Modelling of Pollutant Transport in the Atmosphere - MANHAZ

(e.g. by following a small neutrally buoyant balloon), while Eulerian
properties imply that e.g. wind statistics that can be obtained from
simpler measurements at a fixed points (e.g. at the release point or from
a Met tower).
Five years later F. L. Richardson (1926) presented results from his
observations on "relative atmospheric diffusion". He showed, on a
distance-neighbor graph, that two-particle's relative separation on
average scaled with the particles instantaneous separation. This
observation later led him to formulate his famous “Diffusivity for
relative dispersion α l 4/3 power law ” , where l is the two particles'
instantaneous separation.
Another British scientist, G. K. Batchelor (1952), related relative
dispersion directly to scaling parameters for the turbulence itself, which
has meanwhile been discovered by Russian scientists (an example of a
turbulence scaling parameter is for instance the Kolmogorov's inertial
subrange dissipation rate ε). In his famous article "Diffusion in the Field
of Homogeneous Turbulence, II. The relative motion of particles" G. K.
Batchelor relates the standard deviation for a puff to the dissipation
rate ε for homogeneous 3-dimensional inertial subrange turbulence (σ 2 y α
εT 3 ).
Ad 3. Lagrangian Similarity Theory (Scaling)
The Lagrangian similarity approach. Similarities scaling of turbulence
means that the vertical profiles of the state quantities (such as
temperature, wind speed, humidity, pollutants etc) are uniquely
determined by the so-called scaling parameters, which are: height z above
the ground, air density ρ, buoyancy parameter g/T, surface shear stress
u*, and the vertical flux of heat H/cpρ. The prerequisites for similarity
scaling to apply is that the turbulence is homogeneous and stationary, and
that the vertical fluxes of momentum - ρu*
2 and heat H/cpρ are constant
independent of height. These assumptions can often be fulfilled in the
Planetary Surface Layer (PSL). The origins of similarity scaling for the
atmospheric surface layer turbulence has roots in early work by Russian
academicians Monin and Obukhov, who formed the similarity based Monin-
Obukhov stability parameter "L", see below.
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