A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent the world lines of freely falling fiducial observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function, although the time coordinate lines still follow Killing trajectories to retain the explicitly stationary nature of the coordinate grid. This explains some of the properties of the original Painlev\'e-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the G\"odel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.

Gravitational perturbations of the de Sitter spacetime are investigated using the Regge--Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heun-type for both electric and magnetic multipoles. The solution so obtained is used to study the deviation from an initially radial geodesic due to the perturbation. The spectral properties of the perturbed metric are also analyzed. Finally, gauge- and tetrad-invariant first-order massless perturbations of any spin are explored following the approach of Teukolsky. The existence of closed-form, i.e. Liouvillian, solutions to the radial part of the Teukolsky master equation is discussed.

The turning circle maneuver of a self-propelled tanker like ship model is numerically simulated through the integration of the unsteady Reynolds averaged Navier-Stokes (uRaNS) equations coupled with the equations of the motion of a rigid body. The solution is achieved by means of the unsteady RANS solver ?navis developed at CNR-INSEAN. The focus here is on the analysis of the maneuvering behavior of the ship with two different stern appendages configurations; namely, a twin screw with a single rudder and a twin screw, twin rudder with a central skeg. Each propeller is taken into account by a model based on the actuator disk concept; anyhow, in order to correctly capture the turning maneuvering behavior of the model, a suitable model which takes into account for oblique flow effects has to be considered. Results from a preliminary verification assessment are discussed; validation of the predicted trajectory and the kinematical parameters is provided by comparison with experimental data from free running tests. Maneuvering abilities of the two configurations are discussed; in order to better understand the different behavior of the two configurations, an in depth analysis of the force and moments on the hull and on the individual appendages is provided.

In applied hydrodynamics it is presently a general common task to simulate flow around complex shaped ships with moving appendages. As an example the simulation of a turning circle manoeuvre of a full-appended combatant ship is common in manoeuvrability studies. Nevertheless the accurate numerical simulation of turbulent, unsteady flow around a full appended maneuvering complex-shaped hull is a challenging task, because of the geometrical complexity of the appendages present and their relative movement, generating a very complex hydrodynamic flow.

The correct characterization of wall pressure fluctuations (WPF) and of the response of an elastic structure subjected to turbulent boundary layer (TBL) represents one of the most challenging problems in the fluid structure interaction field. This kind of excitation for an elastic structure is encountered on a number of different engineering applications: in naval field WPF acting along the ship hull impinge on comfort on board high speed vessels and they are also responsible for strong vibrations of the sonar dome, which can degrade the correct functioning of the sensors mounted inside the dome itself. Moreover, the sound pressure levels produced by TBL load acting along the aircraft fuselage can be intense enough to result in an unacceptable cabin noise and can cause a reduction of the lifetime of fuselage panels due to structural fatigue. The study of WPF induced by TBL load in the naval and aeronautical fields are characterized by important differences in terms of both flow and structural characteristics, which provide highly different dynamical responses of a typical naval and aeronautic panel. Nevertheless, the characterization of the TBL load using model scale tests of a ship and an aircraft or sections of them have also strong similarities and for a great number of problems can be analysed using parallel experimental approaches in towing tanks, water channels and wind tunnels. The base of this approach is given by the identification of the most appropriate scaling laws for wall pressure fluctuation spectra and spatial models in the frequency domain, which allow to obtain in principle the full scale spectra from the sole knowledge of few mean flow parameters. Unfortunately, these models are based on very restrictive hypotheses on the nature of the flow and the structure, basically canonical flat boundary layer. Aim of this work is to show how some of the typical perturbations from the canonical flat plate boundary layer, encountered when studying a real structure in naval and aeronautical fields, can interfere in the modelling of this load and to show possible solutions to these specific problems. To examine these features for complex boundary layer, the results of three different experimental campaigns performed at CNR-INSEAN towing tank and CIRA PT-1 transonic wind tunnel are here discussed.

We give a Sobolev inequality with the weight K(x) belonging to the class A_2\cap G_n for the function |u|^t and the weight K(x)^{-1} for |u|^2. The constant in the relevant inequality is seen to depend on the G_n and A_2 constants of the weight.

Motion of test particles in the gravitational field associated with an electromagnetic plane wave is investigated. The interaction with the radiation field is modeled by a force term entering the equations of motion given by the 4-momentum density of radiation observed in the particle's rest frame with a multiplicative constant factor expressing the strength of the interaction itself. Explicit analytical solutions are obtained. Scattering of fields by the electromagnetic wave, i.e., scalar (spin 0), electromagnetic (spin 1) and and massless spin $\frac12$ fields, is studied too.

The motion of matter immersed in a radiation field is affected by radiation drag, as a result of scattering or absorption and re-emission. The resulting friction-like drag, also known as Poynting-Robertson effect, has been recently studied in the general relativistic background of the Schwarzschild and Kerr metric, under the assumption that all photons in the radiation field possess the same angular momentum. We calculate here the signal produced by an emitting point-like specific source moving in a Schwarzschild spacetime under the influence of such a radiation field. We derive the flux, redshift factor and solid angle of the hot spot as a function of (coordinate) time, as well as the time-integrated image of the hot spot as seen by an observer at infinity. The results are then compared with those for a spot moving on a circular geodesic in a Schwarzschild metric.

The motion of a massive test particle inside a thermal (test) photon gas is studied near a Schwarzschild black hole, leading to a novel description of the effect of radiation scattering on the particle trajectory, responsible for half of the Poynting-Robertson effect: the azimuthal radiation drag. Lacking the outward directed radiation pressure of the latter effect, gravitationally bound orbits always decay, leading to capture by the black hole or the central object generating the exterior Schwarzschild field in which this discussion takes place.

The motion of a massive test particle in a Schwarzschild spacetime surrounded by a perfect fluid with equation of state $p_0= w \rho_0$ is investigated. Deviations from geodesic motion are analyzed as a function of the parameter $w$, ranging from $w=1$ which corresponds to the case of massive free scalar fields, down into the so-called ``phantom" energy, with $w<-1$. It is found that the interaction with the fluid leads to capture (escape) of the particle trajectory in the case $1+w>0$ ($<0$), respectively. Based on this result, it is argued that inspection of the trajectories of test particles in the vicinity of a Schwarzschild black hole with matter around may offer a new means of gaining insights into the nature of cosmic matter.

The observer-dependent tidal effects associated with the electric and magnetic parts of the Riemann tensor with respect to an arbitrary family of observers are discussed in a general spacetime in terms of certain \lq\lq tidal indicators.'' The features of such indicators are then explored by specializing our considerations to the family of stationary circularly rotating observers in the equatorial plane of the Kerr spacetime. There exist a number of observer families which are special for several reasons and for each of them such indicators are evaluated. The transformation laws of tidal indicators when passing from one observer to another are also discussed, clarifying the interplay among them. Our analysis shows that no equatorial plane circularly rotating observer in the Kerr spacetime can ever measure a vanishing tidal electric indicator, whereas the family of Carter's observers measures zero tidal magnetic indicator.