Upstream isosurfaces of spanwise vorticity at .
The overall flow pattern with symmetric twisted chainlike vortex dislocations identified by -definition , .
Topology of vortex linking between three components of vorticity in vortex dislocation, . Iso-surfaces of vorticity: , , .
Top view of vortex linking between spanwise and streamwise vorticity in the vortex dislocations at certain middle downstream positions. and represent spanwise vortices with positive and negative signs, respectively. and show the streamwise vorticity branches diverted from the spanwise vortices at two positions with the largest phase differences in spanwise vortices. The vortex linking, back and forth, of two components of vorticity is shown in the figure at .
Distributions of streamwise vorticity at different vertical planes, , (a) ; (b) ; (c) .
Distributions of vertical vorticity at different vertical planes, , (a) ; (b) ; (c) .
Variations of vorticity lines at different downstream positions. The lines pass through several places denoted by the coordinates in the diagram. The background is a spanwise vorticity pattern at the plane of .
Spanwise vortex twisting, vortex splitting, and reconnection represented by the variations of vorticity lines passing through the locations denoted by the coordinates in the diagram. The background is a spanwise vorticity pattern at the plane of .
Behavior of vortex lines among three adjacent spanwise vortices in the chainlike vortex dislocations at . In the figure vortex lines emitted from one side of a spanwise vortex (in the middle) and two adjacent vortices are drawn. Spanwise vortex twisting, vortex branching, complex linking, as well as vortex line winding around the other vortices are illustrated. (a) Three-dimensional view; (b) the end view.
(a) The phase variation of spanwise vortex with spanwise direction at different streamwise positions. (b) The phase difference in spanwise vortex along the spanwise direction.
Contours of vertical fluctuating velocity in the plane at , .
Contours of spanwise fluctuating velocity in plane at , .
Fluctuating velocity profiles (transverse) at different streamwise positions, and , (a) ; (b) ; (c) .
Mean velocity profiles (transverse) at different streamwise positions, and , (a) ; (b) ; (c) .
The time history and corresponding spectra of velocity components of (a) at position of and (b) at position of at certain spanwise positions.
Time sequence of large-scale spotlike modes of vortex dislocation, visualized by (a) -definition and (b) the distribution of streamwise vorticity, with the evolution of time at , 328, and 348, respectively. (a) shows that the spotlike vortex dislocation is produced periodically in the central region. In the vortex dislocation, spanwise vortex splitting and reconnection can be seen clearly. On the other hand, the streamwise vorticity component is mainly produced in the process of spanwise vortex splitting and reconnection, as shown in (b). These distributions also display the periodicity of the appearance of spotlike vortex dislocation pattern, as shown in (a).
Vortex linking in the spotlike vortex dislocation structure illustrated by vortex line behavior at . At the moment a spotlike dislocation structure is passing through at , the spanwise vortex splitting and linking to its adjacent vortices occurred in the middle of the dislocation structure are shown. While at the position of vortex lines show the beginning aspect of another following spotlike dislocation.
Time signals of vertical velocity component at different spanwise positions of . In the central region of the span, , velocity signals show noticeable low amplitude fluctuation. It is periodically produced due to the passage of a vortex dislocation. Away from the central region the signals respond to the passage of a von Kármán vortex row.
The spectra of vertical velocity component . There are two incommensurable frequencies of and in the region of , while only one single peak occurs at . The “beat” frequency, , at 0.0244 can be found. It shows the periodic appearance of spotlike vortex dislocation. Besides there are harmonic peaks in the spectra.
Top view of time sequence of the spanwise systematic modes of vortex dislocation for at (a) , (b) , and (c) . The vortex structures are visualized by -definition . The vortex dislocation is produced successively once each wavelength of the sinusoidal wave disturbance along the span and travels downstream. At , the series dislocations move downstream almost out of the computational domain.
The isovorticity surface of streamwise and vertical components for , (a) and (b) at , 160, and 240. Those components of vorticity are produced by spanwise vortex splitting and reconnection. It is shown that at the Kármán vortex shedding almost disappears, while vertical vorticity still exists and even becomes a dominant component in the wake-type shear flow.
Time series of fluctuation velocity (a) and (b) at for . It is clearly shown that with the increase in time the fluctuation of velocities decreases to zero that means the Kármán vortex shedding has been completely suppressed. These behaviors are consistent with the features of the variation of flow pattern and vorticity distributions in Figs. 20 and 21.
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