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Universal scaling regimes in rotating fluid turbulence

Abhik Basu1,* and Jayanta K. Bhattacharjee2,†

  • 1Theory Division, Saha Institute of Nuclear Physics, Calcutta 700064, West Bengal, India
  • 2Department of Theoretical Physics, Indian Association for the Cultivation of Science, 2A and 2B Raja S C Mullick Road, Calcutta 700032, West Bengal, India

  • *abhik.basu@saha.ac.in; abhik.123@gmail.com
  • †jayanta.bhattacharjee@gmail.com
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Phys. Rev. Fluids 8, 064611 – Published 22 June, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.064611

Abstract

We analyze the scaling properties of the energy spectra in fully developed incompressible turbulence in forced, rotating fluids in three dimensions (3D), which are believed to be characterized by universal scaling exponents in the inertial range. To elucidate the scaling regimes, we set up a scaling analysis of the 3D Navier–Stokes equation for a rotating fluid that is driven by large-scale external forces. We use scaling arguments to extract the scaling exponents, which characterize the different scaling regimes of the energy spectra. We speculate on the intriguing possibility of two-dimensionalization of 3D rotating turbulence within our scaling theory. Our results can be tested in large-scale simulations and relevant laboratory-based experiments.

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References (44)

  1. P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49, 435 (1977).
  2. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Butterworth and Heinemann, Oxford, 1998).
  3. U. Frisch, Turbulence: The legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  4. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR 30, 301 (1941).
  5. G. E. Elsinga and I. Marusic, The anisotropic structure of turbulence and its energy spectrum, Phys. Fluids 28, 011701 (2016).
  6. P. C. Valente, C. B. da Silva, and F. T. Pinho, Energy spectra in elasto-inertial turbulence, Phys. Fluids 28, 075108 (2016).
  7. P. Buchhave and C. M. Velte, Measurement of turbulent spatial structure and kinetic energy spectrum by exact temporal-to-spatial mapping, Phys. Fluids 29, 085109 (2017).
  8. R. H. Kraichnan, Inertial ranges in two-dimensional turbulence, Phys. Fluids 10, 1417 (1967).
  9. J. Paret and P. Tabeling, Experimental Observation of the Two-Dimensional Inverse Energy Cascade, Phys. Rev. Lett. 79, 4162 (1997).
  10. S. Chen, R. E. Ecke, G. L. Eyink, M. Rivera, M. Wan, and Z. Xiao, Physical Mechanism of the Two-Dimensional Inverse Energy Cascade, Phys. Rev. Lett. 96, 084502 (2006).
  11. A. Vallgren and E. Lindborg, The enstrophy cascade in forced two- dimensional turbulence, J. Fluid Mech. 671, 168 (2011).
  12. G. Boffetta and R. E. Ecke, Two-dimensional turbulence, Annu. Rev. Fluid Mech. 44, 427 (2012).
  13. J. Bardina, J. H. Ferziger, and R. S. Rogallo, Effect of rotation on isotropic turbulence: Computation and modelling, J. Fluid Mech. 154, 321 (1985).
  14. Y. Zhou, A phenomenological treatment of rotating turbulence, Phys. Fluids 7, 2092 (1995).
  15. V. M. Canuto and M. S. Dubovikov, Physical Regimes and Dimensional Structure of Rotating Turbulence, Phys. Rev. Lett. 78, 666 (1997).
  16. V. M. Canuto and M. S. Dubovikov, A dynamical model for turbulence. V. The effect of rotation, Phys. Fluids 9, 2132 (1997).
  17. L. M. Smith and F. Waleffe, Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence, Phys. Fluids 11, 1608 (1999).
  18. C. N. Baroud, B. B. Plapp, Z.-S. She, and H. L. Swinney, Anomalous Self-Similarity in a Turbulent Rapidly Rotating Fluid, Phys. Rev. Lett. 88, 114501 (2002).
  19. S. Galtier, Weak inertial-wave turbulence theory, Phys. Rev. E 68, 015301(R) (2003).
  20. W.-C. Müller and M. Thiele, Scaling and energy transfer in rotating turbulence, Europhys. Lett. 77, 34003 (2007).
  21. S. Chakraborty and J. K. Bhattacharjee, Third-order structure function for rotating three-dimensional homogeneous turbulent flow, Phys. Rev. E 76, 036304 (2007).
