Pseudo-turbulence and Kolmogorov scaling in buoyancy-briven bubbly flows

Bubble laden flow are found in many natural and industrial processes. When a suspension of bubbles at moderate volume fractions rises in an otherwise quiescent fluid, the wake of individual bubbles interacts to generates complex spatiotemporal flow patterns also known as pseudo-turbulence or bubble-induced agitation. Such a flow have been characterized by the power spectrum of its velocity fluctuations, which shows a power law scaling with an exponent -3 for scales smaller than the bubble diameter. We investigate the spectral properties of buoyancy-driven bubbly flows for a range of Galilei (ratio of the buoyancy to viscous forces) and Atwood numbers. Our findings reveal that at sufficiently high Galilei numbers and across various Atwood numbers, the velocity power spectrum conforms to Kolmogorov scaling, exhibiting a power-law exponent of -5/3 over scales spanning from the bubble diameter to the dissipation scale. However, for scales smaller than the dissipation range, the physics of pseudo-turbulence is recovered. We use scale-by-scale budget analysis to identify the dominant balances at each scale.