Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-17T05:17:40.177Z Has data issue: false hasContentIssue false
  • English
  • Français

Is vortex stretching the main cause of the turbulent energy cascade?

Published online by Cambridge University Press:  20 November 2019

M. Carbone Open the ORCID record for M. Carbone [Opens in a new window]  and
A. D. Bragg Open the ORCID record for A. D. Bragg [Opens in a new window]
M. Carbone
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129Torino, Italy Department of Civil and Environmental Engineering, Duke University, Durham, NC27708, USA
A. D. Bragg*
Affiliation:
Department of Civil and Environmental Engineering, Duke University, Durham, NC27708, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In three-dimensional turbulence there is on average a cascade of kinetic energy from the largest to the smallest scales of the flow. While the dominant idea is that the cascade occurs through the process of vortex stretching, evidence for this is debated. Here we show theoretically and numerically that vortex stretching is in fact not the main contributor to the average cascade. The main contributor is the self-amplification of the strain-rate field, and we provide several arguments for why its role must not be conflated with that of vortex stretching. Numerical results, however, indicate that vortex stretching plays a more important role during fluctuations of the cascade about its average behaviour. We also resolve a paradox regarding the differing role of vortex stretching on the energy cascade and energy dissipation rate dynamics.

JFM classification

Turbulent Flows: Turbulence theory Vortex Flows: Vortex dynamics
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , R2
Copyright
© 2019 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

Ballouz, J. G. & Ouellette, N. T. 2018 Tensor geometry in the turbulent cascade. J. Fluid Mech. 835, 1048–1064.CrossRefGoogle Scholar
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1 (5), 497–504.CrossRefGoogle Scholar
Borue, V. & Orszag, S. A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31.CrossRefGoogle Scholar
Buaria, D., Pumir, A., Bodenschatz, E. & Yeung, P. K. 2019 Extreme velocity gradients in turbulent flows. New J. Phys. 21 (4), 043004.Google Scholar
Buzzicotti, M., Linkmann, M., Aluie, H., Biferale, L., Brasseur, J. & Meneveau, C. 2018 Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence. J. Turbul. 19 (2), 167–197.CrossRefGoogle Scholar
Chen, S., Sreenivasan, K. R. & Nelkin, M. 1997 Inertial range scalings of dissipation and enstrophy in isotropic turbulence. Phys. Rev. Lett. 79, 1253–1256.CrossRefGoogle Scholar
Danish, M. & Meneveau, C. 2018 Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence. Phys. Rev. Fluids 3, 044604.CrossRefGoogle Scholar
Davidson, P. A. 2004 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Davidson, P. A., Morishita, K. & Kaneda, Y. 2008 On the generation and flux of enstrophy in isotropic turbulence. J. Turbul. 9, N42.Google Scholar
Doan, N. A. K., Swaminathan, N., Davidson, P. A. & Tanahashi, M. 2018 Scale locality of the energy cascade using real space quantities. Phys. Rev. Fluids 3, 084601.CrossRefGoogle Scholar
Donzis, D. A., Yeung, P. K. & Sreenivasan, K. R. 2008 Dissipation and enstrophy in isotropic turbulence: resolution effects and scaling in direct numerical simulations. Phys. Fluids 20 (4), 045108.CrossRefGoogle Scholar
Eyink, G. L. 2006a Cascade of circulations in fluid turbulence. Phys. Rev. E 74, 066302.Google Scholar
Eyink, G. L. 2006b Multi-scale gradient expansion of the turbulent stress tensor. J. Fluid Mech. 549, 159–190.CrossRefGoogle Scholar
Falkovich, G. 2009 Symmetries of the turbulent state. J. Phys. A: Math. Theor. 42 (12), 123001.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Gulitski, G., Kholmyansky, M., Kinzelbach, W., Lüthi, B., Tsinober, A. & Yorish, S. 2007 Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 1. Facilities, methods and some general results. J. Fluid Mech. 589, 57–81.CrossRefGoogle Scholar
Hill, R. J. 1997 Applicability of Kolmogorov’s and Monin’s equations of turbulence. J. Fluid Mech. 353, 67–81.CrossRefGoogle Scholar
Hill, R. J. 2001 Equations relating structure functions of all orders. J. Fluid Mech. 434, 379–388.CrossRefGoogle Scholar
Ireland, P. J., Bragg, A. D. & Collins, L. R. 2016 The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects. J. Fluid Mech. 796, 617–658.CrossRefGoogle Scholar
Ireland, P. J., Vaithianathan, T., Sukheswalla, P. S., Ray, B. & Collins, L. R. 2013 Highly parallel particle-laden flow solver for turbulence research. Comput. Fluids 76, 170–177.CrossRefGoogle Scholar
de Karman, T. & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond. A 164 (917), 192–215.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43 (1), 219–245.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Richardson, L. F. 1922 Weather Prediction by Numerical Process. Cambridge University Press.Google Scholar
Sagaut, P. & Cambon, C. 2018 Homogeneous Turbulence Dynamics. Springer.CrossRefGoogle Scholar
Taylor, G. I. 1932 The transport of vorticity and heat through fluids in turbulent motion. Proc. R. Soc. Lond. A 135 (828), 685–702.CrossRefGoogle Scholar
Taylor, G. I. 1938 Production and dissipation of vorticity in a turbulent fluid. Proc. R. Soc. Lond. A 164 (916), 15–23.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Towns, J., Cockerill, T., Dahan, M., Foster, I., Gaither, K., Grimshaw, A., Hazlewood, V., Lathrop, S., Lifka, D., Peterson, G. D. et al. 2014 XSEDE: accelerating scientific discovery. Comput. Sci. Engng 16 (5), 62–74.CrossRefGoogle Scholar
Tsinober, A. 2001 An Informal Introduction to Turbulence. Kluwer Academic Publishers.Google Scholar