460
15 Vertical Structure of Ocean Waters and Biological Productivity
Localized fronts can also be generated by buoyancy effects, boundary mixing, river plumes and rip currents. All of these topographically generated fronts
affect the distribution of plankton, larvae and sediments. The resulting aggregation controls the distribution of benthic assemblages and pelagic predators.
15.4 Plankton Patchiness in Upper Ocean
Due to the variety of hydrodynamic structures such as currents, gyres, fronts
and eddies, the distribution of plankton in the oceanic surface layer is very
patchy. There is a long cascade of plankton concentration structures ranging
from 1 to 100 km (Mackas and Boyd, 1979). For example, at mid latitudes,
the transfer of variance (considered as a measure of plankton distribution in a
plume) from the size of about 100 km to the scale 1 km occurs during approximately 10 days. One of the mechanisms which causes a transfer of structure
variability from small to large length scales is diffusion. However, diffusion is
insignificant at scales larger than centimetres, where only ensemble-averaged
processes should be represented as diffusive (Abraham, 1998). An alternative
representation of plankton patchiness can be obtained using the theory of turbulent transport (Bennett and Deuman, 1985; Holloway, 1986). Although the
turbulent approach is very powerful, it is difficult to apply for a real plankton
population.
To simplify the calculation, Abraham (1998) proposed a simplified two-dimensional model for turbulent flow. In the model, turbulence is represented
as the sum of N randomly distributed circular eddies. Thus, the final stream
function '!f;(x, t) becomes:
(15.4)
in which Rn and xn = [xn(t), Yn(t)] are the radius and centre position of particular eddies, respectively, while A is a calibration constant. The orientation
of each eddy is a random variable and eddies move with the local velocity:
dXn
~(~)
- = u Xn .
dt
(15.5)
Using the definition of the stream function (see App. C.4), the velocity U (xn)
becomes u(xn) = (a'!f;/ay, -a'!f;/ax).
Each water parcel carries a phytoplankton population density, P, and adult
zooplankton population density, Z. The zooplankton are truly planktonic,
drifting with their respective water parcels, and not able to swim independently. Additionally, water parcel carries some capacity, C, representing the
effect of a limiting nutrient. The proposed model is not a fluid-dynamics model,
but with a proper choice of parameters it provides a simple and easy to implement tool for quasi-geostrophic turbulence. The domain of the model is a
15 Vertical Structure of Ocean Waters and Biological Productivity
Localized fronts can also be generated by buoyancy effects, boundary mixing, river plumes and rip currents. All of these topographically generated fronts
affect the distribution of plankton, larvae and sediments. The resulting aggregation controls the distribution of benthic assemblages and pelagic predators.
15.4 Plankton Patchiness in Upper Ocean
Due to the variety of hydrodynamic structures such as currents, gyres, fronts
and eddies, the distribution of plankton in the oceanic surface layer is very
patchy. There is a long cascade of plankton concentration structures ranging
from 1 to 100 km (Mackas and Boyd, 1979). For example, at mid latitudes,
the transfer of variance (considered as a measure of plankton distribution in a
plume) from the size of about 100 km to the scale 1 km occurs during approximately 10 days. One of the mechanisms which causes a transfer of structure
variability from small to large length scales is diffusion. However, diffusion is
insignificant at scales larger than centimetres, where only ensemble-averaged
processes should be represented as diffusive (Abraham, 1998). An alternative
representation of plankton patchiness can be obtained using the theory of turbulent transport (Bennett and Deuman, 1985; Holloway, 1986). Although the
turbulent approach is very powerful, it is difficult to apply for a real plankton
population.
To simplify the calculation, Abraham (1998) proposed a simplified two-dimensional model for turbulent flow. In the model, turbulence is represented
as the sum of N randomly distributed circular eddies. Thus, the final stream
function '!f;(x, t) becomes:
(15.4)
in which Rn and xn = [xn(t), Yn(t)] are the radius and centre position of particular eddies, respectively, while A is a calibration constant. The orientation
of each eddy is a random variable and eddies move with the local velocity:
dXn
~(~)
- = u Xn .
dt
(15.5)
Using the definition of the stream function (see App. C.4), the velocity U (xn)
becomes u(xn) = (a'!f;/ay, -a'!f;/ax).
Each water parcel carries a phytoplankton population density, P, and adult
zooplankton population density, Z. The zooplankton are truly planktonic,
drifting with their respective water parcels, and not able to swim independently. Additionally, water parcel carries some capacity, C, representing the
effect of a limiting nutrient. The proposed model is not a fluid-dynamics model,
but with a proper choice of parameters it provides a simple and easy to implement tool for quasi-geostrophic turbulence. The domain of the model is a