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Boundary-Layer Meteorology

, Volume 122, Issue 2, pp 367–396 | Cite as

Shear stress partitioning in large patches of roughness in the atmospheric inertial sublayer

  • John A. Gillies
  • William G. Nickling
  • James King
Article

Abstract

Drag partition measurements were made in the atmospheric inertial sublayer for six roughness configurations made up of solid elements in staggered arrays of different roughness densities. The roughness was in the form of a patch within a large open area and in the shape of an equilateral triangle with 60 m long sides. Measurements were obtained of the total shear stress (τ) acting on the surfaces, the surface shear stress on the ground between the elements (τS) and the drag force on the elements for each roughness array. The measurements indicated that τS quickly reduced near the leading edge of the roughness compared with τ, and a τS minimum occurs at a normalized distance (x/h, where h is element height) of \(\approx -42\) (downwind of the roughness leading edge is negative), then recovers to a relatively stable value. The location of the minimum appears to scale with element height and not roughness density. The force on the elements decreases exponentially with normalized downwind distance and this rate of change scales with the roughness density, with the rate of change increasing as roughness density increases. Average τS : τ values for the six roughness surfaces scale predictably as a function of roughness density and in accordance with a shear stress partitioning model. The shear stress partitioning model performed very well in predicting the amount of surface shear stress, given knowledge of the stated input parameters for these patches of roughness. As the shear stress partitioning relationship within the roughness appears to come into equilibrium faster for smaller roughness element sizes it would also appear the shear stress partitioning model can be applied with confidence for smaller patches of smaller roughness elements than those used in this experiment.

Keywords

Atmospheric inertial sublayer Drag partition Roughness arrays Shear stress partitioning 

List of Symbols

Af

frontal area of roughness elements (m2)

Au

unit area over which surface shear stress associated with a roughness element is distributed (m2)

b

element breadth (m)

Cd

surface drag coefficient

Cde

roughness element drag coefficient

Cdr

rough surface drag coefficient

Cds

smooth surface drag coefficient

cv

coefficient of variation

d

displacement height (m)

F

force on a roughness element (N)

g

acceleration due to gravity (m s−2)

h

element height (m)

IBL

internal boundary layer

ISL

inertial sublayer

m

empirical constant between 0 and 1

n

number of roughness elements occupying the ground area of the roughness array

NDD

normalized downwind distance (x/h)

NED

normalized element drag

R

average friction velocity ratio

Rl

local friction velocity ratio at different positions in a roughness array

Re

Reynolds number

Rt

threshold wind friction velocity ratio

SD

standard deviation of a mean value

u

wind speed (m s−1)

u*

wind friction velocity (m s−1)

u* tR

threshold wind friction velocity with roughness elements (m s−1)

u* tS

threshold wind friction velocity of bare surface (m s−1)

x

downwind distance (m)

z

reference height above surface (m)

zw

roughness sublayer height (m)

zo

aerodynamic roughness length (m)

β

ratio of element to surface drag coefficients

φm

dimensionless wind speed gradient

κ

von Kármán constant (0.4)

λ

roughness density

μ

molecular viscosity (N s m−2)

ρa

air density (kg m−3)

σ

roughness element basal area to frontal area ratio

τ

total surface shear stress (N m−2)

τS

surface shear stress on the area not covered by the roughness elements (N m−2)

τR

surface shear stress attributed to the roughness elements (N m−2)

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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • John A. Gillies
    • 1
  • William G. Nickling
    • 2
  • James King
    • 2
  1. 1.Particle Emissions Measurement Laboratory, Division of Atmospheric SciencesDesert Research InstituteRenoUSA
  2. 2.Wind Erosion Laboratory, Department of GeographyUniversity of GuelphGuelphCanada

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