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Third-order structure functions for isotropic turbulence with bidirectional energy transfer

Published online by Cambridge University Press:  02 September 2019

Jin-Han Xie Open the ORCID record for Jin-Han Xie [Opens in a new window]  and
Oliver Bühler Open the ORCID record for Oliver Bühler [Opens in a new window]
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: jhxie@cims.nyu.edu
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Abstract

We derive and test a new heuristic theory for third-order structure functions that resolves the forcing scale in the scenario of simultaneous spectral energy transfer to both small and large scales, which can occur naturally, for example, in rotating stratified turbulence or magnetohydrodynamical (MHD) turbulence. The theory has three parameters – namely the upscale/downscale energy transfer rates and the forcing scale – and it includes the classic inertial-range theories as local limits. When applied to measured data, our global-in-scale theory can deduce the energy transfer rates using the full range of data, therefore it has broader applications compared with the local theories, especially in situations where the data is imperfect. In addition, because of the resolution of forcing scales, the new theory can detect the scales of energy input, which was impossible before. We test our new theory with a two-dimensional simulation of MHD turbulence.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Isotropic turbulence MHD and Electrohydrodynamics: MHD turbulence
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 877 , 25 October 2019 , R3
Copyright
© 2019 Cambridge University Press 

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