First‐order turbulence closure for modelling complex canopy flows

Abstract

Simple first‐order closure remains an attractive way of formulating equations for complex canopy flows when the aim is to find analytic or simple numerical solutions to illustrate fundamental physical processes. Nevertheless, the limitations of such closures must be understood if the resulting models are to illuminate rather than mislead. We propose five conditions that first‐order closures must satisfy, then test two widely used closures against them. The first is the eddy diffusivity based on a mixing length. We discuss the origins of this approach, its use in simple canopy flows and extensions to more complex flows. We find that it satisfies most of the conditions and, because the reasons for its failures are well understood, it is a reliable methodology. The second is the velocity‐squared closure that relates shear stress to the square of mean velocity. Again we discuss the origins of this closure and show that it is based on incorrect physical principles and fails to satisfy any of the five conditions in complex canopy flows; consequently its use can lead to actively misleading conclusions.

Boundary-Layer Flow Over Complex Topography

“…Eddy covariance observations do show countergradient turbulent fluxes in some canopies, suggesting that local parameterisation is not appropriate, however various studies have shown that in practice first order schemes are useful (Grant et al, 2016). The assumptions and limitations of first order canopy closure schemes are analysed by Finnigan et al (2015). There are a number of reasons for the surprising success of first order closure schemes.…”

Turbulence Characteristics Across a Range of Idealized Urban Canopy Geometries

“…Based on similarity arguments Finnigan et al (2015) argued that when most of the momentum is absorbed as drag by the canopy elements rather than by the ground, then there is only one relevant length scale in the canopy (S(z)C d (z)) −1 , which can be interpreted as a drag length scale L c (Belcher et al 2003;Coceal and Belcher 2004). Here S(z) is the sectional obstacle area density (obstacle area facing the wind divided by canopy air volume) and C d (z) is the sectional drag coefficient.…”

“…Vegetation canopy elements are usually either very close together (for example in wheat crops) or form a porous mesh (for example the foliage in a rainforest crown), so the mixing-layer eddies generated at canopy top are much larger than the separation of canopy elements (Raupach et al 1996). These eddies are not local to the canopy elements and are the dominant turbulent motions in the canopy, a point that supports the use of a constant turbulent length scale in vegetation canopy models (Finnigan 2000;Harman and Finnigan 2007;Finnigan et al 2015).…”

Review of “A model-based analysis of foliar NOx deposition” by Erin R. Delaria and Ronald C. Cohen

“…What I could reconstruct is: A) a relationship for in canopy u_star on above canopy u_star is given and the work of Yi et al 2008 is cited as a source. Finnigan et al 2015 showed that some of the assumptions of the work of Yi et al 2008 are error prone. The relationship given might still be applicable but needs additional justification.…”