The coherent structure of the energy cascade in isotropic turbulence

Creators: Park, Danah¹; Lozano-Durán, Adrián^{2, 3}

1. Stanford University
2. Massachusetts Institute of Technology
3. California Institute of Technology

Abstract

The energy cascade, i.e. the transfer of kinetic energy from large-scale to small-scale flow motions, has been the cornerstone of turbulence theories and models since the 1940s. However, understanding the spatial organization of the energy transfer has remained elusive. In this work, we answer the question: What are the characteristic flow patterns surrounding regions of intense energy transfer? To that end, we utilize numerical data of isotropic turbulence to investigate the three-dimensional spatial structure of the energy cascade in the inertial range. Our findings indicate that forward energy-transfer events are predominantly confined in the high strain-rate region created between two distinct zones of elevated enstrophy. On average, these zones manifest in the form of two hairpin-like shapes with opposing orientations. The mean velocity field associated with the energy transfer exhibits a saddle point topology when observed in the frame of reference local to the event. The analysis also shows that the primary driving mechanism for the cascade involves strain-rate self-amplification, which is responsible for 85% of the energy transfer, whereas vortex stretching accounts for less than 15%.

Copyright and License

This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Acknowledgement

This work was supported by the National Science Foundation under Grant No. 2140775.

Contributions

Danah Park and Adrián Lozano-Durán contributed equally to this work.

A.L.-D. conceived the idea, D.P. conducted the data post-processing and developed the code, D.P. and A.L.-D. analyzed the results. All authors reviewed the manuscript.

Data Availability

The datasets generated and analyzed during the current study are available in the Jimenez’s Group repository, https://torroja.dmt.upm.es/turbdata/

Supplemental Material

Supplementary Information (PDF)

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