Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T21:03:32.202Z Has data issue: false hasContentIssue false

Thermal fluctuations in the dissipation range of homogeneous isotropic turbulence

Published online by Cambridge University Press:  24 March 2022

John B. Bell*
Affiliation:
Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Andrew Nonaka
Affiliation:
Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Alejandro L. Garcia
Affiliation:
Department of Physics & Astronomy, San Jose State University, San Jose, CA 95192, USA
Gregory Eyink
Affiliation:
Department of Applied Mathematics & Statistics, Johns Hopkins University, Baltimore, MD 21218, USA
*
Email address for correspondence: [email protected]

Abstract

Using fluctuating hydrodynamics we investigate the effect of thermal fluctuations in the dissipation range of homogeneous isotropic turbulence. Simulations confirm theoretical predictions that the energy spectrum is dominated by these fluctuations at length scales comparable to the Kolmogorov length. We also find that the extreme intermittency in the far-dissipation range predicted by Kraichnan is replaced by Gaussian thermal equipartition.

Type
JFM Papers
Copyright
© The Author(s), 2022. 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

Bandak, D., Eyink, G.L., Mailybaev, A. & Goldenfeld, N. 2021 Thermal noise competes with turbulent fluctuations below millimeter scales. arXiv:2107.03184.Google Scholar
Batchelor, G.K. 1953 The Theory of Homogeneous Turbulence, Cambridge Science Classics. Cambridge University Press.Google Scholar
Betchov, R. 1957 On the fine structure of turbulent flows. J. Fluid Mech. 3 (2), 205216.Google Scholar
Betchov, R. 1961 Thermal agitation and turbulence. In Rarefied Gas Dynamics (ed. L. Talbot), Proceedings of the Second International Symposium on Rarefied Gas Dynamics, University of California, Berkeley, CA, 1960, pp. 307–321. Academic Press.Google Scholar
Boon, J.P. & Yip, S. 1991 Molecular Hydrodynamics. Courier Corporation.Google Scholar
Buaria, D. & Sreenivasan, K.R. 2020 Dissipation range of the energy spectrum in high Reynolds number turbulence. Phys. Rev. Fluids 5 (9), 092601.Google Scholar
Chen, S., Doolen, G., Herring, J.R., Kraichnan, R.H., Orszag, S.A. & She, Z.S. 1993 Far-dissipation range of turbulence. Phys. Rev. Lett. 70 (20), 30513054.Google ScholarPubMed
Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J. & Knuth, D.E. 1996 On the Lambert $W$ function. Adv. Comput. Maths 5 (1), 329359.Google Scholar
Corrsin, S. 1959 Outline of some topics in homogeneous turbulent flow. J. Geophys. Res. 64 (12), 21342150.Google Scholar
De Zarate, J.M.O. & Sengers, J.V. 2006 Hydrodynamic Fluctuations in Fluids and Fluid Mixtures. Elsevier.Google Scholar
Debue, P., Kuzzay, D., Saw, E.-W., Daviaud, F., Dubrulle, B., Canet, L., Rossetto, V. & Wschebor, N. 2018 Experimental test of the crossover between the inertial and the dissipative range in a turbulent swirling flow. Phys. Rev. Fluids 3 (2), 024602.Google Scholar
Delong, S., Griffith, B.E., Vanden-Eijnden, E. & Donev, A. 2013 Temporal integrators for fluctuating hydrodynamics. Phys. Rev. E 87 (3), 033302.Google Scholar
Donev, A., Bell, J.B., de La Fuente, A. & Garcia, A.L. 2011 Diffusive transport by thermal velocity fluctuations. Phys. Rev. Lett. 106 (20), 204501.Google ScholarPubMed
