Axial Vorticity Field

SD vortex is the most dominant vortex. SD vortex is formed behind the sonar dome and detaches and decay, and a new counter rotating SD vortex is formed.
BK vortex is the second dominant vortex. Two BK vortices are generated locally near around the portside and starboard bilge keel positions.
BK vortices grows in size along the aft body, but usually diffused and not clearly seen at the stern.
AKC vortex is the third dominant vortex, which can be seen most clearly behind x = 0.935
Other vortices such as the FK, AK, and FS vortices are not clearly detected due to limited resolution of the measurement in the longitudinal direction (6 x locations along the model length).

1. Sonar dome (SD) vortex

ω_x,max/min is defined such that the maximum ω_x value when ω_x > 0 and the minimum ω_x value when ω_x <0 at a given phase γ position, and at each x location
Time histories of ω_x,max/min are typically 1^st-order dominant harmonic oscillation, of which amplitude and phase angle are designated as H and f, respectively.
H = 292 is the largest at x = 0.135 and drops fast to H = 159 at x = 0.335 and increases gradually to H = 189 at x = 0.735 and then decreases to H = 129 at x = 1.035.
Phase angle f decreases nearly linearly along the model length.

BK vortices are generated in pairs. These two vortices typically have the same direction of rotation whereas different strength according to the direction and magnitude of the nearby incoming cross-flow.
The side where the incoming flow is stronger is referred as the 'wind' side and the other side as the 'leeward' side.
At x = 0.535, although BK vortices are very local and small in size, ω_x,max/min value is large, H = 115 (39% of SD) at the wind side and H = 71 (24% of SD) at the leeward side.
At x = 0.735, BK vortices grow in size but decays in strength, H = 80 (27% of SD) at the wind side and H = 25 (9% of SD) at the leeward side.

x = 0.535	x = 0.735