Numerical and Theoretical Studies of Air Entrainment and Bubble Acoustics under Breaking Waves

Abstract

Bubbles and breaking waves play a critical role in many physical processes. However, bubble formation mechanism, trajectories, and their acoustic signatures are still poorly understood due to the complex process of breaking waves. To study the bubble transport dynamics and their formation mechanism, a technique for Lagrangian tracking of bubbles and detecting their time-evolution behaviors is developed. Five possible behaviors are considered: formation, extinction, continuity, binary fragmentation, and binary coalescence. The technique is based on establishing a network of mappings between bubbles identified at adjacent time instants. The accuracies for continuity, binary fragmentation, and binary coalescence are estimated to be 99.5%, 90%, and 95%, respectively. The algorithm is proved to be accurate and robust by extensive validations using the breaking wave cases. Bubble entrainment mechanism and bubble trajectory are investigated. Air filaments and cavities in plunging breaking waves, generically cylinders, produce bubbles through an interface instability. A generalized dispersion relation is obtained that spans the Rayleigh–Taylor and Plateau–Rayleigh instabilities as cylinder radius varies. The analysis provides insight into the role of surface tension in the formation of bubbles from filaments and cavities. Small filaments break up into bubbles through a Plateau–Rayleigh instability driven through the action of surface tension. Large air cavities produce bubbles through a Rayleigh–Taylor instability driven by gravity and moderated by surface tension, which has a stabilizing effect. Surface tension, interface curvature, and gravity are all important for cases between these two extremes. Bubble trajectories and their interaction with breaking wave flow fields are also studied here. A simulation framework for bubbly flow and the sound radiated by breaking waves is presented. It consists of a two-phase flow solver, an algorithm to track bubbles and bubble creation rates, and a module to compute the sound generated by newly-formed bubbles. The sounds from breaking, third-order Stokes waves of 0.25m wavelength and two slopes are calculated. The results show encouraging agreement with existing laboratory observations and identify the importance of air cylinder breakup in bubble creation.