A uniformly valid asymptotic development of the second order for the velocity and pressure distribution on the surface of slender rotational bodies in incompressible, unsteady potential flow

The results provided by the slender body theory for locations near the end of a slender body are generally not correct, and procedures have been developed for correcting singularities with respect to the air flow velocity distribution on the profile surface. One of these procedures is the method of matched asymptotic expansions reported by Van Dyke (1964). Van Dyke (1954, 1959) has also studied singularities at the end of slender rotational bodies and the elimination of these singularities, taking into account the characteristics of the tangential velocity on the body surface. The present investigation represents an extension of Van Dyke's studies. A uniformly valid development of the velocity distribution on the surface of the body is provided. In addition, a representation of the second order, uniformly valid in the entire flowfield, is given for the velocity potential and the velocity components. The velocity distribution on the surface of the body is, thus, obtained on the basis of a special application of a more general solution.