Turbulence and Dispersion of Contaminants in the Planetary Boundary Layer 55
central regions of the CBL and with small values at z = 0 and z = z i . The formulas
(3.73) and (3.77) describe an inhomogeneous turbulence and consider the memory
effect contained in the autocorrelation function. These parameterizations are particularly suitable to represent turbulent transport of contaminants released from
an elevated continuous point source. On the other hand, Equations 3.75 and 3.79
describe the turbulent transport of contaminants released by infi nite area sources
and, consequently, the parameterization Equations 3.75 and 3.79 allow to represent
the vertical transfer of species as humidity, momentum, and heat in the PBL.
3.5.1 TURBULENT TRANSPORT MODELING OF CONTAMINANTS
DURING THE DECAYING OF A CBL
Equations 3.30, 3.32, 3.77, and 3.79 describe the transport process associated to a
stationary and FDT. This means that a turbulent fi eld as proposed by Kolmogorov
exhibits self-similar and scale-invariance characteristics. However, it is important
to note that about half hour before sunset, over land, the surface heat fl ux (positive during the day) begins to decrease and then the thermals cease to form and
along the time the turbulence tends to disappear in the CBL. The new resulting layer
of air separated from the surface by the stable nocturnal boundary layer presents
characteristics of the decaying convective turbulence (RL). Concerning to this layer,
it is important to note that a large number of elevated stacks release contaminants
around the evening transition. This sunset transition time occurs regularly on a daily
basis and for this situation the derivation of eddy diffusivities in this period provides
a turbulence parameterization for atmospheric diffusion models. The RL is a neutrally stratifi ed elevated layer that is not infl uenced by turbulent transport of surfacerelated characteristics and their properties are generally observed to be initially the
same as those of the recently decayed CBL.
For a homogeneous and isotropic turbulence, an approach to derive eddy diffusivities for convective decaying turbulence in the RL was proposed by Goulart
et al. (2002). This model is based on the budget equation for the TKE in which buoyant contribution was disregarded and only the inertial transfer term is retained. The
results of this approach were compared with a decaying vertical eddy diffusivity
obtained from LES data (Nieuwstadt and Brost, 1986).
From this comparison both vertical eddy diffusivities show a good agreement for
small decaying times. For larger times, as a consequence of –2 exponent obtained for
the decaying vertical velocity variance calculated from LES, the LES vertical eddy
diffusivity decays strongly faster.
More recently, Goulart et al. (2003) developed a theoretical model to study the
TKE decaying in a CBL. This model is also based on the dynamical energy spectrum
equation in which the buoyancy and inertial transfer terms are retained. Different
from Goulart’s papers, Degrazia et al. (2003) by employing Heisenberg’s elementary
decaying turbulence theory derived a vertical eddy diffusivity applied to the RL.
This modeled eddy diffusivity was compared with LES data from NB, and the results
showed that the model is not a good estimator of the vertical velocity variance as
calculated from the LES.
© 2010 by Taylor and Francis Group, LLC
central regions of the CBL and with small values at z = 0 and z = z i . The formulas
(3.73) and (3.77) describe an inhomogeneous turbulence and consider the memory
effect contained in the autocorrelation function. These parameterizations are particularly suitable to represent turbulent transport of contaminants released from
an elevated continuous point source. On the other hand, Equations 3.75 and 3.79
describe the turbulent transport of contaminants released by infi nite area sources
and, consequently, the parameterization Equations 3.75 and 3.79 allow to represent
the vertical transfer of species as humidity, momentum, and heat in the PBL.
3.5.1 TURBULENT TRANSPORT MODELING OF CONTAMINANTS
DURING THE DECAYING OF A CBL
Equations 3.30, 3.32, 3.77, and 3.79 describe the transport process associated to a
stationary and FDT. This means that a turbulent fi eld as proposed by Kolmogorov
exhibits self-similar and scale-invariance characteristics. However, it is important
to note that about half hour before sunset, over land, the surface heat fl ux (positive during the day) begins to decrease and then the thermals cease to form and
along the time the turbulence tends to disappear in the CBL. The new resulting layer
of air separated from the surface by the stable nocturnal boundary layer presents
characteristics of the decaying convective turbulence (RL). Concerning to this layer,
it is important to note that a large number of elevated stacks release contaminants
around the evening transition. This sunset transition time occurs regularly on a daily
basis and for this situation the derivation of eddy diffusivities in this period provides
a turbulence parameterization for atmospheric diffusion models. The RL is a neutrally stratifi ed elevated layer that is not infl uenced by turbulent transport of surfacerelated characteristics and their properties are generally observed to be initially the
same as those of the recently decayed CBL.
For a homogeneous and isotropic turbulence, an approach to derive eddy diffusivities for convective decaying turbulence in the RL was proposed by Goulart
et al. (2002). This model is based on the budget equation for the TKE in which buoyant contribution was disregarded and only the inertial transfer term is retained. The
results of this approach were compared with a decaying vertical eddy diffusivity
obtained from LES data (Nieuwstadt and Brost, 1986).
From this comparison both vertical eddy diffusivities show a good agreement for
small decaying times. For larger times, as a consequence of –2 exponent obtained for
the decaying vertical velocity variance calculated from LES, the LES vertical eddy
diffusivity decays strongly faster.
More recently, Goulart et al. (2003) developed a theoretical model to study the
TKE decaying in a CBL. This model is also based on the dynamical energy spectrum
equation in which the buoyancy and inertial transfer terms are retained. Different
from Goulart’s papers, Degrazia et al. (2003) by employing Heisenberg’s elementary
decaying turbulence theory derived a vertical eddy diffusivity applied to the RL.
This modeled eddy diffusivity was compared with LES data from NB, and the results
showed that the model is not a good estimator of the vertical velocity variance as
calculated from the LES.
© 2010 by Taylor and Francis Group, LLC