Canopy flow Examples of canopy flows canopy characterization Failure of log-law and K-theory in and over canopies Roughness sublayer and canopy flow dynamics Mixing layer analogy for canopies Potential for canopy similarity in wind power plants Acknowledged contribution from Corey Markfort, Iowa State U
Larry Schwarm Kansas Farmers M-O similarity works for Kansas vegetation cover
How about for Dense forest with (more or less) open trunk area
How about for flows over more or less urbanized regions is it a different terrain? do you think the response of turbulence would be to some extent similar?
How about this? (Elk River Industrial Wind Project, Beaumont, KS)
this formula already accounts for an average response to multiple roughness elements
How to reconciliate log law parameterization over canopies With the displacement in height d, we shift up the 0 of the mean velocity accounting for the mean momentum that is absorbed within the canopy. unknowns(3): z 0, u *, d Multiple regression results in at best ±25% error (Bradley Finnigan 1983) d compensate for the curvature of the mean velocity near the canopy top
Jackson introduced the drag partitioning concept: how much drag is related to the single roughness element as compared to the typical rough wall surface 0.7 is quite a good value... d has a dynamic significance. Whatever the origin of z, the displacement height d adjusts the reference level for the velocity profile to the height at which the mean surface shear appears to act. Shiu Yeung Hui and Anthony Crockfor
Aerodynamic force per unit volume
Manes 2011 increased permeability increased shear penetration increased drag perceived by the log layer
Leaf area index requires accurate experimental measurements, but at least we lose the dependency on z (bulk measure at each planar surface location In simulations... Aerodynamic force per unit volume often also estimated as u(z) *u(z)
3D Laser scanning and reconstruction of the volume occupied by single trees Schlegel et al. 2012
Seasonal dependency of the Leaf Area Index (Patton 2011)
canopy geometry log law parameterization FAI =frontal area index in this case we have uniformly vertical roughness elements: no z distribution of the LAI Low sparse canopy High dense canopy (limited shear penetration u * / U h peak in z 0 indicates the worst canopy (or best, depending on the goal) ~0.7h
(roughness sublayer) (roughness sublayer) (ross Primary Production (GPP) Rate of CO 2 being taken out of the atmosphere for photosynthesis measured as a flux of Co 2 Eddy covariance methods base don MO similarity do not work within the canopy
canopy height convective BL Different structure of turbulence within the canopy
The flow within and above a canopy is not a rough wall boundary layer but a mixing layer (different coherent structure contributions) The mixing layer is the turbulence shear flow formed between two co-flowing streams with different velocies. Ghisalberti and Nepf 2006 The characterics of the mixing layer is a strong inflection in the mean velocity profile.
The mixing layer has streamwise periodicity, L s which is proportional to the mean vorticity thickness The characterics of the mixing layer is a strong inflection in the mean velocity profile.
Why we talk about canopy similarity? because all the terrain types we considered at the beginning display mixing layer characteristics
Example of flow development over a canopy SAFL wind tunnel measurements An internal layer develops over the canopy generating a new log-law region where turbulence is in equilibrium with the local roughness
Canopy coherent structures Raupach also called honani waves from the wavy patterns exhibited by flexible vegetation udner the action of the wind H Nepf, MIT iso contour of 2 point correlation of the streamwise or wall normal velocity
Further characteristics of turbulence within canopy Note that a spectral shortcut implies energy is highly dissipated within the canopy, justifying an increase absorbtion of mean momentum by the surface (via enhanced drag) and thus an increased z 0 in the boundary layer parameterization Poggi 2006
Poggi 2006 z/h=1/6 z/h=1/2 z/h=2 recovery towards the classic K41 spectrum see also works (as we move away from the canopy top) C Manes, G Bois, on flows over permeable walls Note that the roughness increase with the wall permeability, consistent with a canopy type of flows
Prandtl mixing length L~prop to z mixing layer scale shedding, Stouhal number, karman vortices
Roughness characterization of a wind farm It does remind of a canopy flow with two different shear regions Wu and Porte Agel 2012, see also the work of Zhang and Markfort
following the original arguments by Raupach 1996