Dynamic Triad Interactions and Evolving Turbulence -- Part 2: Implications for Practical Signals

TL;DR

This paper explores how finite measurement domains and resolution affect the observed triad interactions in turbulent flows, revealing implications for the interpretation of turbulence spectra and non-local interactions.

Contribution

It provides empirical evidence on how finite spatial and temporal sampling broadens interaction conditions and influences turbulence measurements, extending understanding from idealized to practical signals.

Findings

Finite resolution causes decoupling of time and space in turbulence signals.

Fourier components interact with finite delays and broadened frequency windows.

Finite measurement domains significantly impact turbulence spectra and non-local interactions.

Abstract

We investigate how momentum and kinetic energy is transferred between Fourier components (the so-called triad interactions) in measured turbulent flow fields, i.e. in practical, discretely sampled signals with limited temporal and spatial domains. We empirically observe that the finite resolution in experimental investigations causes a decoupling between time and space, which broadens the phase match condition to include both spatial and temporal frequencies as predicted in Part 1. It is also empirically observed that the Fourier components may interact with a finite time delay and within a broadened frequency window (finite overlap widths) in both time and space, as compared to the usual integrals over infinite ranges where Fourier components interact by overlapping Dirac delta functions. Furthermore, it is empirically observed how the finite temporal and spatial measurement domains of velocity records can have a significant effect on the efficiency of the triad interactions and thereby on the shape and development of measured velocity power spectra. These finite spatial/temporal domains thus influence the measured spatial and temporal development of turbulence, the possibility for non-local interactions and hence also non-equilibrium turbulence, e.g. fractal grid generated turbulence.