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

doi:10.1007/s10483-021-2767-7

Abstract

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

2010 MSC Number:

76F02

Feng LIU, Hantao LIU, Hongkai ZHAO, Pengfei LYU. Description of inverse energy cascade in homogeneous isotropic turbulence using an eigenvalue method. Applied Mathematics and Mechanics (English Edition), 2021, 42(9): 1233-1246.

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