Chemistry Reference
In-Depth Information
cate an unstable solution, and hence one which would not be found in real-
ity.
Fig. 4.
Relaxation rates computed according to Eq. 24, for wind speeds
U
10
= 2, 4,
6, 8, 10, 15 m s
-1
. No slicks present. The lowest wind speed curves show the
smallest excursions and vice versa
In order to investigate the possibility that negative values for
ȝ
be a con-
sequence of the numerical implementation of solving
S
(
E
) = 0 by integrat-
ing
' (Eq. 11), the action balance
S
(
N
) = 0 was also solved directly by
solving the polynomial
1
)
S
(
N
)
f
N
f
N
2
f
N
3
0
.
(25)
1
2
3
This equation can have more than one positive solution
N
eq
. If there are
two positive solutions, one is stable (
NS
) and the other one un-
stable. In such cases, the integration method always finds the stable solu-
tion. In those cases where an unstable solution is found, there exists no
second positive solution. So the integration method works well in that re-
spect. As a further check, the relaxation rate was also computed numeri-
cally as
d
d
0
S
' . This led to the same numbers as the ones found pre-
viously from Eq. 24.
1
Note that
f
1
and
f
2
contain
B
'(
k
); the
B
'(
k
) values used here are those obtained
from the integration procedure.
N
