The emergence of bubble-induced scaling in thermal spectra in turbulence

We report on the modification of the spectrum of a passive scalar inside a turbulent flow by the injection of large bubbles. While the spectral modification through bubbles is well known and well analyzed for the velocity fluctuations, little is known on how bubbles change the fluctuations of a passive scalar. Here we uncover the thermal spectral scaling behavior of a turbulent multiphase thermal mixing layer. We trigger the development of a $-3$ spectral scaling by injecting large bubbles ($\text{Re}_{\text{bub}} = \mathcal{O}(10^2)$) with gas volume fractions up to 5\%. For these bubbly flows, the $-5/3$ scaling is still observed at intermediate frequencies but it is followed by a steeper slope for larger frequencies. This $-3$ scaling range extends with increasing gas volume fraction. The $-3$ scaling experiment coincides with the typical energy spectral scaling for the velocity fluctuations in high Reynolds number bubbly flow. We identify the frequency scale of the transition from the $-5/3$ scaling to the $-3$ scaling and show how it depends on the gas volume fraction.