NONLINEAR OSCILLATIONS OF 2-DIMENSIONAL, ROTATING INVISCID DROPS

We examine the nonlinear response of a drop. rotating as a rigid body at fixed angular velocity, to two-dimensional finite-amplitude disturb ances. With these restrictions, the liquid velocity becomes a superpos ition of the solid-body rotation and the gradient of a velocity potent ial. To find the drop motion, we solve an integro-differential Bernoul li's equation for the drop shape and Laplace's equation for the veloci ty potential field within the drop. The integral part of Bernoulli's e quation couples all parts of the drop's surface and sets this problem apart from that of the oscillations of nonrotating drops. We use Galer kin's weighted residual method with finite element basis functions whi ch are deployed on a mesh that deforms in proportion to the deformatio n of the free surface. To alleviate the roundoff error in the initial conditions of the drop motion, we use a Fourier filter which turns off as soon as the highest resolved oscillation mode grows above the mach ine noise level. The results include sequences of drop shapes, Fourier analysis of oscillation frequencies, and evolution in time of the com ponents of total mechanical energy of the drop. The Fourier power spec tral analysis of large-amplitude oscillations at the drop reveals freq uency shifts similar to those of the nonrotating free drops. Constant drop volume, total energy, and angular momentum as well as vanishing m ass flow across the drop surface are the standards of accuracy against which we test the nonlinear motion of the drop over tens or hundreds of oscillation periods. Finally, we demonstrate that our finite elemen t method has superior stability, accuracy, and computational efficienc y over several boundary element algorithms that have previously appear ed in the literature. (C) 1995 Academic Press, Inc.