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Exact third-order structure functions for two-dimensional turbulence

Published online by Cambridge University Press:  30 July 2018

Jin-Han Xie Open the ORCID record for Jin-Han Xie [Opens in a new window]  and
Oliver Bühler
Jin-Han Xie
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Oliver Bühler*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Email address for correspondence: [email protected]
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Abstract

We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 851 , 25 September 2018 , pp. 672 - 686
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Copyright
© 2018 Cambridge University Press 

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References

Augier, P., Galtier, S. & Billant, P. 2012 Kolmogorov laws for stratified turbulence. J. Fluid Mech. 709, 659–670.Google Scholar
Balwada, D., LaCasce, J. H. & Speer, K. G. 2016 Scale-dependent distribution of kinetic energy from surface drifters in the gulf of mexico. Geophys. Res. Lett. 43 (20), 10856–10863.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bernard, D. 1999 Three-point velocity correlation functions in two-dimensional forced turbulence. Phys. Rev. E 60 (5), 6184.Google Scholar
Boffetta, G. & Musacchio, S. 2010 Evidence for the double cascade scenario in two-dimensional turbulence. Phys. Rev. E 82 (1), 016307.Google Scholar
Cerbus, R. T. & Chakraborty, P. 2017 The third-order structure function in two dimensions: the Rashomon effect. Phys. Fluids 29 (11), 111110.Google Scholar
Davidson, P. 2015 Turbulence: an Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of AN Kolmogorov. Cambridge University Press.Google Scholar
Kolmogorov, A. N. 1941 Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, 1st Engl. edn. Pergamon.Google Scholar
Lindborg, E. 1999 Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech. 388, 259–288.Google Scholar
Lindborg, E. & Cho, J. Y. N. 2001 Horizontal velocity structure functions in the upper troposphere and lower stratosphere: 2. Theoretical considerations. J. Geophys. Res. 106 (D10), 10233–10241.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, Volume II: Mechanics of Turbulence, vol. 2. Dover (reprinted 2007).Google Scholar
Poje, A. C, Özgökmen, T. M., Bogucki, D. J. & Kirwan, A. D. 2017 Evidence of a forward energy cascade and Kolmogorov self-similarity in submesoscale ocean surface drifter observations. Phys. Fluids 29 (2), 020701.Google Scholar
Srinivasan, K. & Young, W. R. 2012 Zonostrophic instability. J. Atmos. Sci. 69 (5), 1633–1656.Google Scholar
Yaglom, A. M. 1962 An Introduction to the Theory of Stationary Random Functions. Dover.Google Scholar
Yakhot, V. 1999 Two-dimensional turbulence in the inverse cascade range. Phys. Rev. E 60 (5), 5544–5551.Google Scholar