A Caltech Library Service

Instability wave models for the near-field fluctuations of turbulent jets

Gudmundsson, K. and Colonius, Tim (2011) Instability wave models for the near-field fluctuations of turbulent jets. Journal of Fluid Mechanics, 689 . pp. 97-128. ISSN 0022-1120.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


Previous work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described as linear perturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

Item Type:Article
Related URLs:
URLURL TypeDescription
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2011 Cambridge University Press. Received 16 November 2010; revised 2 August 2011; accepted 17 September 2011; first published online 15 November 2011. The authors wish to thank Professor F. Hussain and Drs D. Rodriguez, A. Samanta and T. Suzuki for fruitful discussions on stability analysis and turbulence. We would also like to express appreciation to Dr J. Bridges and colleagues at the NASA Glenn Research Center for providing us with their data. This work was supported by the Aeroacoustics Research Consortium and TTC Technologies under an SBIR grant from NAVAIR, with Dr J. Spyropolous as technical monitor.
Funding AgencyGrant Number
Aeroacoustics Research ConsortiumUNSPECIFIED
TTC Technologies SBIR grantUNSPECIFIED
Subject Keywords:absolute/convective instability; hydrodynamic noise; jet noise
Record Number:CaltechAUTHORS:20120203-100537724
Persistent URL:
Official Citation:K. Gudmundsson and Tim Colonius (2011). Instability wave models for the near-field fluctuations of turbulent jets. Journal of Fluid Mechanics, 689 , pp 97-128 doi:10.1017/jfm.2011.401
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29118
Deposited By: Jason Perez
Deposited On:03 Feb 2012 18:45
Last Modified:03 Oct 2019 03:38

Repository Staff Only: item control page