I>IFFUSION FROM A CONTINUOUS SOURCE AT SEA
317
technique in that the source was not at a fixed point but attached to a
moored buoy subject to movements due to waves and possibly yawing in the
current. In addition the rate of discharge may have varied with time. It is
thought, however, that these factors would not seriously affect the relative
dispersion in a given cross section. There seems littk doubt that much of the
observed variability was due to inherent properties of the field of flow,
including the presence of large-scak horizontal eddy motion which
produced meandering and distortion of the plume on many occasions. It
becomes essential to adopt a statistical approach, either by making a
number of repeated crossings at each downstream distance x (corresponding
to a given diffusion time t) or by considering the whole plume rather than
separate traverses in deriving representative parameters.
Attempts to derive K , directly from Eq. (1) in finite difference form, or
from the slope of the tangent at a given point to a curve relating 0; to t, led
to highly variable results. The procedure adopted, therefore, was to fit a
power law curve of the form
(2)
u; =at'"
where a and m are constants, to all the data from a given release. This
equation assumes a point source at zero time and cannot be expected to be
valid close to the source. From (I), K, is then given by
(3)
K, = h t m - '
so that K, may be calculated for a given diffusion time t from the fitted
values of a and m.
It follows from (2) and (3) also that
(4)
K, = cdy
where r = 2 (m - l)/m and c is a constant. If 0, is regarded as a measure of
the scale of the distribution, then Eq. (4) represents the dependence of K, on
scale for that particular release.
Before considering the observational values of m, the relation of this index
to theoretical treatments of diffusion may be pointed out. Table I shows the
values of m - 1 and r corresponding to the integral values m = 1,2. and 3.
The case m = I is that of Fickian diffusion with K, constant while rn = 2
TABLE 1. Values of power law indica
m
m - 1
r
Comments
I
0
0
Constant K,
2
I
1
Constant diffusion velocity
3
2
4 Inertialsubra~
317
technique in that the source was not at a fixed point but attached to a
moored buoy subject to movements due to waves and possibly yawing in the
current. In addition the rate of discharge may have varied with time. It is
thought, however, that these factors would not seriously affect the relative
dispersion in a given cross section. There seems littk doubt that much of the
observed variability was due to inherent properties of the field of flow,
including the presence of large-scak horizontal eddy motion which
produced meandering and distortion of the plume on many occasions. It
becomes essential to adopt a statistical approach, either by making a
number of repeated crossings at each downstream distance x (corresponding
to a given diffusion time t) or by considering the whole plume rather than
separate traverses in deriving representative parameters.
Attempts to derive K , directly from Eq. (1) in finite difference form, or
from the slope of the tangent at a given point to a curve relating 0; to t, led
to highly variable results. The procedure adopted, therefore, was to fit a
power law curve of the form
(2)
u; =at'"
where a and m are constants, to all the data from a given release. This
equation assumes a point source at zero time and cannot be expected to be
valid close to the source. From (I), K, is then given by
(3)
K, = h t m - '
so that K, may be calculated for a given diffusion time t from the fitted
values of a and m.
It follows from (2) and (3) also that
(4)
K, = cdy
where r = 2 (m - l)/m and c is a constant. If 0, is regarded as a measure of
the scale of the distribution, then Eq. (4) represents the dependence of K, on
scale for that particular release.
Before considering the observational values of m, the relation of this index
to theoretical treatments of diffusion may be pointed out. Table I shows the
values of m - 1 and r corresponding to the integral values m = 1,2. and 3.
The case m = I is that of Fickian diffusion with K, constant while rn = 2
TABLE 1. Values of power law indica
m
m - 1
r
Comments
I
0
0
Constant K,
2
I
1
Constant diffusion velocity
3
2
4 Inertialsubra~