A partially cavitating hydrofoil in a gust

An analysis is made of a hydrofoil with partial cavitation in a traveling gust. The problem is formulated in the time domain with pressure (acceleration potential) as the fundamental dependent variable. It is shown that, in the limit, as the aspect ratio of the foil becomes large, the second time derivative of the cross-sectional area of the cavity vanishes regardless of the shape of the gust. Integral equations are presented through which the length of the cavity and the unsteady pressure distribution on the foil can be determined. Since these equations are highly nonlinear and require formidable numerical procedures to solve, no attempt is made to solve them. It is shown in an appendix that the earliest possible appearance of a nonvanishing second time derivative of the cross-sectional area of the cavity is to the order of the square of the reciprocal of the aspect ratio and that to this order the pressures at distances large in comparison with the chord of the foil (but not the span) grow logarithmically. It may be inferred from this result that the pressures in the far field can be reduced by increasing the aspect ratio.