A systematic bias in the calculation of spectral density from a 3D spatial grid

TL;DR

This paper identifies a systematic bias in the calculation of spectral density from 3D spatial grids, showing that observed kinks are methodological artifacts rather than physical phenomena, and proposes an improved estimation method.

Contribution

The paper reveals a bias in spectral density estimation from 3D grids and introduces a new method to eliminate spurious kinks for more accurate results.

Findings

Identified systematic kinks at specific wave numbers as methodological artifacts.

Proposed a new estimation method that removes these spurious features.

Enhanced accuracy in spectral density calculations for turbulence analysis.

Abstract

The energy spectral density $E(k)$, where $k$ is the spatial wave number, is a well-known diagnostic of homogeneous turbulence and magnetohydrodynamic turbulence. However in most of the curves plotted by different authors, some systematic kinks can be observed at $k=9$, $k=15$ and $k=19$. We claim that these kinks have no physical meaning, and are in fact the signature of the method which is used to estimate $E(k)$ from a 3D spatial grid. In this paper we give another method, in order to get rid of the spurious kinks and to estimate $E(k)$ much more accurately.