Modal decomposition techniques, flow field and spectral analysis are employed to investigate the wake dynamics and destabilisation mechanisms of a four-bladed marine propeller with or without a nozzle. Numerical simulations are conducted using the Delayed Detached Eddy Simulation (DDES) model for the wake and the Arbitrary Mesh Interface (AMI) method for the blade rotation. The presence of the nozzle significantly reduces the wake's streamwise velocity, delays the wake destabilisation, 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. From modal analysis, the spatial scale of flow phenomena decreases with the increase of modal frequency. Underlying destabilisation 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 (SF). These four destabilisation 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.

The effect of a nozzle on the wake dynamics of a four-bladed propeller operating in an oblique flow is investigated via modal decomposition and flow visualization of the results obtained from numerical simulations using delayed detached eddy simulations. The wake characteristics and destabilization mechanisms of a non-ducted propeller (NP) and ducted propeller (DP) in axisymmetric and oblique flow conditions are systematically analysed. The wake characteristics on the windward side are very different from those on the leeward side in an oblique flow, and the nozzle has a crucial role in mitigating the asymmetry and weakening the wake deflection. More destabilization mechanisms are present in an oblique flow than in an axisymmetric flow, including the asymmetric evolution and destabilization of the helixes on the windward and leeward sides of the NP wake, the interaction between the vortex shedding and the helixes in the DP leeward region, and the generation of a tube-shaped wake envelope around the nozzle and its rolling-up. Moreover, the effect of the nozzle on wake meandering is discussed based on modal analysis.