32 8
K. F. BOWDEN I 3 AL.
on a time scale at the lower limit of the cases considered by Okubo. it is of
some interest to relate our results to his. Okubo showed that the radial
variances a," of all the data, with diffusion timca from 2 hr to 1 month, could
be fitted approximately by the relation
(13)
a,' = 0.0108t2.34
Comparing this equation with a model using a radial diffusion velocity P
and matching the solutions at t = I hour gives P = 0.42 cm/sec, which is
about half the values of B found in the Irish Sea.
Okubo pointed out that the relation predicted by the similarity law of
turbulence, i.e.,
(14)
0; = C&r3
where c is the rate of energy dissipation per unit mass through the turbulence
and C is a constant of order unity, could be fitted quite well to the data, if 1:
varied from one range of time and length scales to another. At the smallscale end, Okubo (1968) showed that, putting C = 1, E = 9.7 x
cm2/sec3 for t between 4 x lo3 and 2 x lo4 sec. Matching the
corresponding equation for a," to a diffusion model and putting t = 1 hour
leads to P = 0.59 cm/scc, which is still only half the values of B found in the
Irish Sea. Since B refers to transverse diffusion and the rate of longitudinal
diffusion is usually several times greater, one might take P = 2 cm/sec as
more typical of the Irish Sea and the corresponding value of E would be an
order of magnitude greater, say 10- ' ~ m ~ / ~ b c ~ .
It would be interesting to have an independent estimate of the energy
dissipation parameter E in the conditions of the present experiments. Taylor
(1918) made an estimate of the overall dissipation of tidal energy in the Irish
Sea which, averaged over the whole volume, would correspond to approximately 0.22 cm2/sec3 per unit mass of water, i.e., about 200 times the value of
c required to account for the observed horizontal diffusivity. However, much
of the dissipation of tidal energy, arising from tidal friction, probably takes
place in a layer near the sea bed. The intensity of turbulence, due to this
cause, is likely to be considerably lower in the surface layer and not all the
energy there will be in thc horizontal components of relevant scale. It would
be unwise to pursue the analogy further than to say that there appears to be
ample turbulent energy available, if it were in the right form, to provide for
the observed rate of horizontal diffusion.
10. CONCLUSION
In general, where features of the apparent diffusion can be related to
identifiable physical processes, such as lateral or vertical shear in the tidal
current or wind-induced current, and can be treated quantitatively from this
K. F. BOWDEN I 3 AL.
on a time scale at the lower limit of the cases considered by Okubo. it is of
some interest to relate our results to his. Okubo showed that the radial
variances a," of all the data, with diffusion timca from 2 hr to 1 month, could
be fitted approximately by the relation
(13)
a,' = 0.0108t2.34
Comparing this equation with a model using a radial diffusion velocity P
and matching the solutions at t = I hour gives P = 0.42 cm/sec, which is
about half the values of B found in the Irish Sea.
Okubo pointed out that the relation predicted by the similarity law of
turbulence, i.e.,
(14)
0; = C&r3
where c is the rate of energy dissipation per unit mass through the turbulence
and C is a constant of order unity, could be fitted quite well to the data, if 1:
varied from one range of time and length scales to another. At the smallscale end, Okubo (1968) showed that, putting C = 1, E = 9.7 x
cm2/sec3 for t between 4 x lo3 and 2 x lo4 sec. Matching the
corresponding equation for a," to a diffusion model and putting t = 1 hour
leads to P = 0.59 cm/scc, which is still only half the values of B found in the
Irish Sea. Since B refers to transverse diffusion and the rate of longitudinal
diffusion is usually several times greater, one might take P = 2 cm/sec as
more typical of the Irish Sea and the corresponding value of E would be an
order of magnitude greater, say 10- ' ~ m ~ / ~ b c ~ .
It would be interesting to have an independent estimate of the energy
dissipation parameter E in the conditions of the present experiments. Taylor
(1918) made an estimate of the overall dissipation of tidal energy in the Irish
Sea which, averaged over the whole volume, would correspond to approximately 0.22 cm2/sec3 per unit mass of water, i.e., about 200 times the value of
c required to account for the observed horizontal diffusivity. However, much
of the dissipation of tidal energy, arising from tidal friction, probably takes
place in a layer near the sea bed. The intensity of turbulence, due to this
cause, is likely to be considerably lower in the surface layer and not all the
energy there will be in thc horizontal components of relevant scale. It would
be unwise to pursue the analogy further than to say that there appears to be
ample turbulent energy available, if it were in the right form, to provide for
the observed rate of horizontal diffusion.
10. CONCLUSION
In general, where features of the apparent diffusion can be related to
identifiable physical processes, such as lateral or vertical shear in the tidal
current or wind-induced current, and can be treated quantitatively from this