Intermediate Stage of Development of Patterns of Vorticity

Part of Free-surface Wave Interaction with a Horizontal Cylinder,
an M.S. thesis by Peter Oshkai. Department of Mechanical Engineering and Mechanics. Lehigh University.

The next sequence of events is represented in Figure 7b by frames N = 11 and 15. For deep submergence (top row), vorticity concentration A is on the return part of its trajectory, about to collide with the cylinder at N = 11, and only a small residual of the post-collision process is evident at N = 15. On the other hand, the major vortex A at intermediate submergence (middle row) does not directly encounter the cylinder and remains intact at N = 15. At the shallowest submergence (bottom row), generation of vortex A is retarded relative to deeper values of submergence, and it occurs from the bottom surface of the cylinder at N = 11. At N = 15, the separated vortex A is located well away from the surface of the cylinder. At all levels of submergence, for the images at N = 15, an additional concentration of vorticity A' is generated from the left side of the cylinder; it is the sequel to the originally generated vortex A from an earlier portion of the wave cycle. The degree of concentration of vorticity A' appears to increase with decreasing submergence.

Moreover, all levels of submergence of the cylinder exhibit formation of vorticity concentrations B and D. The sequence of events leading to their initial development at N = 11, as well as their subsequent evolution at N = 15, is similar for deep (top row) and intermediate (middle row) values of submergence. At shallow submergence (bottom row of images), however, vortex B separates early from the surface of the cylinder, and at N = 11, appears immediately beneath extended vorticity concentration A. At a later time, N = 15, concentration B moves well to the left of the cylinder.

Further, vorticity concentration C continues its orbital trajectory about the cylinder at deep submergence in images N = 11 and 15, collides with the free-surface at N = 1 for intermediate submergence, and remains well submerged beneath the free-surface at the shallowest submergence, both in images N = 11 and 15.

A distinctive feature of the vorticity field development at the shallowest submergence of the cylinder is generation of an additional concentration of vorticity E from the free-surface at N = 15. It is induced by vortex D. All of these events at the shallowest submergence produce two sets of triplet vortices at N = 15; together, they form an array of six counter-rotating vortices.


pmo2@lehigh.edu