# Does within-canopy wind direction correlate with wind above the planetary bounday layer?

Wind above the planetary boundary layer (PBL) tends to be fairly smooth and constant over short periods of time. Below the planetary boundary layer, the smoothness is broken by eddies caused by friction with the land surface. Below the canopy, wind is presumably even more turbulent, and much slower on average. I'm interested to know how the over-all effect of those eddies changes wind direction within the canopy.

How much do eddies between the PBL and the ground disperse wind direction? Is wind direction below the canopy still correlated with the wind direction above the PBL? And does wind speed follow a similar pattern?

Turbulence is a property of the flow, not a physical characteristic of the fluid. Turbulent flows in nature are evolving due to external influences and at present time there are very few evolving turbulent flows which are well understood. The boundary conditions, such as distribution of canopy, geomorphology, all play a crucial role in determining the turbulent dynamics. All turbulent flows are different but they have similar intrinsic dynamics and through statistical means one can relate the properties of the mean flow to the turbulent dynamics.

"Big whorls have little whorls That feed on their velocity; And little whorls have lesser whorls; And so on to viscosity."

Lewis Fry Richardson

Turbulence is a multiscale phenomenon where small eddies in turbulence have very short timescales. This alone tends to make them statistically independent from the mean flow. Therefore, smallscale motion depends only on the rate at which it is supplied energy from the larger scales, and the rate at which kinetic energy is dissipated into heat. The two rates of change are assumed the same so that the net rate of change is small comparing to the rate of dissipation.

This is the basis for Kolmogorov's universal equilibrium theory. It basically says that the rate of energy supply to smallscale eddies is equal to the the dissipation rate:

$$U^3/L \sim \epsilon \, .$$

In other words, the dissipative effects of viscosity can be estimated from the large scale dynamics, which are effectively inviscid. Inertial effects cause a transfer of energy from small to large wavenumber space by vortex stretching.The mean flow kinetic energy transforms into turbulent energy in the form of large eddies which cascade down to smaller eddies and so on, the remaining fluctuations are ultimately dissipated by viscous damping.

Turbulent velocity fluctuations generate large momentum fluxes between different regions of the flow which is a process analogous to stress (Reynolds stresses). The Reynolds stress is what quantifies the contribution of the turbulent motion to the mean flow. Because the momentum transfer mechanism resembles molecular diffusion, turbulent moment exchange is modeled with an eddy viscosity.

All this discussion is still inside the boundary layer itself. Outside the boundary layer is the mean wind which supplies the necessary shear for turbulence inside the boundary layer. Although this wind is not affected by the turbulent fluctuations within the boundary layer, it is the reason why they exist.

• Um.. thanks, but I don't think that answers my question, which may have been phrased poorly. Basically, I want to know if the mean wind direction and speed is the same above and below the canopy, and how strongly it is correlated (where "mean" is over some short period, say 30 minutes). That is, if you've got a 30 knot noreaster above the canopy, what would you expect the distribution of wind direction and speed (wind-rose?) to be below the canopy? – naught101 Apr 9 '15 at 0:59