Velocity fluctuations for bubbly flows at small <i>Re</i>

We experimentally investigate the effect of Reynolds number ( $Re$ ) on the turbulence induced by the motion of bubbles in a quiescent Newtonian fluid at small $Re$ . The energy spectra, $E(k)$ , are determined from the decaying turbulence behind the bubble swarm obtained using particle image velocimetry. We show that when $Re \sim O(100)$ , the slope of the normalized energy spectra is no longer independent of the gas volume fraction and the $k^{-3}$ subrange is significantly narrower, where $k$ is the wavenumber. This is further corroborated using second-order longitudinal velocity structure function and spatial correlation of the velocity behind the bubble swarm. On further decreasing the bubble Reynolds number ( $O(1) &lt; Re &lt; O(10)$ ), the signature $k^{-3}$ of the energy spectra for the bubble-induced turbulence is replaced by $k^{-5/3}$ scaling. Thus, we provide experimental evidence to the claim by Mazzitelli et al. ( Phys. Fluids , vol. 15, 2003, pp. L5–L8) that at low Reynolds numbers the normalized energy spectra of the bubble-induced turbulence will no longer show the $k^{-3}$ scaling because of the absence of bubble wake and that the energy spectra will depend on the number of bubbles, thus being non-universal.