A robust and accurate technique for Lagrangian tracking of bubbles and detecting fragmentation and coalescence

Abstract A technique for Lagrangian tracking of bubbles and detecting their time-evolution behaviors is presented. 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 mappings are determined by selecting the minimum from a set of pseudo-distance errors, which are themselves based on constraints imposed on bubble position, velocity, and volume between adjacent time instants. The technique is validated through numerical inspection of the pseudo-distance errors and visual verification of over 16000 bubble events identified in a simulated breaking wave. The accuracies for continuity, binary fragmentation, and binary coalescence are estimated to be 99.5 % , 90 % , and 95 % , respectively, when the analysis is limited to bubbles of sizes of at least two grid lengths. The effects of varying pseudo-distance error parameters and time resolution are also investigated. The technique robustly tracks bubbles and the occurrence of binary fragmentation and binary coalescence in a breaking wave when these processes occur away from the complex air–water interface structures and bubbles are of comparable scale. Detecting the fragmentation and coalescence of large-scale and complex air–water interfaces remains an outstanding problem.