A GENERAL AND FORMAL SLENDER-BODY THEORY IN THE NON-LIGHTING CASE

In this paper, an alternative and integral method is proposed in order to build a formal slender-body theory valid up to high orders with re spect to the slenderness ratio epsilon and for a non-lifting body whic h is not necessarily of circular cross-section. The method consists of asymptotically expanding and inverting the Fredholm integral equation of the second kind bearing on the unknown source density, which may b e spread on the boundary of the body. For such a treatment, the concep t of integration in the finite-part sense of Hadamard is powerful. The source density is then given up to order o(epsilon(3)) and the pressu re coefficient is provided on the body up to order O(epsilon(4)log eps ilon). Throughout this paper, special attention is also paid to the ma in considered case of the axially symmetric slender body.