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

Rashmi Ramadugu; Vikash Pandey; Prasad Perlekar

paper

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

arXiv:2212.04989

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 $E (k) \sim k$ for $k < k_{d}$ , $E (k) \sim k^{- 5}$ for $k > k_{d}$ , and an intermediate scaling range with $E (k) \sim k^{- 3}$ around $k \sim k_{d}$ . We perform an energy budget analysis to understand the dominant balances and explain the observed scaling behavior. 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.