Spectral turbulence kinetic energy budget and scale-based velocity decomposition for turbulence in bubble plumes

We conducted a spectral analysis of the turbulence kinetic energy (TKE) budget in a bubble plume using particle image velocimetry with fluorescent particles. Our findings confirmed the hypothesis of an inverse energy cascade in the bubble plume, where TKE is transferred from small to large eddies. This is attributed to direct injection of TKE by bubble passages across a wide range of scales, in contrast to canonical shear production of TKE in large scales. Turbulence dissipation was identified as the primary sink of the bubble-produced TKE and occurred at all scales. The decomposition of velocities using the critical length scale of inter-scale energy transfer allowed us to distinguish between large- and small-scale motions in the bubble plume. The large-scale turbulent fluctuations exhibited a skewed distribution and were likely associated with the return flow after bubble passage and the velocities induced by the bubble wake. The small-scale turbulent fluctuations followed a Gaussian distribution relatively well. The large-scale motions contributed to over half of the Reynolds stresses, while there were significant small-scale contributions to the normal stresses near the plume center but not to the shear stress. The large-scale motions in the vorticity field induced a street of vertically elongated vortex pairs, while the small-scale vortices exhibited similar sizes in both horizontal and vertical directions.

Automated summary

We analyzed the turbulence kinetic energy (TKE) budget in a bubble plume using particle image velocimetry with fluorescent particles. Our findings confirmed the presence of an inverse energy cascade in the bubble plume, with TKE being transferred from small to large eddies. This is due to direct injection of TKE by bubble passages across different scales, rather than shear production in large scales. Turbulence dissipation was identified as the primary sink for the TKE produced by the bubbles. By decomposing velocities based on the critical length scale of energy transfer, we were able to distinguish between large- and small-scale motions in the bubble plume. The large-scale motions exhibited a skewed distribution and were likely associated with the return flow after bubble passage and the velocities induced by the bubble wake. The small-scale motions followed a Gaussian distribution relatively well.