General Systems Theory Concepts in Atmospheric Flows - Rain Formation in Warm Clouds: General Systems Theory - page 13

1.6 Atmospheric Aerosol (Particulates) Size Spectrum

The atmospheric eddies hold in suspension the aerosols and thus the size spectrum
of the atmospheric aerosols is dependent on the vertical velocity spectrum of the
atmospheric eddies as shown below. Earlier Liu ( 1956 ) has studied the problem
of the dispersion of material particles in a turbulent fluid and remarks that particle
dispersion constitutes a direct and striking manifestation of the mechanism of fluid
turbulence. Grabowskii and Wang ( 2013 ) discuss multiscale nature of turbulent
cloud microphysical processes and its significant impact on warm rain initiation.
The aerosols are held in suspension by the eddy vertical velocity perturbations.
Thus, the suspended aerosol mass concentration m at any level z will be directly re-
lated to the vertical velocity perturbation W at z , i.e., W ~ mg , where g is the acceler-
ation due to gravity. Substituting in Eq. (1.6) for W and w * in terms of aerosol mass
concentrations m and m * , respectively, at normalized height z and at surface layer,
the vertical variation of aerosol mass concentration flux is obtained as follows:

mmfz = * . (1.10)

1.6.1 Vertical Variation of Aerosol Mean Volume Radius

The mean volume radius of aerosol increases with height as shown in the following.
The velocity perturbation W is represented by an eddy continuum of correspond-
ing size (length) scales z . The aerosol mass flux across unit cross-section per unit
time is obtained by normalizing the velocity perturbation W with respect to the
corresponding length scale z to give the volume flux of air equal to Wz and can be
expressed as follows from Eq. (1.6):

2

(1.11)

Wz wfzz wfz = ( ) . =

* *

The corresponding normalized moisture flux perturbation is equal to qz , where q
is the moisture content per unit volume at level z . Substituting for q from Eq. (1.7)

2

(1.12)

qz = normalized moisture fluxatlevel zqfz = .

*

The moisture flux increases with height resulting in increase of mean volume radius
of cloud condensation nuclei (CCN) because of condensation of water vapor. The
corresponding CCN (aerosol) mean volume radius r a at height z is given in terms
of the aerosol number concentration N at level z and mean volume radius r as at the
surface as follows from Eq. (1.12)

4
3

4
3

3 3 2

π rN rNfz

a

= π . (1.13)

as *