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=11

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=<p>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 <italic>E</italic>(<italic>k</italic>) ∼ <italic>k</italic> for <italic>k</italic> &lt; <italic>k</italic><sub><italic>d</italic></sub>, <italic>E</italic>(<italic>k</italic>) ∼ <italic>k</italic><sup>−5</sup> for <italic>k</italic> &gt; <italic>k</italic><sub><italic>d</italic></sub>, and an intermediate scaling range with <italic>E</italic>(<italic>k</italic>) ∼ <italic>k</italic><sup>−3</sup> around <italic>k</italic> ∼ <italic>k</italic><sub><italic>d</italic></sub>. We perform an energy budget analysis to understand the dominant balances and explain the observed scaling behavior. For <italic>k</italic> &lt; <italic>k</italic><sub><italic>d</italic></sub>, energy injection balances dissipation due to drag, whereas for <italic>k</italic> &gt; <italic>k</italic><sub><italic>d</italic></sub>, 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.</p>