The acoustic analogy is adopted to characterise the signature of a seven-bladed submarine propeller, relying on a high-fidelity large-eddy simulation, performed on a computational grid consisting of 840 million points. Results demonstrate that the nonlinear terms of the Ffowcs-Williams and Hawkings equation quickly become dominant moving away from the propeller along the direction of its wake development. While the linear terms experience a decay moving downstream, the nonlinear terms grow in the near wake, as a result of the development of wake instability. In particular, this growth affects frequencies lower than the blade frequency. Therefore, the acoustic signature of the propeller is mainly tonal in the near field only, due to the thickness and loading components of noise from the surface of the propeller and the periodic perturbation caused by its tip vortices. They develop instability at a faster rate, compared with the hub vortex, triggering the process of energy cascade towards higher frequencies and contributing in this way to broadband noise.

The bare nucleon-nucleon interaction is essential for the production of pair correlations in nuclei, but an important contribution also arises from the induced interaction resulting from the exchange of collective vibrations between nucleons moving in time reversal states close to the Fermi energy. The pairing field resulting from the summed interaction is strongly peaked at the nuclear surface. It is possible to reproduce the detailed spatial dependence of this field by using either a local approximation, which fully takes into account finite size effects, or a contact interaction, with parameters that are quite different from those commonly used in more phenomenological approaches.

Large eddy simulations are presented on the wake flow of a notional propeller (the INSEAN E1658), upstream of a NACA0020 hydrofoil of infinite spanwise extent, mimicking propeller–rudder interaction. Results show that the flow physics is dominated by the interaction between the coherent structures populating the wake of the propeller and the surface of the hydrofoil. The suction and pressure side branches of the tip vortices move towards inner and outer radii, respectively. The hub vortex is split into two branches at the leading edge of the hydrofoil. The two branches of the hub vortex shift in the opposite direction, compared to the tip vortices, towards the rudder suction sides. As a result, a contraction of the propeller wake on the suction sides occurs, leading to increased levels of shear stress and turbulence. At downstream locations along the hydrofoil the spanwise deflection of the suction side branches of the tip vortices affects the trajectory of the overall propeller wake, including also the smaller helical vortices across the span of the wake of each blade and the two branches of the hub vortex on the two sides of the hydrofoil. This cross-stream shift persists, producing a strong anti-symmetry of the overall wake.