NONLINEAR OSCILLATIONS OF DROPS WITH INTERNAL CIRCULATION

Nonlinear oscillations of viscous Liquid drops with and without initia l internal circulation are investigated. The full Navier-Stokes equati ons are solved for a liquid drop surrounded by a dynamically inactive ambient gas. The Galerkin/finite element technique along with the spin e-flux method for the advection of the free boundaries are used. Inter nal circulations are generated by imposing a constant velocity at the surface of the drop and obtaining the steady state velocity field for a fixed drop shape. Oscillations of drops subject to small to large am plitude, and for the second-, third-, fourth-, and fifth-mode disturba nces are considered. New data on the period and the decay factor of th e oscillations are reported. The internal circulation in a drop releas ed from an even-mode shape results in the transfer of energy mainly be tween the even modes. The internal circulation in a drop released from an odd-mode shape results in the transfer of energy between both odd and even modes. In general, the internal circulations generated by a c onstant surface velocity tend to transfer energy from any mode of drop oscillations to the second mode. This tendency increases as the stren gth of the internal circulation increases. (C) 1998 American Institute of Physics.