DIFFUSION FROM A CONTINUOUS SOURCE AT SEA
327
the Texel lightvessel in the southern North Sea, Meerburg (1972), for rather
shorter diffusion times (4 to 12 min), derived values of K, which increased
with time. Analyzing his data in terms of a diffusion velocity B leads to a
median value of B = 2.7 cm/sec, which is about twke the Irish Sea values.
Recent experiments in the Liverpool Bay area, but using instantaneous
discharges and on a larger scale, have been described by Barrett et al. (1972)
and Talbot (1972). In Talbot’s experiment, in which a patch of rhodamine B
dye was traced for a 5day period, the transvem c d f k i e n t K , continued to
increase with time for over 60 hr, eventually approaching an asymptotic
value. For the first 12 hr the data, analyzed in terms of diffusion velocity,
corresponded to a B of 1.05 cm/sec, in good agreement with the results given
above. The experiments of Barrett et al., using a difkrent technique, also
gave values of K, increasing with time but corresponding to a B of about
half the value found above or that derived from Talbot’s data.
The physical interpretation of the diffusion velocity E is uncertain: it may
contain a component due to the interaction of current shear and vertical
diffusion. An estimate of the possible magnitude of the effect on K, of a shear
in the transverse component of velocity Y may be obtained from Okubo’s
(1967) analysis for the case of an unbounded sea, since the vertical spread in
these experiments was relatively small. For a steady current and a uniform
shear, this leads to an effective K, given by
(11)
K, = K,(dV/&)’t2
The effective diffusion coefficient would thus increase with tZ instead of with
1, as for a constant diffusion velocity B. However, matching the equations for
a particular diffusion time to leads to an effective Be given by
(12)
s,’ = K,(dV/dz)2t,
Taking B, = 1 cm/sec, K, = 10 cm2/sec, and to = 30 min as typical values,
IdV/dzI = 0.75 sec- I , corresponding to a shear in the transverse component of velocity of 3.75 cm/sec in 5 m. A shear of this magnitude may well
have been present, although no current measurements of sufficient accuracy
to detect it were made.
Another possible physical model is that of diffusion in a field of turbulence
which differs from a state of horizontal local isotropy by having energy
injected in the range of eddy scales concerned, i.e., from a few metres up to
several tens of metres. The source might be in the action of surface waves,
small-scale patterns of flow induced by the wind or eddies in the tidal
currents. Okubo (1968, 1971) made an attempt on these lines to systematize
the results of the much larger number of experiments with instantanecus
releases, analyzed in terms of a model involving radially symmetrical diNusion. Although the present experiments were with continuous releases and
327
the Texel lightvessel in the southern North Sea, Meerburg (1972), for rather
shorter diffusion times (4 to 12 min), derived values of K, which increased
with time. Analyzing his data in terms of a diffusion velocity B leads to a
median value of B = 2.7 cm/sec, which is about twke the Irish Sea values.
Recent experiments in the Liverpool Bay area, but using instantaneous
discharges and on a larger scale, have been described by Barrett et al. (1972)
and Talbot (1972). In Talbot’s experiment, in which a patch of rhodamine B
dye was traced for a 5day period, the transvem c d f k i e n t K , continued to
increase with time for over 60 hr, eventually approaching an asymptotic
value. For the first 12 hr the data, analyzed in terms of diffusion velocity,
corresponded to a B of 1.05 cm/sec, in good agreement with the results given
above. The experiments of Barrett et al., using a difkrent technique, also
gave values of K, increasing with time but corresponding to a B of about
half the value found above or that derived from Talbot’s data.
The physical interpretation of the diffusion velocity E is uncertain: it may
contain a component due to the interaction of current shear and vertical
diffusion. An estimate of the possible magnitude of the effect on K, of a shear
in the transverse component of velocity Y may be obtained from Okubo’s
(1967) analysis for the case of an unbounded sea, since the vertical spread in
these experiments was relatively small. For a steady current and a uniform
shear, this leads to an effective K, given by
(11)
K, = K,(dV/&)’t2
The effective diffusion coefficient would thus increase with tZ instead of with
1, as for a constant diffusion velocity B. However, matching the equations for
a particular diffusion time to leads to an effective Be given by
(12)
s,’ = K,(dV/dz)2t,
Taking B, = 1 cm/sec, K, = 10 cm2/sec, and to = 30 min as typical values,
IdV/dzI = 0.75 sec- I , corresponding to a shear in the transverse component of velocity of 3.75 cm/sec in 5 m. A shear of this magnitude may well
have been present, although no current measurements of sufficient accuracy
to detect it were made.
Another possible physical model is that of diffusion in a field of turbulence
which differs from a state of horizontal local isotropy by having energy
injected in the range of eddy scales concerned, i.e., from a few metres up to
several tens of metres. The source might be in the action of surface waves,
small-scale patterns of flow induced by the wind or eddies in the tidal
currents. Okubo (1968, 1971) made an attempt on these lines to systematize
the results of the much larger number of experiments with instantanecus
releases, analyzed in terms of a model involving radially symmetrical diNusion. Although the present experiments were with continuous releases and