Vibrations of a body in a bounded volume of viscous fluid (Q1067901)

The problem of the vibrations of a body in a bounded volume of viscous fluid has been studied on a number of occasions. The main attention has been devoted to determining the hydrodynamic characteristics of elements in the form of rods. Analytic solution of the problem is possible only in the simplest cases. In the present paper, in which large Reynolds numbers are considered, the asymptotic method of Vishik and Lyusternik and Chernous'ko is used to consider the general problem of translational vibrations of an axisymmetric body in an axisymmetric volume of fluid. Equations of motion of the body and expressions for the coefficients due to the viscosity of the fluid are obtained. It is shown that in the first approximation these coefficients differ only by a constant factor and are completely determined if the solution to the problem for an ideal fluid is known. Examples are given of the determination of the ''viscous'' added mass and the damping coefficient for some bodies and cavities. In the case of an ideal fluid, general estimates are obtained for the added mass and also for the influence of nonlinearity.