Phase-Averaged Velocity Field

1. Axial velocity U field

The overall trend of U is
- Thin boundary layer (BL) at the bow.
- BL grows along the model length and becomes very thick at the stern.

The shape and size of the BL are
- typically asymmetric about the model center plane,
- change continuously with time
- possibly interacting with the flow induced by nearby vortices.

Dead flow zone (e.g., where U < 0.5, the dark-blue colored contour level in the figure) appear at the stern, locally inside the BL and in the wake near at the free surface.

U_mean is the average U value over the region where U < 0.9 at each x location
U_mean oscillates with γ at all x locations
Period mean value of the U_mean time history, H₀, is almost flat along the model length (H₀ ≈ 0.8) up to x = 9.935, and then moderately decrease at x = 0.135 (H₀ = 0.75)
The oscillation amplitude, H₂, is as well nearly constant (H₂ ≈ 0.009 or 1.2% of H₀), and then increases rather sharply at the stern (H₂ = 0.023 or 3% of H₀ at x = 1.035)

U_min is the minimum U value within the flow field at each x location
U_min time histories as well exhibit oscillations along with the pure yaw motion, i.e., with γ.
Contrary to U_mean, the period mean H₀ and the oscillation amplitude H₂ of U_min time histories are not flat, but change along the model length.
H₀ = 0.67 at x = 0.135 and decreases nearly linearly along x, and H₀ = 0.39 at x = 0.135.
H₂ = 0.015 (2% of H₀) at x = 0.135 and increases gradually to H₂ = 0.038 (9% of H₀) at x = 0.935, then sharply to H₂ = 0.071 (18% of H₀) at x = 1.035.