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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: obuhler@cims.nyu.edu
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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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