  22. S. Chakraborty, Signatures of two-dimensionalisation of 3D turbulence in the presence of rotation, Europhys. Lett. 79, 14002 (2007).
  23. D. Mininni, A. Alexakis, and A. Pouquet, Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers, Phys. Fluids 21, 015108 (2009).
  24. S. Chakraborty, M. H. Jensen, and A. Sarkar, On two-dimensionalization of three-dimensional turbulence in shell models, Eur. Phys. J. B 73, 447 (2010).
  25. M. K. Sharma, M. K. Verma, and S. Chakraborty, On the energy spectrum of rapidly rotating forced turbulence, Phys. Fluids 30, 115102 (2018).
  26. M. K. Sharma, M. K. Verma, and S. Chakraborty, Anisotropic energy transfers in rapidly rotating turbulence, Phys. Fluids 31, 085117 (2019).
  27. S. K. Rathor, S. Chakraborty, and S. S. Ray, Dynamic scaling in rotating turbulence: A shell model study, Phys. Rev. E 105, L063102 (2022).
  28. C. Cambon and L. Jacquin, Spectral approach to non-isotropic turbulence subjected to rotation, J. Fluid Mech. 202, 295 (1989).
  29. A. Basu and J. K. Bhattacharjee, Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties, Phys. Rev. E 85, 026311 (2012).
  30. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley Eastern, New Delhi, 1975).
  31. A. Raichaudhuri, The Physics of Fluids and Plasmas (Cambridge University Press, Cambridge, 1998).
  32. A. Basu and J. K. Bhattacharjee, Varieties of scaling regimes in hydromagnetic turbulence, Phys. Rev. E 98, 062143 (2018).
  33. O. Zeman, A note on the spectra and decay of rotating homogeneous turbulence, Phys. Fluids 6, 3221 (1994).
  34. See, e.g., J. R. Herring and O. Métais, Numerical experiments in forced stably stratified turbulence, J. Fluid Mech. 202, 97 (1989); M. L. Waite and P. Bartello, Stratified turbulence dominated by vortical motion, ibid. 517, 281 (1999); O. Praud, A. M. Fincham, and J. Sommeria, Decaying grid turbulence in a strongly stratified fluid, ibid. 522, 1 (2005); S. Basak and S. Sarkar, Dynamics of a stratified shear layer with horizontal shear, ibid. 568, 19 (2006); J. J. Riley and E. Lindborg, Stratified turbulence: A possible interpretation of some geophysical turbulence, J. Atmos. Sci. 65, 2416 (2008); J. J. Riley and S. M. de Bruyn Kops, Dynamics of turbulence strongly influenced by buoyancy, Phys. Fluids 15, 2047 (2003); S. Almalkie and S. M. de Bruyn Kops, Kinetic energy dynamics in forced, homogeneous, and axisymmetric stably stratified turbulence, J. Turbul. 13, 1 (2012).
  35. A. Basu and J. K. Bhattacharjee, Kolmogorov or Bolgiano-Obukhov scaling: Universal energy spectra in stably stratified turbulent fluids, Phys. Rev. E 100, 033117 (2019).
  36. A. Delache, C. Cambon, and F. Godeferd, Scale by scale anisotropy in freely decaying rotating turbulence, Phys. Fluids 26, 025104 (2014).
  37. J. A. Brons, P. J. Thomas, and A. Pothérat, Mean flow anisotropy without waves in rotating turbulence, J. Fluid Mech. 889, A37 (2020).
  38. P. Sagaut and C. Cambon, Homogeneous Turbulence Dynamics, Monograph (Springer, New York, 2018), Chaps. 2 and 7.
  39. C. Cambon, N. N. Mansour, and F. S. Godefard, Energy transfer in rotating turbulence, J. Fluid Mech. 337, 303 (1997).
  40. F. Bellet, F. S. Godeferd, J. F. Scott, and C. Cambon, Wave turbulence in rapidly rotating flows, J. Fluid Mech. 562, 83 (2006).
  41. D. Das, A. Basu, M. Barma, and S. Ramaswamy, Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves, Phys. Rev. E 64, 021402 (2001).
  42. R. H. Kraichnan, Helical turbulence and absolute equilibrium, J. Fluid Mech. 59, 745 (1973).
  43. S. K. Rathor, M. K. Sharma, S. S. Ray, and S. Chakraborty, Bridging inertial and dissipation range statistics in rotating turbulence, Phys. Fluids 32, 095104 (2020).
  44. P.-F. Yang, A. Pumir, and H. Xu, Generalized self-similar spectrum and the effect of large-scale in decaying homogeneous isotropic turbulence, New J. Phys. 20, 103035 (2018).

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Phys. Rev. Fluids 8, 064611– Published 22 June, 2023
  • Received 1 December 2022
  • Accepted 19 May 2023
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