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Bispectral decomposition and energy transfer in a turbulent jet

Published online by Cambridge University Press:  18 December 2025

Akhil Nekkanti Open the ORCID record for Akhil Nekkanti [Opens in a new window] ,
Ethan Pickering Open the ORCID record for Ethan Pickering [Opens in a new window] ,
Oliver T. Schmidt Open the ORCID record for Oliver T. Schmidt [Opens in a new window]  and
Tim Colonius
Akhil Nekkanti*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology , Pasadena, CA, USA
Ethan Pickering
Affiliation:
Bayer Crop Science, Boston, MA, USA
Oliver T. Schmidt
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, USA
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology , Pasadena, CA, USA
*
Corresponding author: Akhil Nekkanti, aknekkan@caltech.edu
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Abstract

The triadic interactions and nonlinear energy transfer are investigated in a subsonic turbulent jet at $Re = 450\,000$. The primary focus is on the role of these interactions in the formation and attenuation of streaky structures. To this end, we employ bispectral mode decomposition, a technique that extracts coherent structures associated with dominant triadic interactions. A strong triadic correlation is identified between Kelvin–Helmholtz (KH) wavepackets and streaks: interactions between counter-rotating KH waves generates streamwise vortices, which subsequently give rise to streaks through the lift-up mechanism. The most energetic streaks occur at azimuthal wavenumber $m = 2$, with the dominant contributing triad being $[m_1, m_2, m_3] = [1, 1, 2]$. The spectral energy budget reveals that the net effect of nonlinear triadic interactions is an energy loss from the streaks. As these streaks convect downstream, they engage in further nonlinear interactions with other frequencies, which drain their energy and ultimately lead to their attenuation. Further analysis identifies the dominant scales and direction of energy transfer across different spatial regions of the jet. While the turbulent jet exhibits a forward energy cascade in a global sense, the direction of energy transfer varies locally: in the shear layer near the nozzle exit, triadic interactions among smaller scales dominate, resulting in an inverse energy cascade, whereas farther downstream, beyond the end of the potential core, interactions among larger scales prevail, leading to a forward cascade.

JFM classification

Wakes/Jets: Jets Instability: Nonlinear instability Nonlinear Dynamical Systems: Nonlinear Dynamical Systems

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JFM Papers
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Journal of Fluid Mechanics , Volume 1025 , 25 December 2025 , A35
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© The Author(s), 2025. Published by Cambridge University Press

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