DNS of air-water interface instabilities for flow over a bump in a shallow water flume

Air-water interface instabilities are commonly observed in wave breaking processes both in nature and in many fields of engineering; thus, their physics and modeling/simulation capabilities are important. The experimental studies of flows over a bump in a shallow water flume by Gui et. al (2014a; 2014b) displayed an air-water interface instability, bulge-scar, that was never observed in prior experimental studies. Although, extensive experimental studies were conducted, the complete physical mechanics could not be explained due to challenges with the experimental measurements caused by large range of temporal and spatial scales associated with the physics, and sensitivity of the experiments. High-fidelity direct numerical simulations were conducted to replicate the experiment where the temporal and spatial scales can be captured, and the sensitive experimental parameters can be controlled. Additionally, a new approach was developed by combining a traditional method for identifying important experimental parameters, Buckingham pi theorem, and machine learning. The combination of the experimental, numerical and machine learning approaches yielded insights into the physics of the bulge-scar instability which could not have been possible without integrating all three approaches. The bulge-scar formation was found to be related to vortex structures and pressure distribution underneath and across the air-water interface. Reynolds number and wave steepness were identified as the important parameters and were used to develop a model for the bulge-scar instability.