Energy spectra of buoyancy-driven bubbly flow in a vertical Hele-Shaw cell

Abstract

We present direct numerical simulations (DNS) study of confined buoyancy-driven bubbly flows in a Hele-Shaw setup. We investigate the spectral properties of the flow and make comparisons with experiments. The energy spectrum obtained from the gap-averaged velocity field shows E(k) ∼ k for k < kd, E(k) ∼ k−5 for k > kd, and an intermediate scaling range with E(k) ∼ k−3 around k ∼ kd. We perform an energy budget analysis to understand the dominant balances and explain the observed scaling behavior. For k < kd, energy injection balances dissipation due to drag, whereas for k > kd, the net injection balances net dissipation. We also show that the Navier-Stokes equation with a linear drag can be used to approximate large scale flow properties of bubbly Hele-Shaw flow.