Influence of gaseous cavities in ship-hydrodynamic problems: a simplified study

Several phenomena of interest in ship hydrodynamics involve the presence of time-varying air cavities in the water flow. Two of the most well known, with important practical consequences, are the erosion of propeller blades and the noise. The former is connected with propellers working near the air-water interface and, in particular, to the formation of air cavities during cavitation events. It is caused by the propeller interaction with the air-water two-phase fluid and represents a danger for the success of the vessel operations. The latter is connected with entrapment of air cavities during breaking and fragmentation of the air-water interface. It is a consequence of the collapse of such bubbles evolving in the surrounding water and its major relevance is in military context. Cavitating bubbles are characterized by a uniform interior pressure equal to the vapor pressure. Instead, entrapped cavities have in principle a non uniform pressure. However, in many practical cases their inner pressure can be approximated as uniform with value generally time dependent, in particular compressibility may matter. Assuming a uniform pressure in the cavity means that the effect of the interior air flow on the surrounding water and structures is neglected.