This equation is like Eq. (2.3), which is related to momentum flux and vertical
gradient velocity in the laminar boundary layer. Taking Eq. (2.19) and combining it
with Eqs. (2.10), (2.15), and (2.17) gives
K M ¼ ku à z À d
ð
Þ¼lu Ã
ð2:20Þ
if z exceeds d at a given height, the turbulent diffusivity is equal to the product of
friction velocity and size of eddies. Thus, in the surface layer directly above vegetation, the magnitude of a specified gradient will decrease in height to compensate
for the linear increase in height of turbulent diffusivity.
Definitions of turbulent diffusivity coefficients for sensible heat, water vapor or
any other gas, K H , K V, and K s , are analogous
K H¼ÀH= @ qc p T
ð Þ=@z
½
ð2:21Þ
K v ¼ ÀLE= @ qq
ð Þ=@z
½
ð 2:22Þ
K s ¼ ÀF= @ qS
ð Þ=@z
½
ð 2:23Þ
In Eq. (2.22), variable q represents the density of moist air and variable q is the
specific humidity defined as the mass of water vapour per unit mass of humid air
(see Eqs. (4.13) and (4.14), pg. 116). Specfic humidity is a variable useful for issues
of water vapour transport at lower atmosphere, because it is independent of temperature (see Eq. 3.23 in pg. 38). Variables @qq=@z, @qS=@z, H, LE, and F are,
respectively, the gradients for absolute humidity, concentration of a hypothetical
gas (e.g. CO 2 ), sensible heat flux, latent heat flux, and evapotranspiration and flux
of a hypothetical gas.
Analysis of aerodynamic drag is based on concepts that are analogous to Ohm's
Law in electrical circuits
Electrical resistance ¼
potencial difference
current intensity
ð2:24Þ
If the potential difference is substituted by the concentration (quantity per unit
volume) and the intensity of the current substituted by the flux (quantity per unit
area per unit time), for the linear momentum, then Eq. (2.24) becomes
Aerodynamic resistance ¼
Concentration difference
flux
ð2:25Þ
For a scalar or vector quantity of dimension Q, the concentration dimensions are
Q/L and those for the flux are Q/TL
2 , so that the aerodynamic resistance dimensions
become T/L or (velocity)
−1 .
2.2 Turbulent Diffusivity Coefficients
21
gradient velocity in the laminar boundary layer. Taking Eq. (2.19) and combining it
with Eqs. (2.10), (2.15), and (2.17) gives
K M ¼ ku à z À d
ð
Þ¼lu Ã
ð2:20Þ
if z exceeds d at a given height, the turbulent diffusivity is equal to the product of
friction velocity and size of eddies. Thus, in the surface layer directly above vegetation, the magnitude of a specified gradient will decrease in height to compensate
for the linear increase in height of turbulent diffusivity.
Definitions of turbulent diffusivity coefficients for sensible heat, water vapor or
any other gas, K H , K V, and K s , are analogous
K H¼ÀH= @ qc p T
ð Þ=@z
½
ð2:21Þ
K v ¼ ÀLE= @ qq
ð Þ=@z
½
ð 2:22Þ
K s ¼ ÀF= @ qS
ð Þ=@z
½
ð 2:23Þ
In Eq. (2.22), variable q represents the density of moist air and variable q is the
specific humidity defined as the mass of water vapour per unit mass of humid air
(see Eqs. (4.13) and (4.14), pg. 116). Specfic humidity is a variable useful for issues
of water vapour transport at lower atmosphere, because it is independent of temperature (see Eq. 3.23 in pg. 38). Variables @qq=@z, @qS=@z, H, LE, and F are,
respectively, the gradients for absolute humidity, concentration of a hypothetical
gas (e.g. CO 2 ), sensible heat flux, latent heat flux, and evapotranspiration and flux
of a hypothetical gas.
Analysis of aerodynamic drag is based on concepts that are analogous to Ohm's
Law in electrical circuits
Electrical resistance ¼
potencial difference
current intensity
ð2:24Þ
If the potential difference is substituted by the concentration (quantity per unit
volume) and the intensity of the current substituted by the flux (quantity per unit
area per unit time), for the linear momentum, then Eq. (2.24) becomes
Aerodynamic resistance ¼
Concentration difference
flux
ð2:25Þ
For a scalar or vector quantity of dimension Q, the concentration dimensions are
Q/L and those for the flux are Q/TL
2 , so that the aerodynamic resistance dimensions
become T/L or (velocity)
−1 .
2.2 Turbulent Diffusivity Coefficients
21