A meandering plume model can predict the mean concentration as well as the higher
order concentration statistics that are required when addressing topics such as
'peak-to-mean' concentration ratios, odour estimates, uncertainty in air quality
models, and accidental release of toxic and flammable gases.
We have developed a simple and practical meandering plume model for the prediction
of concentration statistics due to a point source (stack) within the daytime convective
boundary layer. There the vertical turbulence is highly inhomogeneous and positively
skewed, resulting in counter-gradient concentration fluxes that cannot be satisfactorily
described by standard models (e.g., by a gradient-transfer model or by a Gaussian
plume model).
The meandering-plume concept was first applied by Gifford (1959) for homogeneous
Gaussian turbulence conditions, assuming that the total dispersion consists of
two independent parts: a meandering part and a relative-diffusion part. The fluctuations
are produced solely by the meandering of the ensemble-mean instantaneous plume.
Application to the convective boundary layer has not been properly attempted until
now.
Our meandering plume model overcomes the problems of the skewed turbulence characteristics
of the convective boundary layer. The meander component in the model is derived
from a one-particle Lagrangian stochastic dispersion model by requiring that the
meander and relative dispersion components correctly balance the first two total
dispersion moments. Balancing of the third total moment implies a skewed relative
dispersion, for which a bi-Gaussian distribution is used. The relative dispersion
variance is parameterised, and the in-plume fluctuations in the relative coordinate
system are accounted for via a gamma probability density function. The model reverts
to the standard formulation for homogeneous Gaussian turbulent flows. It has been
tested using laboratory data on the mean concentration and fluctuation intensity
(see Luhar et al., 2000).
The above animation shows a sequence of 15 random realisations of an instantaneous
plume as described by the skewed meandering-plume model in the vertical plane.
The horizontal axis is the downwind distance scaled by u zi /w* while
the vertical axis is the height scaled by zi, where u is the
mean wind speed, zi is the boundary-layer height and w* is the
convective velocity scale. The source is at a height of 0.25 zi. The colour
of the plume in the animation is proportional to the crosswind centreline concentration;
the classic looping (or meandering) pattern of the plume under convective conditions
can be observed. At short distances (less than about 1.5), meandering controls
the concentration fluctuation intensity, while the in-plume fluctuations dominate
at larger distances. The plume descends to the ground more often than it travels
upwards, suggesting a mean descent of the locus of the averaged
plume, as confirmed by field and laboratory studies.
References
Gifford, F. A., 1959. Statistical properties of a fluctuating plume dispersion
model. Advances in Geophysics 6, 117-137.
Luhar, A. K., Hibberd, M. F. and Borgas, M. S., 2000. A skewed meandering-plume
model for concentration statistics in the convective boundary layer. Atmospheric
Environment, 34, 3599-3616.
The code for the animator can be viewed here. For
more information, e-mail: ashok.luhar@csiro.au
