- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Breakdown of Kolmogorov scaling and modified energy transfer in bubble-laden turbulence

Andrea Montessori*

Marco Lauricella

Aritra Mukherjee

Luca Brandt

  • Department of Civil, Computer Science and Aeronautical Technologies Engineering, Roma Tre University, Rome, Italy

  • Dipartimento di Ingegneria dell'Ambiente, del Territorio e delle Infrastrutture, Politecnico di Torino, Torino, Italy

  • *Contact author: andrea.montessori@uniroma3.it
PDF

Phys. Rev. Fluids 11, 024605 – Published 12 February, 2026

DOI: https://doi.org/10.1103/5qh1-dpcs

Abstract

We investigate the effect of a dispersed bubble phase on forced homogeneous and isotropic turbulence using high-resolution high-performance simulations based on the lattice Boltzmann method. While the classical Kolmogorov energy cascade is largely preserved when considering the system as a whole, a phase-specific analysis reveals striking deviations from the classical turbulence scaling. In particular, the gas phase exhibits significant departures from Kolmogorov's predictions, whereas the continuous liquid phase retains a turbulence structure consistent with classical expectations up to 24% in gas volume fractions. These findings suggest that, despite the presence of a dispersed phase, the global energy transfer remains close to a universal behavior. At the same time, phase-specific interactions are shown to introduce modifications to the turbulent dynamics at small scales. In particular, the gas phase exhibits a nearly flat spectrum at low wave numbers followed by a k−3 scaling at intermediate scales pointing to the presence of patterns of localized bursts uniformly distributed between two finite wavelengths. Our results aim at deepening the understanding of multiphase turbulence, particularly in the context of energy transfer mechanisms and phase interactions in bubble-laden flows. This study provides a framework for future investigations into the fundamental properties of multiphase turbulence and its implications for environmental, atmospheric, and industrial flows.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (47)

