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

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.

Automated summary

The inverse energy cascade in homogeneous isotropic turbulence is described using an eigenvalue method, quantitatively capturing the backward energy transfer process and applicable to both isotropic turbulence and resolved velocity fields. This method, based on the product of eigenvalues of the rate-of-strain tensor, is easier to obtain compared to traditional velocity derivative skewness S-k, and has potential for extension to anisotropic turbulence. The presented description aims to inspire future research on modeling the backward energy transfer process and improve the accurate prediction of complex flows.