Interpretations of the linear phase angle trend of SD Vortex ω_x,max/min value

The FS of SD ω_x,max/min time history can be written as

ω_x,max/min = f(t) = H·sin(ωt + f)

The constant slope of linear phase change can be written as

df/dx = -118.9˚/L ≈ -2π/3L

where L is the model length. 

This suggests that the phase term in f(t) is a function of x such that

f(x) = -(m/L)x + f₀

where m = 2π/3 and f₀ = π

Thus, ω_x,max/min propagates in space and time in a wave-like form such that

f(x,t) = H(x)·sin(kx-ωt)

Wave number k = m/L (wave length λ = 2π/k = 2πL/m).  Circular frequency ω = 2πf where f = T^-1 and T is the period of pure yaw motion (i.e. the shedding frequency of SD).

Then, the phase velocity

v_p = ω/k = λ/T = 2πfL/m

Or in non-dimensional form

v_p/U_C = (2π/m)·St

where St = fL/U_C is the Strouhal number of SD vortex shedding.

For f = 0.134 Hz, L = 3.048 m, and U_C = 1.531 m/s, St = 0.2668, and with m = 2π/3,

v_p = 0.8·U_C

This indicates that ω_x,max/min propagates along the model length with a speed about 80% of U_C.