An analytical model for water entry cavity of bodies of revolution in two-dimensional background flow

The dynamics of the cavity created by water entry of a body of revolution into two-dimensional background flow is investigated in this paper. The background flow, whether quiescent or moving, is the undisturbed flow by the water entry cavity. It is assumed to have a larger characteristic length, and a smaller characteristic velocity than the cavity. The cavity attached behind an impact body is regarded as a slender, deformable air cylinder. To consider the azimuthal disturbance in the cavity surface, the potential flow is described using the mode decomposition method in a moving coordinate system. The deduced approximate model suggests that the azimuthal disturbance of the initial conditions, the pressure gradient or the movement of background flow, results in the non-uniform three-dimensional deformation of the cavity. Moreover, the approximate model can reduce to several cavity models proposed for different types of water entry problems. The model is further validated by the favorable comparison with the available experimental results measured in quiescent and moving background flow.