Chapter 2: SEA SURFACE MICROLAYER
where 1 1.0528
b
and 2 1.07733
b
. Substituting t
w from (2.113) into
(2.111) transforms formula (2.111) into a functional dependence of the
impact crater radius solely on the raindrop radius:
1/ 4
2
2
1
2
0
0
0
exp
/
k
c
w b b
r r
r
r
gr
X
M
§
·
ª
º
¬
¼
¨
¸
¨
¸
©
¹
.
(2.114)
The area that is subject to renewal due to the raindrop impact is equal to
the impact crater area. The number of drops of size 0
0
r dr
r
that reach the
surface per unit time and unit area is
0
0
0
t
n r w r dr , where
0
n r is the
drop size distribution in the atmosphere near the water surface. Respectively,
Craeye and
(1998) represented the crater flux density (i.e., the
production rate of crater area per unit area and unit time) as follows:
2
0
0
0
0
c
k
k
t
r
F
r r n r w r dr
S
f
³
.
(2.115)
Representing the distribution of the rain above the sea surface by the
Marshall-Palmer drop size spectrum (1.65) and substituting relationships
(2.113) into equation (2.115), and (2.114) into (2.115) results in the
following formula:
1/ 2
2
2
1
2
0
2
2
0
0
0
1
2
0
0
exp
/
exp
/
.
c
k
c
r
w b b
r r
F
r
gr
n r w b b
r r dr
X
X
X
X
S M
f
§
·
ª
º
¬
¼
¨
¸ u
¨
¸
©
¹
ª
º
¬
¼
³
(2.116)
The renewal time is then defined as the inverse of the impact-flux density F k ,
1/
r
k
t
F
(2.117)
The calculation of the integral on the right side of (2.116) and substituting
the result into (2.117) leads to
127
X
Schl ssel
ü