On the Added Mass of Wrinkled Discs

leads to a sequence of BVPs for φn in the unperturbed domain (r > a); φ0 is the unperturbed solution and subsequent φn are forced by φm with m < n. The idea behind the boundary perturbation technique is old and familiar. For example, it is used in the theory of small-amplitude water waves, wherein the nonlinear boundary conditions on the (unknown) free surface z = F (x, y) are ‘linearized’ about the mean free surface z = 0. The work of G.H. Darwin is also of interest. He wrote five papers in 1879 on the motions of an incompressible viscous fluid inside a perturbed sphere He neglected the inertia terms in the Navier–Stokes equations (Stokes approximation) giving a linear interior BVP, which he solved for ‘small deviations from sphericity’, to first order in ε. He argued that one could take account of these deviations by imposing certain tractions on r = a, and then solved the corresponding BVP inside the sphere. His method is applicable to any f although he was mainly interested in spheroidal surfaces. In this paper, we describe an alternative method. First, we reduce the BVP to a boundary integral equation (BIE) over S. We rewrite