Ecoinformatics Problems of Global Climate Change - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 474

hence, depend on z i . The total energy of turbulence is a composition of two energies
generated by mechanical ( ˃ wm ) and convective ( ˃ wc ) forces:

2 2 2

r

w ¼ r wm þ r wc :

ð 5 : 13 Þ

It is assumed here that mechanical and convective forces do not correlate. Then,
by analogy, we can write:

2 2 2

r

z ¼ r zm þ r zc :

ð 5 : 14 Þ

r

zc value is calculated on the assumption that

The

d
dt r zc ¼ r wc z ðÞ;

where t ¼ u = : u ð 5 : 15 Þ

Here z 0 is the effective height at which the vertical turbulence is calculated.
Dependences on the height for

˃ wc are parameterized with relationships:

(

2 = 3

54w 2

1 : z ðÞ z = for z 0 : 1z i ;

\

2

r

wc ¼

ð 5 : 16 Þ

33w 2

0 : for z 0 : 1z i ;

where the level z = 0.1z i corresponds to similar values of the vertical constituent of
turbulence.
Let h s be the height of the pollutants u. Then using

Eqs. ( 5.15 )and( 5.16 ) we obtain the relationship between h s and z i . For h s ≥

' jet and t have the scale x =

0.1z i

the following approximation is valid:

2

33w 2 t 2

r

zc ¼ 0

: ð 5 : 17 Þ

With h s < 0.1zi i we have:

8
<

2 = 3 t 2

54w 2

1 : ð h s = z i Þ for r zc \ h s ;

3

83w z 1 = 3 33h 2 = 3

s

0 : t þ 0 : for h s r zc \ 0 : 1z i ;

zc ¼

r i

:

2

z 1 = 3
i

231h 2 = 3
s

0 : 581w t þ 0 : 0 : 05z i for r zc 0 : 1z i

The mechanical constituent in Eq. ( 5.14 ) is calculated on the assumption that
variations of the vertical gradient due to mechanical mixing are constant in the
boundary layer and determined with the relationship:

2
wm ¼ 1

2u 2 r :

;

ð 5 : 18 Þ

where u * is the friction rate.