Size-Independent Richardson Constant in Turbulent Bubble Pair Dispersion

Turbulence promotes rapid bubble dispersion, extending bubble residence times in the ocean and playing a central role in air-sea gas exchange. Yet, the dynamics of this dispersion remain poorly understood, particularly when turbulent fluctuations dominate over buoyant forces. As bubbles separate, they enter a superdiffusive regime characterized by the Richardson constant, which quantifies the dispersion rate. This constant is influenced by two competing mechanisms: larger bubbles acquire more kinetic energy due to preferential sampling of energetic flow regions, while at the same time, the direction of their relative velocity becomes increasingly misaligned with their separation vector. This misalignment reduces the efficiency with which the acquired energy drives pair separation. These two effects, absent for passive tracers, largely offset each other, leading to a Richardson constant that is lower in magnitude but independent of bubble size. To capture this behavior, we develop a model that predicts the alignment dynamics and resulting dispersion rate, providing a framework for understanding the transport of buoyant particles in turbulent flows.