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8 Transport in the Oceans and Coastal Zone
8.4.2 Diffusion of Tracers in the Ocean
Radioactive Isotopes. Atmospheric nuclear experiments in the 1950s and
1960s resulted in a large number of radioactive elements which finally settled
at the ocean surface and penetrated deep in the ocean. After nuclear explosions in the Bikini and Enewetak atolls in the Pacific Ocean, it was found
that radioactive elements had been transported a distance of 2000 km during
four months and a distance of 7000 km during eight months (Ozmidov, 1986).
Among radioactive elements which pose a large danger for human and ocean
organisms are isotopes of Caesium 137Cs and Strontium 90Sr with half-lives of
about 30 years, and Cerium 144Ce with a half-life of about one year. These
isotopes are almost totally diluted in ocean water and are therefore very useful
tracers for studying diffusion.
In the upper ocean layer, above the thermocline, water mixing is intensive
and radioactive elements reach the thermocline rather quickly in comparison
with the characteristic time for diffusion in the deeper ocean. For isotopes
with a long half-life, the coefficient of vertical diffusion, K z, is usually treated
as a constant value. Additionally, at the sea surface, the flux of radioactive
elements is assumed to be known, i.e.:
iN I
{O for t < 0
Kz 8z z=o =
Q for t 2:: O.
(8.86)
For large areas of the ocean surface, the horizontal gradients of radioactive
element concentrations are negligible. The vertical advection velocity, w, is
usually also small. Thus, the concentration of radioactive elements can be
found from the solution of an equation similar to Eq. (8.22), but with a different
boundary condition at the sea surface (Eq. 8.86), and with a turbulent diffusion
coefficient, K z, instead of the molecular diffusion coefficient D, i. e.:
(8.87)
The solution of Eq. (8.87) becomes:
(8.88)
in which (= z/v'Kzt. Error function erf(x) is defined by Eq. (C.174).
Experiments have shown that the coefficients of turbulent diffusion of the isotope 90Sr in the Atlantic and Pacific Oceans are about 17.2 cm 2 /s and 6 cm 2 /s,
respectively. In Fig. 8.10, the vertical distribution of concentration for Atlantic
conditions is shown. The flux of 9 0 Sr from the atmosphere was determined
as 7.4x 10- 6 Bq/m 2 /s using Ozmidov (1986) data. The unit of radioactivity,
becquerel, (Bq), named after the discoverer Henri Becquerel (1852-1908), is
defined as one decay per second. Fig. 8.10 shows that it takes almost 3 years
for the 90Sr to reach the water depth of 750 m in the Atlantic Ocean.
8 Transport in the Oceans and Coastal Zone
8.4.2 Diffusion of Tracers in the Ocean
Radioactive Isotopes. Atmospheric nuclear experiments in the 1950s and
1960s resulted in a large number of radioactive elements which finally settled
at the ocean surface and penetrated deep in the ocean. After nuclear explosions in the Bikini and Enewetak atolls in the Pacific Ocean, it was found
that radioactive elements had been transported a distance of 2000 km during
four months and a distance of 7000 km during eight months (Ozmidov, 1986).
Among radioactive elements which pose a large danger for human and ocean
organisms are isotopes of Caesium 137Cs and Strontium 90Sr with half-lives of
about 30 years, and Cerium 144Ce with a half-life of about one year. These
isotopes are almost totally diluted in ocean water and are therefore very useful
tracers for studying diffusion.
In the upper ocean layer, above the thermocline, water mixing is intensive
and radioactive elements reach the thermocline rather quickly in comparison
with the characteristic time for diffusion in the deeper ocean. For isotopes
with a long half-life, the coefficient of vertical diffusion, K z, is usually treated
as a constant value. Additionally, at the sea surface, the flux of radioactive
elements is assumed to be known, i.e.:
iN I
{O for t < 0
Kz 8z z=o =
Q for t 2:: O.
(8.86)
For large areas of the ocean surface, the horizontal gradients of radioactive
element concentrations are negligible. The vertical advection velocity, w, is
usually also small. Thus, the concentration of radioactive elements can be
found from the solution of an equation similar to Eq. (8.22), but with a different
boundary condition at the sea surface (Eq. 8.86), and with a turbulent diffusion
coefficient, K z, instead of the molecular diffusion coefficient D, i. e.:
(8.87)
The solution of Eq. (8.87) becomes:
(8.88)
in which (= z/v'Kzt. Error function erf(x) is defined by Eq. (C.174).
Experiments have shown that the coefficients of turbulent diffusion of the isotope 90Sr in the Atlantic and Pacific Oceans are about 17.2 cm 2 /s and 6 cm 2 /s,
respectively. In Fig. 8.10, the vertical distribution of concentration for Atlantic
conditions is shown. The flux of 9 0 Sr from the atmosphere was determined
as 7.4x 10- 6 Bq/m 2 /s using Ozmidov (1986) data. The unit of radioactivity,
becquerel, (Bq), named after the discoverer Henri Becquerel (1852-1908), is
defined as one decay per second. Fig. 8.10 shows that it takes almost 3 years
for the 90Sr to reach the water depth of 750 m in the Atlantic Ocean.