Vortex Formation from a Cylinder in Shallow Water: Effect of Cylinder Oscillation
Submitted by rdn217 on Wed, 2013-10-16 12:53
Vortex formation from a cylinder in shallow water: Effect of cylinder oscillation. The shallow water system of the previous layout is subjected to azimuthal oscillations of the cylinder. In the left column, the perturbation is at the most unstable frequency fsL of the shear layer, and in the middle and right columns, it is at the frequency fk of inherent Kármán vortex formation. In absence of oscillation of the cylinder, values of Reynolds number Re instability parameter S are such that neither shear layer nor Kármán-like vortices occur. In the left column, the perturbation at the shear layer frequency fe/fsL = 1, and at a low amplitude θm = 1.8°, which corresponds to an arc amplitude of A/D = 0.016, induces rapid formation of the shear layer vortices, with well-defined saddle points in the streamline topology. For excitation at the Kármán frequency, the middle column of images shows an instant corresponding to the extreme counterclockwise position. The shear layer remains stable. In the right column of images, corresponding to a position close to the maximum counterclockwise rotation of the cylinder, the vorticity layer is substantially deflected inward, and the corresponding pattern of streamline topology shows a well-defined focus and saddle point in the near-wake region. Re = UD/ν = 4,400; S = cfD/hw = 0.23.
Abstract:
The unstable structure of the near-wake of a vertical cylinder, in a fully-developed, laminar free-surface layer, is characterized in relation to the unsteadiness of the horseshoe (necklace) vortex system about the upstream surface of the cylinder. A cinema technique of high-image-density particle image velocimetry allows space-time imaging of the critical regions of the flow and thereby wholefield representations of patterns of the flow structure, in conjunction with spectra and cross-spectra at a large number of points over the flow domain. Over the range of Reynolds number considered, the onset of large-scale, Kármán vortex formation remains suppressed in the near-wake, but increase of Reynolds number above a threshold value yields the onset and development of an instability mode that takes the form of a varicose, as opposed to a sinuous, pattern of vortices. It is related to the unsteadiness of the horseshoe (necklace) vortex system on the upstream side of the cylinder. The process of vortex formation in the near-wake is interpreted in terms of multiple, coexisting layers of vorticity due to both the horseshoe vortices and the vorticity layer associated with separation from the cylinder. Furthermore, it is demonstrated that when the near-wake is stable at a sufficiently low value of Reynolds number, application of external perturbations at the most unstable frequency of the separating shear layers can lead to destabilization of the near-wake to a sinuous mode of small-scale vortical structures. Moreover, perturbations applied at the expected frequency of large-scale Kármán vortex formation can also lead to destabilization of the near-wake in this mode. These types of perturbations lead to substantial alterations of the patterns of vorticity and streamline topology, as well as Reynolds stresses and entrainment velocities of the separating shear layers, along the bed, relative to patterns above the bed.
Album:
Vortex Systems in Shallow Water
