Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-28T10:11:02.267Z Has data issue: false hasContentIssue false

Locality of triad interaction and Kolmogorov constant in inertial wave turbulence

Published online by Cambridge University Press:  23 January 2023

Vincent David*
Affiliation:
Laboratoire de Physique des Plasmas, École Polytechnique, 91128 Palaiseau CEDEX, France Université Paris-Saclay, IPP, CNRS, Observatoire Paris-Meudon, France
Sébastien Galtier
Affiliation:
Laboratoire de Physique des Plasmas, École Polytechnique, 91128 Palaiseau CEDEX, France Université Paris-Saclay, IPP, CNRS, Observatoire Paris-Meudon, France Institut Universitaire de France
*
Email address for correspondence: vincent.david@lpp.polytechnique.fr

Abstract

Using the theory of wave turbulence for rapidly rotating incompressible fluids derived by Galtier (Phys. Rev. E, vol. 68, 2003, 015301), we find the locality conditions that the solutions of the kinetic equation must satisfy. We show that the exact anisotropic Kolmogorov–Zakharov spectrum satisfies these conditions, which justifies the existence of this constant (positive) energy flux solution. Although a direct cascade is predicted in the transverse ($\perp$) and parallel ($\parallel$) directions to the rotation axis, we show numerically that in the latter case some triadic interactions can have a negative contribution to the energy flux, while in the former case all interactions contribute to a positive flux. Neglecting the parallel energy flux, we estimate the Kolmogorov constant at $C_K \simeq 0.749$. These results provide theoretical support for recent numerical and experimental studies.

Type
JFM Rapids
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Baroud, C.N., Plapp, B.B., She, Z.S. & Swinney, H.L. 2002 Anomalous self-similarity in a turbulent rapidly rotating fluid. Phys. Rev. Lett. 88 (11), 114501.CrossRefGoogle Scholar
Bellet, F., Godeferd, F.S., Scott, J.F. & Cambon, C. 2006 Wave turbulence in rapidly rotating flows. J. Fluid Mech. 562, 83121.CrossRefGoogle Scholar
Biferale, L., Musacchio, S. & Toschi, F. 2012 Inverse energy cascade in three-dimensional isotropic turbulence. Phys. Rev. Lett. 108 (16), 164501.CrossRefGoogle ScholarPubMed
van Bokhoven, L.J.A., Clercx, H.J.H., van Heijst, G.J.F. & Trieling, R.R. 2009 Experiments on rapidly rotating turbulent flows. Phys. Fluids 21 (9), 096601.CrossRefGoogle Scholar
Buzzicotti, M., Aluie, H., Biferale, L. & Linkmann, M. 2018 Energy transfer in turbulence under rotation. Phys. Rev. Fluids 3 (3), 034802.CrossRefGoogle Scholar
Campagne, A., Gallet, B., Moisy, F. & Cortet, P.-P. 2014 Direct and inverse energy cascades in a forced rotating turbulence experiment. Phys. Fluids 26 (12), 125112.CrossRefGoogle Scholar
David, V. & Galtier, S. 2019 $k_{\perp }^{-8/3}$ spectrum in kinetic Alfvén wave turbulence: implications for the solar wind. Astrophys. J. Lett. 880 (1), L10.CrossRefGoogle Scholar
Galtier, S. 2003 Weak inertial-wave turbulence theory. Phys. Rev. E 68, 015301.CrossRefGoogle ScholarPubMed
Galtier, S. 2023 Physics of Wave Turbulence. Cambridge University Press.Google Scholar
Galtier, S. & David, V. 2020 Inertial/kinetic-Alfvén wave turbulence: a twin problem in the limit of local interactions. Phys. Rev. Fluids 5 (4), 044603.CrossRefGoogle Scholar
Godeferd, F.S. & Moisy, F. 2015 Structure and dynamics of rotating turbulence: a review of recent experimental and numerical results. Appl. Mech. Rev. 67 (3), 030802.CrossRefGoogle Scholar
van Kan, A. & Alexakis, A. 2020 Critical transition in fast-rotating turbulence within highly elongated domains. J. Fluid Mech. 899, A33.CrossRefGoogle Scholar
Lamriben, C., Cortet, P.-P. & Moisy, F. 2011 Direct measurements of anisotropic energy transfers in a rotating turbulence experiment. Phys. Rev. Lett. 107 (2), 024503.CrossRefGoogle Scholar
Le Reun, T., Favier, B., Barker, A.J. & Le Bars, M. 2017 Inertial wave turbulence driven by elliptical instability. Phys. Rev. Lett. 119 (3), 034502.CrossRefGoogle ScholarPubMed
Le Reun, T., Favier, B. & Le Bars, M. 2020 Evidence of the Zakharov–Kolmogorov spectrum in numerical simulations of inertial wave turbulence. Europhys. Lett. 132 (6), 64002.CrossRefGoogle Scholar
Monsalve, E., Brunet, M., Gallet, B. & Cortet, P.-P. 2020 Quantitative experimental observation of weak inertial-wave turbulence. Phys. Rev. Lett. 125, 254502.CrossRefGoogle ScholarPubMed
Morize, C., Moisy, F. & Rabaud, M. 2005 Decaying grid-generated turbulence in a rotating tank. Phys. Fluids 17 (9), 095105.CrossRefGoogle Scholar
Nazarenko, S. 2011 Wave Turbulence, Lecture Notes in Physics, vol. 825. Springer.CrossRefGoogle Scholar
Pouquet, A. & Mininni, P.D. 2010 The interplay between helicity and rotation in turbulence: implications for scaling laws and small-scale dynamics. Phil. Trans. R. Soc. A 368 (1916), 16351662.CrossRefGoogle ScholarPubMed
Pouquet, A., Sen, A., Rosenberg, D., Mininni, P.D. & Baerenzung, J. 2013 Inverse cascades in turbulence and the case of rotating flows. Phys. Scr. T155, 014032.CrossRefGoogle Scholar
Seshasayanan, K. & Alexakis, A. 2018 Condensates in rotating turbulent flows. J. Fluid Mech. 841, 434462.CrossRefGoogle Scholar
Sharma, M.K., Verma, M.K. & Chakraborty, S. 2019 Anisotropic energy transfers in rapidly rotating turbulence. Phys. Fluids 31 (8), 085117.CrossRefGoogle Scholar
Smith, L.M. & Waleffe, F. 1999 Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids 11 (6), 16081622.CrossRefGoogle Scholar
Yarom, E., Salhov, A. & Sharon, E. 2017 Experimental quantification of nonlinear time scales in inertial wave rotating turbulence. Phys. Rev. Fluids 2 (12), 122601.CrossRefGoogle Scholar
Yarom, E. & Sharon, E. 2014 Experimental observation of steady inertial wave turbulence in deep rotating flows. Nat. Phys. 10 (7), 510514.CrossRefGoogle Scholar
Yokoyama, N. & Takaoka, M. 2021 Energy-flux vector in anisotropic turbulence: application to rotating turbulence. J. Fluid Mech. 908, A17.CrossRefGoogle Scholar
Zakharov, V.E., L'Vov, V.S. & Falkovich, G. 1992 Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer.CrossRefGoogle Scholar