Modal decomposition techniques, flow field, and spectral analysis are employed to investigate the wake dynamics and destabilization mechanisms of a four-bladed marine propeller with or without a nozzle. Numerical simulations are conducted using the delayed detached eddy simulation model for the wake and the arbitrary mesh interface method for the blade rotation. The presence of the nozzle significantly reduces the wake's streamwise velocity, delays the wake destabilization, increases the wake length, and changes the morphologies of wake vortices. In particular, the hub vortex in the ducted propeller wake is broken down into chaotic turbulence by the perturbation of the backflow. Two modal decomposition methods, namely, proper orthogonal decomposition and dynamic mode decomposition, are used to decompose the vorticity magnitude in the rotor wake field. From modal analysis, the spatial scale of flow phenomena decreases with the increase in modal frequency. Underlying destabilization mechanisms in the wake correspond to some characteristic frequencies. The interaction of each sheet vortex with the previously shed tip (leakage) vortices occurs at blade passing frequency (BPF). The pairing of adjacent tip (leakage) vortices occurs at half-BPF. The long-wave instability of the hub vortex and the wake meandering are stochastic processes, each of which occurs at a frequency lower or equal to shaft frequency. These four destabilization mechanisms can approximately reconstruct the large-scale flow phenomena in the wake. Moreover, each sheet vortex's alternating connection and disconnection with the previously shed tip (leakage) vortices cause the short-wave instability of the tip (leakage) vortices and generate the secondary vortices. The radial expansion motion of large-scale helical vortices in the outer slipstream dominates the wake meandering phenomenon.
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