Coastal (including sea-breeze) fumigation is a turbulent dispersion process: a plume, released from a tall stack within
the stable (or neutral) onshore breeze, is entrained into the growing thermal internal boundary layer (TIBL) that forms over
land. The plume is subsequently mixed to the ground by the convective turbulence within the TIBL (see
illustration).
This coastal fumigation generally persists for several hours, and may lead to high ground level concentrations of pollutants.
Mathematical modelling of fumigation is of considerable practical importance since many potentially polluting installations are located
on the coast.
Several fumigation models are currently in use for regulatory applications (e.g. Misra, 1980). However,
most models assume that a plume mixes instantaneously and/or uniformlyin the vertical immediately after it has encountered the TIBL.
This assumption has been shown to yield inaccurate predictions of the GLC when the entrainment rate is large and/or the vertical plume spread
small at the plume-TIBL interface (Luhar and Sawford, 1996). Also, no allowance is made in the current regulatory models
to account for the inhomogeneity and skewness of convective turbulence within the TIBL.
We have developed a new analytical model of fumigation based on a probability density function (PDF) approach
(Luhar, 1995; Luhar and Sawford, 1996). It represents the vertical mixing process more realistically
than the existing models by accounting for non-instantaneous and non-uniform mixing and including the skewness effects through the use of a
bi-Gaussian PDF. The model has been applied to simulate data from the Kwinana
Coastal Fumigation Study, and our water tank experiments(Hibberd and Luhar, 1996).
The top plot in the animation shows a sequence of fumigation patterns (represented by the centreline concentration) determined by the PDF model
for 12 values of non-dimensional entrainment rate (we /w *) distributed between 0.01 (slow) and 0.3 (fast).
Here we is the TIBL growth rate at the point where the plume centreline intersects the top of the TIBL and w*
is the convective velocity scale in the turbulent TIBL. The colour of the plume is proportional to the concentration, and the green line represents
the parabolic growth of the TIBL downwind.
The bottom plot shows the corresponding ground level concentrations. A form of mixed-layer scaling has been used so that the distribution of
concentrations becomes a function of only we /w* and the plume spread in the stable layer above the TIBL. In the animation,
the plume spread in the stable layer is fixed (Briggs' (1973) rural dispersion parameters for stability F (from Panofsky and Dutton,
1984)), so the concentration distribution is a function of only the entrainment rate.
The downwind distance from the coastline is scaled by U zio/ w*, while height is z scaled by zio.
Here U is the mean wind speed, and zio is the effective height of the plume. Ground level concentration is scaled by
q /(U z2io), where q is the point-source mass emission rate.
The animation shows that when the entrainment rate is smaller, the area of interaction between the plume and the TIBL is larger:
the plume is more diluted prior to its entrainment into the TIBL and the GLC curve is flatter, with a smaller peak value occurring further downwind.
When the entrainment rate is larger, the more concentrated plume entrains into the TIBL over shorter downwind distances and the GLC distribution is
more peaked.
An example: calculate GLCs during coastal fumigation
(Use [Tab] key or Mouse to move to entry boxes)
(See the Mixing Height Model
on this Site to estimate surface heat flux and vertical temperature gradient.)
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