Potential flow past a sphere touching a tangent plane

The uniform ideal flow past an impermeable sphere in contact with an impermeable plane is calculated, and the potential Φ is expressed as an integral over solutions in tangent sphere coordinates, up to an unknown function α. An ordinary differential equation satisfied by α is solved numerically to a high degree of accuracy and then a detailed presentation of the potential near the sphere is given. The potential near to the point of contact is analysed separately using a theory appropriate to crevice regions, and the two solutions are matched. The potential Φ is interpreted as the pressure impulse, P, for which the uniform gradient is specified far from the sphere. This provides information about the impulsive velocity and the net fluid impulse on the sphere or other blunt body near a region of wave impact.