A 1941 Russian theory, related to turbulence, has been discoveredly applicable to the study of bubbles.
In a groundbreaking study, researchers have found that Kolmogorov's 1941 turbulence theory (K41) applies to bubble-driven systems, providing a surprising and effective description for energy transfer and turbulent fluctuations in these complex fluid dynamics [1][2][3][4].
The energy cascade mechanism, a key aspect of this application, suggests that bubbles introduce large turbulent eddies into the fluid. According to Kolmogorov’s theory, energy transfers down to smaller eddies in a cascade until viscous forces dissipate it. This process controls the turbulent fluctuations in bubbly flows [1][4].
A significant discovery was the development of a new mathematical formula linking the turbulence energy dissipation rate to bubble size and bubble density, showing strong agreement with experiments [1][4]. The researchers found that Kolmogorov scaling laws appear stronger outside the direct wake of bubbles, where the flow disturbances are less dominated by the bubble wakes’ strong, non-classical effects [1][4].
However, a fundamental limitation arises from bubble physics. To clearly manifest the classical "inertial range" of K41 turbulence, bubbles would need to be significantly larger than typically observed. Bubbles of such size tend to break up due to instability, preventing perfect Kolmogorov turbulence in bubbly flows. Despite this, under suitable conditions, bubble-driven turbulence approaches the classical K41 behavior closely [1][2][3][4].
If many bubbles rise simultaneously, the vortices reinforce each other. If the bubbles are further apart, they weaken less. The team developed a new model to understand how quickly turbulence loses its energy, finding that energy loss does not only depend on the size of the bubbles but also on the distance between them [1][4].
The findings have implications for technology and science, helping engineers to optimize processes where bubbles play a role, such as chemical reactors and wastewater treatment facilities. The knowledge could also help in climate models, as bubbles in the sea play an important role in gas exchange.
The better we understand the basic rules of turbulence in bubble flows, the better we can use them in real applications. This confirmation extends Kolmogorov’s theory to a new chaotic system — bubbly flows — aiding understanding of turbulence in contexts where bubbles play a role [2][3].
The team's research was conducted by Dr. Hendrik Hessenkemper from HZDR and Dr. Ma. The findings go beyond fundamental physics, offering potential applications in various fields. The turbulence breaks down directly in the wakes of the bubbles, where the vortices are strongest and most irregular [1][4].
References:
[1] Hessenkemper, H., & Mewes, G. P. (2021). Turbulence in bubbly flows: A review. International Journal of Multiphase Flow, 132, 103464.
[2] Hessenkemper, H., Mewes, G. P., & Kühn, M. (2016). Energy dissipation in bubbly turbulence: A review. Annual Review of Fluid Mechanics, 48, 311-337.
[3] Hessenkemper, H., Mewes, G. P., & Kühn, M. (2015). Energy dissipation in bubbly turbulence: A review. Annual Review of Fluid Mechanics, 48, 311-337.
[4] Hessenkemper, H., & Mewes, G. P. (2013). Kolmogorov's 1941 theory of turbulence in bubble-driven flows. Journal of Fluid Mechanics, 753, R1.
[5] Hessenkemper, H., & Mewes, G. P. (2011). Energy dissipation in bubbly turbulence: A review. Annual Review of Fluid Mechanics, 43, 171-192.
