Bubble-Mass Cascade in Decaying Turbulent Flows

We investigate a novel regime in turbulent bubbly flows dominated by coalescence, which controls bubble evolution. When turbulence intensity is high, but bubbles are sub-Hinze, breakup is suppressed and an inverse bubble-mass cascade emerges: bubble mass is transferred from small to large bubbles via turbulence-enhanced coalescence. Experiments in high-speed duct flows and DNS of homogeneous isotropic turbulence ($Re_\lambda \geq 550$) reveal robust scaling: the maximum bubble size grows as $D_{\max}(t) \sim (\epsilon^{1/3} t)^{3/2}$, and the size distribution evolves toward $f(d) \sim d^{-3/2}$. Building on new theory, we derive scale-by-scale coalescence fluxes and locality functions, including analytic expressions for both deterministic and Gaussian outcome kernels. In this regime, the coalescence rate scales as $\Gamma(d) \sim d^{7/3}$, with upward flux $W_c(D)$ uniform for $d