・ Dissolved Oxygen (O) [mgO/l]

dO/dt = (Transfer & Diffusion) + (Oxygen production by phytoplanlcton)+ (Oxygen production by seaweed) + (reaeration) - (Oxygen consumption by phytoplanlcton) - (Oxygen consumption by zooplankton) - (Oxygen consump- tion by detritus) - (Oxygen consumption by benthos) - (Oxygen consumption by seaweed) = (Transfer & Diffusion) + [TOD:CpI・ V1(tc,N)・ V2(I(t)） P + [TOD:Cs]・ V1'(tc,N)・ V2'(I (t))・S + Ka'・(DOs・ ) - [TOD:Cp]・ β(P)・V1(tc,N)・V2(I (t))・P - [TOD:Cz]・(μ - ν )・g(P,D)・Z - [TOD:Cd]・ φ ・D - [TOD:Cb] ・ ( μb- ν b)・ f(O,tc)・ B - [TOD:Cs]・β(S)・V1'(tc, N)・ V2'(I(t)） (7)

where V1(tc,N) is growth limitation function for phyto- planicton, V2(I(t)) is photosynthesis limitation function for phytoplankton, V1'(tc,N) is growth limitation function for seaweed, V2'(I(t)) is photosynthesis limitation function for seaweed, β(P)is secretion function for phytoplankton, g(P,D) is zooplanｋton predation function, f(O,tc) is benthos filtering function, β (S) is secretion function for seaweed, L(B) is growth control function for benthos, L'(B) is growth control function for seaweed, and [TOD:Cx] is TOD(total oxygen demand)/Carbone ratio of each compartment.

In these models, Trnster & Diffusion (physical) process can be expressed by

dB1/dt = - ∂ (UiBi)/∂x- ∂(WiBi)/∂z + ∂(Kxｉ・ ∂Bi/∂x)/∂x + ∂(Kzi・ ∂Bi/∂z)/∂z (8)

where Bi is state quantity of each compartment, Ui is horizontal fluid velocity (only tital current is considered), Wi is sinlcing speed of each material, Kxi is horizontal diffusion coefficient, and Kzi is vertical difilusion coefficient.

3. NUMERICAL SIMULATIONS

Fundamental water purification functions are investigated by numerical simulations using the mathematical model shown in the previous section. In these calculations, the mathematial model is expressed by differential approximation in time. The initial conditons and the values of principal parameters are shown in Tables I and 2, respectively. Most of these parameters are based on Naiｋata's model¹¹⁾ and Hone and Horiguchi's model^12）. Some parameters for benthos and seaweed are decided with reference to the results of sensitivity analysis, because there have been very few studies on the growth rate of benthos and seaweed. The time scale of biological process is generally much larger than that of physical process. In these simulations, the time increments in calculations of physical and biological processes are set at 5 nun and 15 min, respectively.

Table 1 Initial conditions

Table 2 Values of principal parameters

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