Donev, A., Vanden-Eijnden, E., Garcia, A. & Bell, J. 2010 On the accuracy of finite-volume schemes for fluctuating hydrodynamics. Commun. Appl. Maths Comput. Sci. 5, 149197.Google Scholar
Español, P., Anero, J.G. & Zúñiga, I. 2009 Microscopic derivation of discrete hydrodynamics. J. Chem. Phys. 131 (24), 244117.Google ScholarPubMed
Eswaran, V. & Pope, S.B. 1988 An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16 (3), 257278.Google Scholar
Eyink, G., Bandak, D., Goldenfeld, N. & Mailybaev, A.A. 2021 Dissipation-range fluid turbulence and thermal noise. arXiv:2107.13954.Google Scholar
Eyink, G. & Jafari, A. 2021 High Schmidt-number turbulent advection and giant concentration fluctuations. arXiv:2112.13115.Google Scholar
Frisch, U. & Kolmogorov, A.N. 1995 Turbulence: The Legacy of AN Kolmogorov. Cambridge University Press.Google Scholar
Gallis, M.A., Torczynski, J.R., Krygier, M.C., Bitter, N.P. & Plimpton, S.J. 2021 Turbulence at the edge of continuum. Phys. Rev. Fluids 6 (1), 013401.Google Scholar
Gardiner, C.W. 1985 Handbook of Stochastic Methods, vol. 3. Springer.Google Scholar
Garratt, J.R. 1994 The atmospheric boundary layer. Earth Sci. Rev. 37 (1–2), 89134.Google Scholar
Kharche, S., Bon-Mardion, M., Moro, J.-P., Peinke, J., Rousset, B. & Girard, A. 2018 Scaling laws and intermittency in cryogenic turbulence using SHREK experiment. In iTi Conference on Turbulence (ed. R. Orlu, A. Talamelli, J. Peinke & M. Oberlack), pp. 179–184. Springer.Google Scholar
Khurshid, S., Donzis, D.A. & Sreenivasan, K.R. 2018 Energy spectrum in the dissipation range. Phys. Rev. Fluids 3 (8), 082601.Google Scholar
Kolmogorov, A.N. 1941 The local structure of isotropic turbulence in an incompressible viscous fluid. In Dokl. Akad. Nauk SSSR, vol. 30, pp. 301–305.Google Scholar
Kraichnan, R.H. 1967 Intermittency in the very small scales of turbulence. Phys. Fluids 10 (9), 20802082.Google Scholar
Landau, L.D. & Lifshitz, E.M. 1959 Fluid Mechanics, Course of Theoretical Physics, vol. 6. Pergamon Press.Google Scholar
Luchini, P. 2017 Receptivity to thermal noise of the boundary layer over a swept wing. AIAA J. 55 (1), 121130.Google Scholar
McMullen, R., Krygier, M., Torczynski, J. & Gallis, M. 2021 The smallest scales of turbulence in gases are not described by the Navier–Stokes equations. Bull. Am. Phys. Soc. 66.Google Scholar
Moser, R.D. 2006 On the validity of the continuum approximation in high Reynolds number turbulence. Phys. Fluids 18 (7), 078105.Google Scholar
Nonaka, A., Sun, Y., Bell, J. & Donev, A. 2015 Low Mach number fluctuating hydrodynamics of binary liquid mixtures. Commun. Appl. Maths Comput. Sci. 10 (2), 163204.Google Scholar
Pope, S.B. 2001 Turbulent Flows. IOP Publishing.Google Scholar
Segur, J.B. & Oberstar, H.E. 1951 Viscosity of glycerol and its aqueous solutions. Ind. Engng Chem. 43 (9), 21172120.Google Scholar
Thorpe, S.A. 2007 An Introduction to Ocean Turbulence. Cambridge University Press.Google Scholar
Usabiaga, F.B., Bell, J.B., Delgado-Buscalioni, R., Donev, A., Fai, T.G., Griffith, B.E. & Peskin, C.S. 2012 Staggered schemes for fluctuating hydrodynamics. SIAM J. Multiscale Model. Simul. 10 (4), 13691408.Google Scholar
Zubarev, D.N. & Morozov, V.G. 1983 Statistical mechanics of nonlinear hydrodynamic fluctuations. Physica A 120 (3), 411467.Google Scholar
Supplementary material: File

Bell et al. supplementary material

Bell et al. supplementary material

Download Bell et al. supplementary material(File)
File 249.1 KB