Vortex formation from a cylinder in shallow water

Abstract

The near wake of a vertical, circular cylinder in shallow water is investigated using a combination of visualization marker and a technique of high-image-density particle image velocimetry. The formation of a large-scale Kármán vortex involves upward ejection of fluid through its center, which eventual leads to a horizontal vortex that induces significant distortion of the free surface. The strength of this secondary vortex is, however, an order of magnitude smaller than that of the large-scale Kármán vortex. Using global, instantaneous imaging, the relationship between patterns of streamline topology and vorticity is established for successive phases of the oscillation cycle, and in horizontal planes at and above the bed. The sequence of phase-referenced states shows that it is possible to identify topological characteristics, including the location of a specific critical (saddle) point that are consistent at elevations on and above the bed. In turn, the sequential development of topological streamline and vorticity patterns is related to time-averaged representations. At the bed, the time-averaged streamline topology downstream of the base of the cylinder takes on a form known as an owl face of the first kind, which was originally defined for a completely different exterior flow. Immediately adjacent to the base of the cylinder, an additional system of saddle points is located at either end of a nodal line. At locations above the bed, one of the two principal saddle points of the owl face of the first kind disappears and the principal foci are transformed from a stable to an unstable state. Furthermore, at progressive elevations above the bed, the degree of concentration of vorticity of the major, large-scale vortex successively decreases. In turn, the foregoing features are related to the patterns of Reynolds stress and velocity fluctuation at and above the bed.