Pseudo-turbulence in two-dimensional buoyancy-driven bubbly flows: A DNS study.

We present a direct numerical simulation (DNS) study of buoyancy-driven bubbly flows in two dimensions. We employ the volume of fluid (VOF) method to track the bubble interface. To investigate the spectral properties of the flow, we derive the scale-by-scale energy budget equation. We show that the Galilei number (Ga) controls different scaling regimes in the energy spectrum. For high Galilei numbers, we find the presence of an inverse energy cascade. Our study indicates that the density ratio of the bubble with the ambient fluid or the presence of coalescence between the bubbles does not alter the scaling behaviour.