Spectral dynamics of natural and forced supersonic twin-rectangular jet flow

Abstract

We study the stationary, intermittent, and nonlinear dynamics of natural and forced supersonic twin-rectangular turbulent jets using spectral modal decomposition. We decompose large-eddy simulation data into four reflectional symmetry components about the major and minor axes. In the natural jet, spectral proper orthogonal decomposition (SPOD) uncovers two resonant instabilities antisymmetric about the major axis. Known as screech tones, the more energetic of the two is symmetric about the minor axis and steady, while the other is intermittent. We test the hypothesis that flow symmetry can be leveraged for control design. Time-periodic forcing symmetric about the major and minor axes is implemented using a plasma actuation model, and succeeds in removing screech from a different symmetry component. We investigate the spectral peaks of the forced jet using an extension of bispectral mode decomposition (BMD), where the bispectrum is bounded by unity and which conditionally recovers the SPOD. We explain the appearance of harmonic peaks as three sets of triadic interactions between reflectional symmetries, forming an interconnected triad network. BMD modes of active triads distil coherent structures comprising multiple coupled instabilities, including Kelvin-Helmholtz, core, and guided-jet modes (G-JM). Downstream-propagating core modes can be symmetric or antisymmetric about the major axis, whereas upstream-propagating G-JM responsible for screech closure (Edgington-Mitchell et al., 2022, JFM) are antisymmetric only. The dependence of G-JM on symmetry hence translates from the azimuthal symmetry of the round jet to the dihedral group symmetry of the twin-rectangular jet, and explains why the twin jet exhibits antisymmetric but not symmetric screech modes.