324
K. F. BOWDEN Br AL.
8. ABSOLUTE AND RELATIVE DIFFUSION
The foregoing discussion has been concerned with the relative diffusion of
the dye plume about its centre of mass, neglecting any movement of the
centre of mass itself. In most experiments this was unavoidable since the
movements of the ship were not tracked with sutkient accuracy to enable
absolute determinations of position to be made. An example will now be
given of a release in which a large number of crossings were made at a
constant distance downstream from the source and the necessary accuracy
in position was attained to be able to locate the concentration measurements
in absolute coordinates.
Figure 6 shows the concentration curves for 18 crossings at the same
distance from the source (corresponding to a diffusion time of 1.03 _+
0.15 x lo3 sec), plotted against actual distance y perpendicular to the mean
axis of the plume. The individual crossings show pronounced variability, in
the position of the centre of mass, the relative variance, and the peak concentration. The broken line is the average concentration curve for the 18 crossings, having a lower peak value and a larger standard deviation than the
average values of the individual curves. Figure 7 shows 10 of the 18 curves in
the previous figure plotted with their centres of mass coincident. They are
seen to vary considerably, both in the laterally integrated concenti ation and
in the shape of the curve. The standard deviations of the 18 curves ranged
from 7 to 16.5 m, i.e., by a factor of 2.4, while the peak concentration varied
by a factor of 6.
Let om denote the absolute standard deviation of the meandering plume
and a", the mean standard deviation of the curves relative to their own
centres of mass. Similarly, let C,, and Cp, be the peak concentration of the
absolute curve and the mean peak concentration of the individual curves
respectively. If both the absolute and relative distributions were Gaussian in
form and there were no meandering in the vertical one would expect
(10)
CPKP, = q a b ,
as shown by Gifford (1959).
The observed values in the above experiment were
om = 34.2 m,
Q, = 10.6 m
Thus nY/cry, = 3.2. The ratio of the peak concentrations was
CpJCp, = 2.4
The difference between the observed ratios, 3.2 and 2.4, is within experimental error. If meandering occurred in the vertical as well, the ratio
K. F. BOWDEN Br AL.
8. ABSOLUTE AND RELATIVE DIFFUSION
The foregoing discussion has been concerned with the relative diffusion of
the dye plume about its centre of mass, neglecting any movement of the
centre of mass itself. In most experiments this was unavoidable since the
movements of the ship were not tracked with sutkient accuracy to enable
absolute determinations of position to be made. An example will now be
given of a release in which a large number of crossings were made at a
constant distance downstream from the source and the necessary accuracy
in position was attained to be able to locate the concentration measurements
in absolute coordinates.
Figure 6 shows the concentration curves for 18 crossings at the same
distance from the source (corresponding to a diffusion time of 1.03 _+
0.15 x lo3 sec), plotted against actual distance y perpendicular to the mean
axis of the plume. The individual crossings show pronounced variability, in
the position of the centre of mass, the relative variance, and the peak concentration. The broken line is the average concentration curve for the 18 crossings, having a lower peak value and a larger standard deviation than the
average values of the individual curves. Figure 7 shows 10 of the 18 curves in
the previous figure plotted with their centres of mass coincident. They are
seen to vary considerably, both in the laterally integrated concenti ation and
in the shape of the curve. The standard deviations of the 18 curves ranged
from 7 to 16.5 m, i.e., by a factor of 2.4, while the peak concentration varied
by a factor of 6.
Let om denote the absolute standard deviation of the meandering plume
and a", the mean standard deviation of the curves relative to their own
centres of mass. Similarly, let C,, and Cp, be the peak concentration of the
absolute curve and the mean peak concentration of the individual curves
respectively. If both the absolute and relative distributions were Gaussian in
form and there were no meandering in the vertical one would expect
(10)
CPKP, = q a b ,
as shown by Gifford (1959).
The observed values in the above experiment were
om = 34.2 m,
Q, = 10.6 m
Thus nY/cry, = 3.2. The ratio of the peak concentrations was
CpJCp, = 2.4
The difference between the observed ratios, 3.2 and 2.4, is within experimental error. If meandering occurred in the vertical as well, the ratio