Deducing the velocity field of wind from the motion of plants I am developing a project for the subject of fluid mechanics and I had a question. The project we want to develop involves using wind and a small hill as a giant wind tunnel. The hill is filled with wheat and when there is wind, the wheat is bent and you can see a black spot propagating through the field. I thought that if the speed of those spots where measured, you could have the velocity field close to the surface for the whole hill. Then we could apply the equations to determine if the velocity field of a horizontal wind with that obstacle corresponds to the experimental results.
I assume that the propagation of the black spots is the speed of wind in that small region.  The main question I have is regarding how wind behaves. Could I consider that the entering wind has the same speed in the vertical axis ?. Worded in another way, is wind locally uniform ? The hill is surrounded by flat ground, so there are not any obstacles surrounding it.
 A: I like the idea and the ambition of your question, however, there are some difficulties.
Firstly, and most importantly, as @Anders Sandberg rightly commentated, the flow is indeed turbulent, so there is no uniformity we can hope for (neither in space nor in time). What could be a goal is to measure statistics of the flow, long-term averages etc.
Some more details:

*

*The black spot you mention might be what is know as a "cat's paw", a turbulent phenomenon that is often seen in dark or rippled spots sweeping over a water surface. (https://www.youtube.com/watch?v=WzCajzzfu-k) (An interesting reference not just for this aspect might be R.S. Scorer's "Environmental Aerodynamics".)

*There is no uniformity of velocity in the vertical direction: Over a flat surface the velocity profile increases as the log of the vertical coordinate. (https://en.wikipedia.org/wiki/Law_of_the_wall) Boundary conditions for this also depend on surface roughness - i.e. a wheat field has a different influence on this profile as compared to bare ground.

*The hill changes the above-mentioned logarithmic profile and in part diverts the flow to the sides, around it (depending on shape, height etc. etc. For more detail - but probably overkill for your project description - there are some papers by Jackson&Hunt, mid- to late seventies, on a perturbative calculation of that flow profile.).

A: These spots you see are the waves generated on the plant canopy due to the coherent turbulent structures in the wind field. This waves are also called honami and they are mostly associated with the sweep and ejection type of structures. A sweep event means a higher momentum air moving downwards. In general, the convective (advective) velocities are not identical to the local flow velocity, but will be close. Remember, that sweep structures are higher-momentum regions and will be somewhat faster. Ejections, on the other hand, will be somewhat slower.
They have been studied for a long time. See, for example, Finnigan (1979) Turbulence in waving wheat. A simple mathematical model was proposed by Finnigan & Mulhearn (1978)
The wind profile in the atmospheric surface layer (the lowest part of the atmospheric boundary layer) can most often be modeled as logarithmic as the link to the law-of-the-wall given by kricheli shows. However, the law-of-the wall proper is for smooth surfaces. The rough wall profiles are usually formulated using equivalent sand paper roughness engineering, but boundary layer meteorology uses a different description.
Firstly you have to shift your zero plane (the zero-plane-displacement parameter d) and the in real atmosphere there will be departures from the logarithmic wind profile due to stability according to the Monin-Obukhov similarity theory.
The roughness length is an important parameter for the surface layer velocity profile. Unfortunately, it is not a constant and will definitely depend on the velocity itself because of the interaction of the flow with the plant canopy.
