreds of microns. One important instance of bubble generation is near the ship hulls, where turbulent boundary layer interactions with the free surface result in a large amount of macro and micro bubble entrainment. Due to their dominant buoyancy forces, large bubbles come to the interface and leave the domain much faster than micro bubbles. Micro bubbles stay under the interface for a long time and leave a trail behind the ships. Due to the complexity of this problem, we have considered a simpler case of a hydraulic jump, where turbulence interactions with a free surface generating a continuous stream of wave breaking. In this work we aim to understand the structure of the interface, the length scales associated with them, and the local shape of the interface. Finally, we assess whether micro-bubble generation is plausible in this scenario. Pumphrey & Elmore (1990) have characterized different bubble-generation scenarios for the case of a drop impacting a flat surface, parameterized on the drop diameter and impact velocity. Based on this study, we can assess whether the impact phenomena occurring in a turbulent hydraulic jump are prone to producing micro bubbles. A hydraulic jump with a Froude number of 2 and a Reynolds number of 11000, based on inlet height and velocity, is simulated with the physical density ratio of 831 after an experiment by Murzyn et al. (2005). Large bubbles are observed to form in a patch structure with the specific frequency matching the peak in the velocity energy spectrum.