Bispectral decomposition and energy transfer in a turbulent jet

TL;DR

This paper uses bispectral mode decomposition to analyze nonlinear energy transfer in a turbulent jet, revealing the roles of triadic interactions and the spatial variation of energy cascades.

Contribution

It introduces bispectral mode decomposition for studying triadic interactions in turbulent jets, highlighting the spatial and spectral dynamics of energy transfer.

Findings

Triadic interactions involve Kelvin-Helmholtz waves and streaks.

Energy transfer direction varies spatially, with inverse cascade near the nozzle.

Forward cascade dominates downstream beyond the potential core.

Abstract

We employ bispectral mode decomposition (BMD) to investigate coherent triadic interactions and nonlinear energy transfer in a subsonic turbulent jet. BMD extracts the flow structures corresponding to the dominant triadic interactions. We find a strong triadic correlation among the Kelvin-Helmholtz wavepacket, its conjugate, and the streaks. The most energetic streaks occur at the azimuthal wavenumber $m=2$, with the dominant contributing azimuthal wavenumber triad being $[m_1,m_2,m_3]=[1,1,2]$. The spectral energy budget reveals that nonlinear triadic interactions represent an energy loss to the streaks. Analysis across a wide range of frequencies and azimuthal wavenumbers identifies the direction of nonlinear energy transfer and the spatial regions where these transfers are most active. The turbulent jet exhibits a forward energy cascade in a global sense, though the direction of energy transfer varies locally. In the shear layer near the nozzle exit, triadic interactions between relatively smaller scales are dominant, leading to an inverse energy cascade. Farther downstream, beyond the end of the potential core, triadic interactions between larger scales dominate, resulting in a forward energy cascade.