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Nonequilibrium fluctuations of the direct cascade in surface quasi-geostrophic turbulence

V. J. Valadão1,2,*, T. Ceccotti1, G. Boffetta1,2, and S. Musacchio1,2

  • *Contact author: victor.dejesusvaladao@unito.it
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Phys. Rev. Fluids 9, 094601 – Published 3 September, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.094601

Abstract

We study the temporal fluctuations of the flux of surface potential energy in surface quasi-geostrophic (SQG) turbulence. By means of high-resolution, direct numerical simulations of the SQG model in the regime of forced and dissipated cascade of temperature variance, we show that the instantaneous imbalance in the energy budget originates a subleading correction to the spectrum of the turbulent cascade. Using a multiple-scale approach combined with a dimensional closure we derive a theoretical prediction for the power-law behavior of the corrections, which holds for a class of turbulent transport equations known as α turbulence. Further, we apply a method to disentangle the equilibrium and nonequilibrium contribution in the instantaneous spectra, which can be generalized to other turbulent systems.

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References (30)

  1. W. Blumen, Uniform potential vorticity flow: Part I. Theory of wave interactions and two-dimensional turbulence, J. Atmos. Sci. 35, 774 (1978).
  2. R. Salmon, Lectures on Geophysical Fluid Dynamics (Oxford University Press, New York, 1998).
  3. M. Juckes, Quasigeostrophic dynamics of the tropopause, J. Atmos. Sci. 51, 2756 (1994).
  4. G. Lapeyre and P. Klein, Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory, J. Phys. Ocean. 36, 165 (2006).
  5. L. Siegelman, P. Klein, A. P. Ingersoll, S. P. Ewald, W. R. Young, A. Bracco, A. Mura, A. Adriani, D. Grassi, C. Plainaki et al., Moist convection drives an upscale energy transfer at Jovian high latitudes, Nat. Phys. 18, 357 (2022).
  6. R. T. Pierrehumbert, I. M. Held, and K. L. Swanson, Spectra of local and nonlocal two-dimensional turbulence, Chaos Solit. Fract. 4, 1111 (1994).
  7. I. M. Held, R. T. Pierrehumbert, S. T. Garner, and K. L. Swanson, Surface quasi-geostrophic dynamics, J. Fluid Mech. 282, 1 (1995).
  8. A. Celani, M. Cencini, A. Mazzino, and M. Vergassola, Active and passive fields face to face, New J. Phys. 6, 72 (2004).
  9. G. Lapeyre, Surface quasi-geostrophy, Fluids 2, 7 (2017).
  10. A. Foussard, S. Berti, X. Perrot, and G. Lapeyre, Relative dispersion in generalized two-dimensional turbulence, J. Fluid Mech. 821, 358 (2017).
  11. P. Constantin, A. J. Majda, and E. Tabak, Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar, Nonlinearity 7, 1495 (1994).
  12. P. Constantin and J. Wu, Behavior of solutions of 2D quasi-geostrophic equations, SIAM J. Math. Anal. 30, 937 (1999).
  13. N. Valade, S. Thalabard, and J. Bec, Anomalous dissipation and spontaneous stochasticity in deterministic surface quasi-geostrophic flow, in Annales Henri Poincaré, Vol. 25 (Springer, 2024), pp. 1261–1283.
  14. A. Yoshizawa, Nonequilibrium effect of the turbulent-energy-production process on the inertial-range energy spectrum, Phys. Rev. E 49, 4065 (1994).
  15. S. L. Woodruff and R. Rubinstein, Multiple-scale perturbation analysis of slowly evolving turbulence, J. Fluid Mech. 565, 95 (2006).
  16. K. Horiuti and T. Ozawa, Multimode stretched spiral vortex and nonequilibrium energy spectrum in homogeneous shear flow turbulence, Phys. Fluids 23, 035107 (2011).
  17. K. Horiuti and T. Tamaki, Nonequilibrium energy spectrum in the subgrid-scale one-equation model in large-eddy simulation, Phys. Fluids 25, 125104 (2013).
  18. L. Fang and W. J. Bos, An EDQNM study of the dissipation rate in isotropic non-equilibrium turbulence, J. Turbul. 24, 217 (2023).
  19. S. Berti, G. Boffetta, and S. Musacchio, Mean flow and fluctuations in the three-dimensional turbulent cellular flow, Phys. Rev. Fluids 8, 054601 (2023).
  20. R. Araki and W. J. Bos, Inertial range scaling of inhomogeneous turbulence, J. Fluid Mech. 978, A9 (2024).
  21. W. J. Bos, Unsteady and inhomogeneous turbulent fluctuations around isotropic equilibrium, Atmosphere 15, 547 (2024).
  22. T. Watanabe and T. Iwayama, Unified scaling theory for local and non-local transfers in generalized two-dimensional turbulence, J. Phys. Soc. Jpn. 73, 3319 (2004).
  23. U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  24. W. J. T. Bos and R. Rubinstein, Dissipation in unsteady turbulence, Phys. Rev. Fluids 2, 022601(R) (2017).
  25. G. K. Batchelor, The theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1953).
  26. L. S. Kovasznay, Spectrum of locally isotropic turbulence, J. Aeron. Sci. 15, 745 (1948).
  27. J. P. Boyd, Chebyshev and Fourier Spectral Methods (Courier Corporation, New York, 2001).
  28. V. J. Valadão, G. Boffetta, M. Crialesi-Esposito, F. De Lillo, and S. Musacchio, Spectrum correction on Ekman-Navier-Stokes equation in two-dimensions, arXiv:2408.15735.
  29. E. Lindborg, Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech. 388, 259 (1999).
  30. D. Bernard, Three-point velocity correlation functions in two-dimensional forced turbulence, Phys. Rev. E 60, 6184 (1999).

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Phys. Rev. Fluids 9, 094601– Published 3 September, 2024
  • Received 11 June 2024
  • Accepted 21 August 2024
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