Description of inverse energy cascade in homogeneous isotropic turbulence using an eigenvalue method

Feng LIU, Hantao LIU, Hongkai ZHAO, Pengfei LYU

doi:10.1007/s10483-021-2767-7

Applied Mathematics and Mechanics >

2021 , Vol. 42 >Issue 9: 1233 - 1246

DOI: https://doi.org/10.1007/s10483-021-2767-7

Articles

Description of inverse energy cascade in homogeneous isotropic turbulence using an eigenvalue method

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1. Research Center of Shanxi Province for Solar Energy Engineering and Technology, School of Energy and Power Engineering, North University of China, Taiyuan 030051, China;
2. National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, School of Energy and Power Engineering, Beihang University, Beijing 100191, China

Received date: 2021-03-25

Revised date: 2021-06-08

Online published: 2021-09-07

Supported by

the National Natural Science Foundation of China (Nos. 12002318 and 51976203), the Central Government Guides Local Science and Technology Development Fund Projects (No. YDZX20191400002850), and the Science Foundation of North University of China (No. XJJ201929)

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Abstract

A description of inverse energy cascade (from small scale to large scale) in homogeneous isotropic turbulence is introduced by using an eigenvalue method. We show a special isotropic turbulence, in which the initial condition is constructed by reversing the velocity field in space, i.e., the time-reversed turbulence. It is shown that the product of eigenvalues of the rate-of-strain tensor can quantitatively describe the backward energy transfer process. This description is consistent to the velocity derivative skewness S_k. However, compared with S_k, it is easier to be obtained, and it is expected to be extended to anisotropic turbulence. Furthermore, this description also works for the resolved velocity field, which means that it can be used in engineering turbulent flows. The description presented here is desired to inspire future investigation for the modeling of the backward energy transfer process and lay the foundation for the accurate prediction of complex flows.

Key words： inverse energy cascade; homogeneous isotropic turbulence; eigenvalue method; turbulence model

Cite this article

Feng LIU, Hantao LIU, Hongkai ZHAO, Pengfei LYU . Description of inverse energy cascade in homogeneous isotropic turbulence using an eigenvalue method[J]. Applied Mathematics and Mechanics, 2021 , 42(9) : 1233 -1246 . DOI: 10.1007/s10483-021-2767-7

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