AUTHOR=Ramadugu Rashmi , Pandey Vikash , Perlekar Prasad 

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

JOURNAL=Frontiers in Physics

VOLUME=Volume 11 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1112304

DOI=10.3389/fphy.2023.1112304

ISSN=2296-424X

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 $kk_d$, 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.  \MOD{For $kk_d$, 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.