Added mass of a pair of disks at small separation

Abstract

Inviscid irrotational flow around a pair of coaxial disks is considered in the limit in which the distance 2h between the disks is small compared to their radius a. The disks have zero thickness and accelerate away from one another along their common axis. The added mass M of each accelerating disk is increased by the presence of the other disk. Analytic predictions are obtained when h/a ≪ 1, with M ~ πa/(8h)-ln(h/a)/2+0.77875+. . . The term O(a/h) can be obtained by means of an inviscid analysis of approximately unidirectional flow within the gap between the disks, but the correction terms have not been reported previously. The irrotational flow problem satisfies Neumann boundary conditions on the surface of the disks, but is otherwise analogous to the Dirichlet problem of the capacitance of a pair of charged disks, which has been the subject of much study and controversy.