The derivation of eeective equations for pressure wave propagation in a bubbly uid at very low void fractions is examined. A Vlasov-type equation is derived for the probability distribution of the bubbles in phase space instead of computing eeective equations in terms of averaged quantities. This provides a more general description of the bubble mixture and contains previously derived eeective ...

We present a direct numerical simulation (DNS) study of buoyancy-driven bubbly flows in the presence large-scale driving that generates turbulence. On increasing turbulence intensity: ( ) bubble trajectories become more curved and b average rise velocity bubbles decreases. find energy spectrum flow shows pseudo-turbulence scaling for length scales smaller than diameter Kolmogorov larger diamete...

We analyze the statistical properties of bubble models for the large-scale distribution of galaxies. To this aim, we realize static simulations, in which galaxies are mostly randomly arranged in the regions surrounding bubbles. As a first test, we realize simulations of the Lick map, by suitably projecting the three-dimensional simulations. In this way, we are able to safely compare the angular...