Experimental investigation of the turbulent cascade development by injection of single large-scale Fourier modes

TL;DR

This experimental study investigates how injecting a single large-scale Fourier mode into a jet flow influences the development of turbulence spectra and cascade delays, providing insights into turbulence dynamics and modeling.

Contribution

It introduces an experimental method to analyze the spectral development and cascade delays caused by a single Fourier mode injection in turbulent flows.

Findings

Spectral components develop downstream as predicted by cascade theory.

Measured cascade delays align with theoretical and numerical models.

Initial conditions significantly affect spectral evolution in turbulence.

Abstract

The current work presents an experimental investigation of the dynamic interactions between flow scales caused by repeated actions of the nonlinear term of the Navier-Stokes equation. Injecting a narrow band oscillation, representing a single Fourier mode, into a round jet flow allows the measurement of the downstream generation and development of higher harmonic spectral components and to measure when these components are eventually absorbed into fully developed turbulence. Furthermore, the dynamic evolution of the measured power spectra observed corresponds well to the measured cascaded delays reported by others. Closely matching spectral development and cascade delays have also been derived directly from a one-dimensional solution of the Navier-Stokes equation described in a companion paper. The results in the current work provide vital information about how initial conditions influence development of the shape of the spectrum and about the extent of the time scales in the triad interaction process, which should be of significance to turbulence modelers.