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The vortex–body interaction problem, which characterizes the flow field of a rudder placed downstream of a single-blade marine rotor, is investigated by numerical simulations. The particular topology of the propeller wake, consisting of a helicoidal vortex detached from the blade tips (tip vortex) and a longitudinal, streamwise oriented vortex originating at the hub (hub vortex), embraces two representative mechanisms of vortex–body collisions: the tip vortices impact almost orthogonally to the mean plane, whereas the hub vortex travels in the mean plane of the wing (rudder), perpendicularly to its leading edge. The two vortices evolve independently only during the approaching and collision phases. The passage along the body is instead characterized by strong interaction with the boundary layer on the rudder and is followed by reconnection and merging in the middle and far wake. The features of the wake were investigated by the $\unicode[STIX]{x1D706}_{2}$-criterion (Jeong & Hussain, J. Fluid Mech., vol. 285, 1995, pp. 69–94) and typical flow variables (pressure, velocity and vorticity) of the instantaneous flow field; wall pressure spectra were analysed and related to the tip and hub vortices evolution, revealing a non-obvious behaviour of the loading on the rudder that can be related to undesired unsteady loads.

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Modal decomposition techniques are used to analyse the wake field past a marine propeller achieved by previous numerical simulations (Muscari et al. Comput. Fluids, vol. 73, 2013, pp. 65–79). In particular, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used to identify the most energetic modes and those that play a dominant role in the inception of the destabilization mechanisms. Two different operating conditions, representative of light and high loading conditions, are considered. The analysis shows a strong dependence of temporal and spatial scales of the process on the propeller loading and correlates the spatial shape of the modes and the temporal scales with the evolution and destabilization mechanisms of the wake past the propeller. At light loading condition, due to the stable evolution of the wake, both POD and DMD describe the flow field by the non-interacting evolution of the tip and hub vortex. The flow is mainly associated with the ordered convection of the tip vortex and the corresponding dominant modes, identified by both decompositions, are characterized by spatial wavelengths and frequencies related to the blade passing frequency and its multiples, whereas the dynamic of the hub vortex has a negligible contribution. At high loading condition, POD and DMD identify a marked separation of the flow field close to the propeller and in the far field, as a consequence of wake breakdown. The tonal modes are prevalent only near to the propeller, where the flow is stable; on the contrary, in the transition region a number of spatial and temporal scales appear. In particular, the phenomenon of destabilization of the wake, originated by the coupling of consecutive tip vortices, and the mechanisms of hub–tip vortex interaction and wake meandering are identified by both POD and DMD.