Local spectrum of commutation error in large eddy simulations

Abstract

In this Brief Communication we present a new mathematical tool, which we call local spectrum analysis, that can be used to obtain information about local spectral content of the commutation error in large eddy simulations and its dependence on the filter shape and the non-uniformity of the filter width. To illustrate these theoretical findings, the local commutation spectrum analysis is applied to the results of 2563 direct numerical simulation of forced homogeneous turbulence at Reλ=168. The results confirm strong dependence of the spectral content of the commutation error on the filter shape: the spectrum is wide for smooth filters like Gaussian, while for filters, that are close to the sharp cut-off, the spectral content is localized. It is also demonstrated that the amplitude of the commutation error is linearly proportional to the filter width stretching factor.