Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets

TL;DR

This study characterizes lift-up, Kelvin-Helmholtz, and Orr mechanisms in turbulent jets using global resolvent analysis and SPOD, revealing their dominance regions and structures across different Mach numbers and frequencies.

Contribution

It provides a comprehensive global analysis of three key amplification mechanisms in turbulent jets, linking local and global dynamics and identifying their spatial and spectral dominance.

Findings

Lift-up mechanism dominates at low St/m ratios.

Streamwise vortices and streaks are observed throughout the jet.

Azimuthal wavenumber of streaks varies with streamwise distance.

Abstract

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin-Helmholtz, and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211-237) at low Strouhal number ($St$) and non-zero azimuthal wavenumbers ($m$). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes, and sensitivity analysis distinguishes the three mechanisms and the regions of frequency-wavenumber space where each dominates, finding lift-up to be dominant as $St/m \rightarrow 0$. Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core.