Spectral Properties of Bubbly Turbulent Flows

Suspension of deformable bubbles are ubiquitous in nature, their presence can dramatically alter the rheological properties of flows. We present a DNS study to investigate the spectral properties of the buoyancy-driven bubbly flows in the presence of large scale driving that generates turbulence. The non-dimensional Galilei ($50<{\rm Ga}<300$) and Reynolds ($50<{\rm Re}<150$) numbers characterize the flow. Consistent with the experiments, we show that the energy spectrum shows a pseudo-turbulence scaling ($E(k) \sim k^{-3}$) for length scales smaller than the bubble diameter and a Kolmogorov scaling ($E(k) \sim k^{-5/3}$) for scales larger than the bubble diameter. We present a scale-by-scale energy budget analysis to unravel the dominant balances in different regimes.