Spatial-temporal correlation and fluctuating propagation characteristics of bubbles based on a coupled model of oscillation and migration

Bubble oscillation and migration are complex dynamic processes that have been extensively studied for the applications of ocean engineering. However, the intricate coupling and interactions among various parameters that affect bubble oscillation and migration remain unclear. In particular, the correlation between bubble dynamics and abrupt alterations in the flow field is not defined. Here, based on a developed bubble dynamics model, a spatial-temporal correlation method was applied to bubble calculations to build quantitative correlations among the bubble deformation, motion and characteristic pressures for the first time. Subsequently, the sharp changes in the flow field caused by bubble oscillation and migration behaviours were further explored to reveal the fluctuating propagation mechanism and instability in the flow field. The results indicated that increasing water depth and initial static pressure, along with decreasing bubble equilibrium radius and initial oscillation velocity, led to a higher bubble oscillation frequency. However, these factors reduced the duration of each migration process, resulting in a smaller total migration. Surface tension stands out as the preeminent factor exerting influence on both the migration displacement and the velocity. In contrast, the bubble wall serves as the principal determinant for the migration acceleration. Furthermore, the propagation of bubble dynamics is influenced by the combined effects of bubble growth, collapse, and migration. Pressure propagation correlates most strongly with bubble radius, followed by migration velocity and acceleration, while other parameters exhibit weaker correlations with pressure. This study emphasizes the bubble interaction mechanism and propagation characteristics.