Spatial instability waves associated with lowfrequency noise radiation at shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equations are solved to obtain the mean flow fields, which serve as the baseflow for linear stability analysis. The chevron jet has more complicated instability waves than the round jet, where three types of instability modes are identified in the vicinity of the nozzle, corresponding to radial shear, azimuthal shear, and their integrated effect of the baseflow, respectively. The most unstable frequency of all chevron modes and round modes in both jets decrease as the axial location moves downstream. Besides, the azimuthal shear effect related modes are more unstable than radial shear effect related modes at low frequencies. Compared to a round jet, a chevron jet reduces the growth rate of the most unstable modes at downstream locations. Moreover, linearized Euler equations are employed to obtain the beam pattern of pressure generated by spatially evolving instability waves at a dominant low frequency St = 0.3, and the acoustic efficiencies of these linear wavepackets are evaluated for both jets. It is found that the acoustic efficiency of linear wavepacket is able to be reduced greatly in the chevron jet, compared to the round jet.

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The adjoint-based control of noise emission for two supersonic turbulent jets with different temperature ratios is attempted by modifying the inlet perturbations. The major noise emission of supersonic jets can be modeled by the spatially developing instability waves, which are obtained by solving parabolized stability equation (PSE) based on the solution of Reynolds-averaged Navier-Stokes equations. The closed-loop control system based on the adjoint PSE is constructed, with the objective function of both total perturbation energy and pressure perturbations. The final objective of this work is to modify the inlet Kelvin-Helmholtz modes, which produce lowest-level far-field noise in supersonic turbulent jets. The results show that the near-field coherent structures acting as sound sources and far-field noise intensity generated by optimal perturbations in isothermal and heated jets could be decreased greatly compared with the original inlet perturbations from linear stability theory. Moreover, the energy-based and pressure-based optimization give similar control efficiency in the noise reduction, although there are some minor differences in optimal inlet perturbations. This indicates that by considering the near-field disturbance energy in the noise control framework, which is easier to measure in real experiments, one can obtain the same benefits as the measurement of far-field pressure.