  1. F. Veron, Ocean spray, Annu. Rev. Fluid Mech. 47, 507 (2015).
  2. P. Chandran, S. Bakshi, and D. Chatterjee, Study on the characteristics of hydrogen bubble formation and its transport during electrolysis of water, Chem. Eng. Sci. 138, 99 (2015).
  3. A. Angulo, P. van der Linde, H. Gardeniers, M. Modestino, and D. F. Rivas, Influence of bubbles on the energy conversion efficiency of electrochemical reactors, Joule 4, 555 (2020).
  4. E. D. Christensen and R. Deigaard, Large eddy simulation of breaking waves, Coastal Eng. 42, 53 (2001).
  5. A. Iafrati, Numerical study of the effects of the breaking intensity on wave breaking flows, J. Fluid Mech. 622, 371 (2009).
  6. E. K. Bigg and C. Leck, The composition of fragments of bubbles bursting at the ocean surface, J. Geophys. Res.: Atmos. 113, 2007JD009078 (2008).
  7. F. Caupin and E. Herbert, Cavitation in water: A review, C. R. Phys. 7, 1000 (2006).
  8. A. Bureiko, A. Trybala, N. Kovalchuk, and V. Starov, Current applications of foams formed from mixed surfactant–polymer solutions, Adv. Colloid Interface Sci. 222, 670 (2015).
  9. A. Montessori, M. Lauricella, N. Tirelli, and S. Succi, Mesoscale modelling of near-contact interactions for complex flowing interfaces, J. Fluid Mech. 872, 327 (2019).
  10. M. Crialesi-Esposito, M. E. Rosti, S. Chibbaro, and L. Brandt, Modulation of homogeneous and isotropic turbulence in emulsions, J. Fluid Mech. 940, A19 (2022).
  11. Y. Zhou, Interacting scales and energy transfer in isotropic turbulence, Phys. Fluids 5, 2511 (1993).
  12. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000).
  13. J. C. Vassilicos, Dissipation in turbulent flows, Annu. Rev. Fluid Mech. 47, 95 (2015).
  14. S. Allen, D. Allen, K. Moss, G. Le Roux, V. R. Phoenix, and J. E. Sonke, Examination of the ocean as a source for atmospheric microplastics, PLoS One 15, e0232746 (2020).
  15. N. Kantarci, F. Borak, and K. O. Ulgen, Bubble column reactors, Process Biochem. 40, 2263 (2005).
  16. M. S. Plesset and A. Prosperetti, Bubble dynamics and cavitation, Annu. Rev. Fluid Mech. 9, 145 (1977).
  17. V. Mathai, D. Lohse, and C. Sun, Bubbly and buoyant particle–laden turbulent flows, Annu. Rev. Condens. Matter Phys. 11, 529 (2020).
  18. A. Montessori, L. A. Hegele, and M. Lauricella, A thread-safe lattice Boltzmann model for multicomponent turbulent jet simulations, AIAA J. 63, 1005 (2025).
  19. A. Montessori, M. La Rocca, G. Amati, M. Lauricella, A. Tiribocchi, and S. Succi, High-order thread-safe lattice Boltzmann model for high performance computing turbulent flow simulations, Phys. Fluids 36, 035171 (2024).
  20. M. Lauricella, A. Mukherjee, L. Brandt, S. Succi, D. Izbassarov, and A. Montessori, acclb: A high-performance lattice Boltzmann code for multiphase turbulence on multi-gpu architectures, Proc. Comput. Sci. 267, 40 (2025).
  21. S. Succi, The Lattice Boltzmann Equation: For Complex States of Flowing Matter (Oxford University Press, Oxford, 2018).
  22. T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E. M. Viggen, The Lattice Boltzmann Method, Graduate Texts in Physics (Springer International Publishing, Cham, 2017), Vol. 10.
  23. J. Kim, A continuous surface tension force formulation for diffuse-interface models, J. Comput. Phys. 204, 784 (2005).
  24. C.-W. Shu, High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD, Int. J. Comput. Fluid Dyn. 17, 107 (2003).
  25. M. Lauricella, A. Tiribocchi, S. Succi, L. Brandt, A. Mukherjee, M. La Rocca, and A. Montessori, Thread-safe multiphase lattice Boltzmann model for droplet and bubble dynamics at high density and viscosity contrasts, Phys. Fluids 37, 072111 (2025).
  26. A. Montessori, M. Lauricella, A. Tiribocchi, M. Durve, M. La Rocca, G. Amati, F. Bonaccorso, and S. Succi, Thread-safe lattice Boltzmann for high-performance computing on gpus, J. Comput. Sci. 74, 102165 (2023).
  27. Z. Guo, C. Zheng, and B. Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E 65, 046308 (2002).
  28. A. Fakhari, T. Mitchell, C. Leonardi, and D. Bolster, Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios, Phys. Rev. E 96, 053301 (2017).
  29. K. Singh and A. Komrakova, Comparison of forcing schemes to sustain homogeneous isotropic turbulence, Phys. Fluids 36, 015126 (2024).
  30. A. Rivière, W. Mostert, S. Perrard, and L. Deike, Sub-Hinze scale bubble production in turbulent bubble break-up, J. Fluid Mech. 917, A40 (2021).
  31. M. Turisini, M. Cestari, and G. Amati, Leonardo: A pan-european pre-exascale supercomputer for HPC and AI applications, J. Large-Scale Res. Facilities JLSRF 9, 1 (2024).
  32. U. Frisch and A. N. Kolmogorov, Turbulence: The legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  33. S. Zhao, E. Cheng, X. Qiu, I. Burnett, and J. C. chun Liu, Pressure spectra in turbulent flows in the inertial and the dissipation ranges, J. Acoust. Soc. Am. 140, 4178 (2016).
  34. T. Ishihara, T. Gotoh, and Y. Kaneda, Study of high–reynolds number isotropic turbulence by direct numerical simulation, Annu. Rev. Fluid Mech. 41, 165 (2009).
  35. W. McComb, Theory of turbulence, Rep. Prog. Phys. 58, 1117 (1995).
  36. G. B. Deane and M. D. Stokes, Scale dependence of bubble creation mechanisms in breaking waves, Nature (London) 418, 839 (2002).
  37. C. Martínez-Bazán, J. L. Montañes, and J. C. Lasheras, On the breakup of an air bubble injected into a fully developed turbulent flow. Part 2. Size PDF of the resulting daughter bubbles, J. Fluid Mech. 401, 183 (1999).
  38. M. Crialesi-Esposito, G. Boffetta, L. Brandt, S. Chibbaro, and S. Musacchio, Intermittency in turbulent emulsions, J. Fluid Mech. 972, A37 (2023).
  39. V. Pandey, D. Mitra, and P. Perlekar, Turbulence modulation in buoyancy-driven bubbly flows, J. Fluid Mech. 932, A19 (2022).
  40. V. Pandey, R. Ramadugu, and P. Perlekar, Liquid velocity fluctuations and energy spectra in three-dimensional buoyancy-driven bubbly flows, J. Fluid Mech. 884, R6 (2020).
  41. M. S. Dodd and A. Ferrante, On the interaction of Taylor length scale size droplets and isotropic turbulence, J. Fluid Mech. 806, 356 (2016).
  42. M. Crialesi-Esposito, S. Chibbaro, and L. Brandt, The interaction of droplet dynamics and turbulence cascade, Commun. Phys. 6, 5 (2023).
  43. M. Saeedipour and S. Schneiderbauer, Enstrophy transport rates determine the Kolmogorov-Hinze scale in turbulent fragmentation of droplets, Phys. Rev. Fluids 10, 044301 (2025).
  44. S. Elghobashi, Direct numerical simulation of turbulent flows laden with droplets or bubbles, Annu. Rev. Fluid Mech. 51, 217 (2019).
  45. P. Perlekar, Kinetic energy spectra and flux in turbulent phase-separating symmetric binary-fluid mixtures, J. Fluid Mech. 873, 459 (2019).
  46. P. Cifani, J. Kuerten, and B. Geurts, Flow and bubble statistics of turbulent bubble-laden downflow channel, Int. J. Multiphase Flow 126, 103244 (2020).
  47. F. Risso, Theoretical model for k−3 spectra in dispersed multiphase flows, Phys. Fluids 23, 011701 (2011).

Outline

Information

Phys. Rev. Fluids 11, 024605– Published 12 February, 2026
  • Received 1 October 2025
  • Accepted 13 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation