I am trying to understand the calculation of the wind speeds at forest edge. I am pretty new in wind simulation and profiles in general, so I am sorry if asking simple questions.
I have found that it is possible to calculate the wind speed as log wind profile based on friction velocity, roughness length (${z0}$), zero place displacement (${d}$), and von Karman's constant (${k}$). As I am working at forest edge, my estimates are:
z0 = 0.06 # m, roughness length, 1/10 of the surface roughness, forest:0.5-1m
d = h/3*2 # m, zero place displacement, height (m) above the ground with 0 wind speed (2/3 or 3/4 of average height of obstacles)
k = 0.41 # no unit, von Karman constant
Formula:
# predict speeds for individual segments of the tree
u_z = frict_velocity/k*log((z-d)/z0)
However, it seems that friction velocity is not a constant, and needs to be calculated based on the wind speed measured at two heights. Well, I don't have two heights. The highest estimation I can get is that wind speed above canopy is ${12ms^{-1}}$ and at the height ${d}$ is 0, as estimated above. The formula is specified as shear velocity:
u_canopy = 12 # speed on canopy top
u_d = 0 # speed on height d, which is 0
z_canopy = 25 # height of the canopy, equals tree height
z_d = d # height of the wind speed 0, equals to d
frict_velocity = k*(u_canopy - u_d)/log((z_canopy - d)/(z_d - d))
Well, this approach obviously predict just values higher than ${d}$, even if all tree segments should have 0 value instead.
Is my prediction of the wind speed on every segment ${z}$ right? Or, is there a way how to simply use the "friction velocity" constant, as I don't have wind speed estimation at two vertical heights?
My goal is to predict wind speed on every segment (${z}$) and convert it to wind force to uproot the tree. The models should be included within a simulation study, so instead of specific single tree condition I am hoping to get some more general relationships.
