  A large eddy simulation is performed to study secondary tones generated by a
NACA0012 airfoil at angle of attack of $\alpha = 3^{\circ}$ with freestream
Mach number of $M_{\infty} = 0.3$ and Reynolds number of $Re = 5 \times 10^4$.
Laminar separation bubbles are observed over the suction side and near the
trailing edge, on the pressure side. Flow visualization and spectral analysis
are employed to investigate vortex shedding aft of the suction side separation
bubble. Vortex interaction results in merging or bursting such that coherent
structures or turbulent packets are advected towards the trailing edge leading
to different levels of noise emission. Despite the intermittent occurrence of
laminar-turbulent transition, the noise spectrum depicts a main tone with
multiple equidistant secondary tones. To understand the role of flow
instabilities on the tones, the linearized Navier-Stokes equations are examined
in its operator form through bi-global stability and resolvent analyses, and by
time evolution of disturbances using a matrix-free method. These linear global
analyses reveal amplification of disturbances over the suction side separation
bubble. Non-normality of the linear operator leads to further transient
amplification due to modal interaction among eigenvectors. Two-point, one time
autocovariance calculations of pressure along the spanwise direction elucidate
aspects of the acoustic feedback loop mechanism in the non-linear solutions.
This feedback process is self-sustained by acoustic waves radiated from the
trailing edge, which reach the most sensitive flow location between the leading
edge and the separation bubble, as identified by the resolvent analysis.
Leading edge disturbances arising from secondary diffraction and phase
interference among the most unstable frequencies computed in the eigenspectrum
are also shown to have an important role in the feedback loop.
