Interaction between rotating elliptic cylinder and fixed circular cylinder

The general planar motion of an elliptic cylinder through an inviscid and i ncompressible fluid in the vicinity of a fixed circular cylinder is investi gated analytically. The velocity potential is derived by using the successi ve-image method and the perturbation method, and it is used to determine th e hydrodynamic interactions between them. In a relative coordinate system m oving with the uniform flow, the kinetic energy of the fluid is expressed a s a function of 15 generalized added masses due to the motion of these two cylinders. The generalized added masses are then employed to determine the translational and rotational motion of the elliptic cylinder based on the d ynamic equations of motion that are Obtained from Lagrange's equations of m otion. Numerical results show that the initial configuration of the ellipti c cylinder greatly affects its subsequent motions.