THE DYNAMICS OF BUBBLES IN PERIODIC VORTEX FLOWS

To analyze the dynamics of small, spherical, rigid bubbles in a certai n class of turbulent shear flows dominated by large scale coherent vor tical structures, we model the plane free shear layer with a periodic array of Stuart vortices. The equation of motion of the bubbles is the n integrated numerically to obtain the Lagrangian description of the b ubbles, the long-term dynamics of which depends on the free-stream Rey nolds number, the Stokes number, the gravitational field, and the stre ngth of the vortices. Depending on the values of these four parameters , it is found that either there exists a stable equilibrium point near the center of each vortex, where bubble accumulation occurs, or all b ubbles escape from captivity by the vortices. In the limiting case of dominant viscous drag forces, an Eulerian description of the ''bubble flow field'' is derived. Furthermore, the divergence of this flow fiel d is negative in the neighborhood of a vortex center, where it achieve s its minimum. This indicates that bubbles accumulation may indeed exi st, and thus qualitatively confirms the more general numerical results obtained without the assumption of dominant viscous drag forces.