  Detailed flow dissection using Dynamic Mode Decomposition (DMD) and Proper
Orthogonal Decomposition (POD) is carried out to investigate the dynamics of
the flow-field around a NACA-0012 aerofoil at a Reynolds number of $5\times
10^4$, Mach number of $0.4$, and at various angles of attack around the onset
of stall. Three distinct dominant flow modes are identified by the DMD and the
POD: 1) a globally oscillating flow mode at a low-frequency (LFO mode 1); 2) a
locally oscillating flow mode on the suction surface of the aerofoil at a
low-frequency (LFO mode 2); and 3) a locally oscillating flow mode along the
wake of the aerofoil at a high-frequency (HFO mode). The LFO mode 1 features
the globally oscillating-flow around the aerofoil, the oscillating-pressure
along the aerofoil chord, and the process that creates and sustains the triad
of vortices. The LFO mode 2 features the expansion and advection of the
upstream vortex (UV) of the TCV. The HFO mode originates at the aerofoil
leading-edge and features the oscillating mode along the aerofoil wake. The HFO
mode exists at all of the investigated angles of attack and causes a global
oscillation in the flow-field. The global flow oscillation around the aerofoil
interacts with the laminar portion of the separated shear layer in the vicinity
of the leading-edge and triggers an inviscid absolute instability that creates
and sustains the TCV. When the UV of the TCV expands, it advects downstream and
energies the HFO mode. The LFO mode 1, the LFO mode 2, and the HFO mode
mutually strengthen each other until the LFO mode 1 and 2 overtake the HFO mode
at the onset of stall. At the angles of attack $9.7^{\circ} \leq \alpha \leq
10.0^{\circ}$ the low-frequency flow oscillation (LFO) phenomenon is fully
developed. At higher angles of attack, the HFO mode overtakes the LFO mode 2,
and the aerofoil undergoes a full stall.
