# Reaeration By Turbulent Flow Over A Dam

Reareation will occur when water falls over a dam, weir, or other structure in the stream. To simulate this form of reaeration, a “structure” command line is added in the watershed configuration file (.fig) at every point along the stream where flow over a structure occurs.

            The amount of reaeration that occurs is a function of the oxygen deficit above the structure and a reaeration coefficient:

                  $$\Delta Ox\_{str}=D\_a-D\_b=D\_a(1-\frac{1}{rea})$$                                               7:3.5.10

where $$\Delta Ox\_{str}$$ is the change in dissolved oxygen concentration (mg O$$\_2$$/L), $$D\_a$$ is the oxygen deficit above the structure (mg O$$\_2$$/L), $$D\_b$$ is the oxygen deficit below the structure (mg O$$\_2$$/L), and $$rea$$ is the reaeration coefficient.

           The oxygen deficit above the structure, $$D\_a$$, is calculated:

                  $$D\_a=Ox\_{sat}-Ox\_{str}$$                                                                       7:3.5.11

where $$Ox\_{sat}$$ is the equilibrium saturation oxygen concentration (mg O$$*2$$/L), and $$Ox*{str}$$ is the dissolved oxygen concentration in the stream (mg O$$\_2$$/L).

            Butts and Evans (1983) documents the following relationship that can be used to estimate the reaeration coefficient:

 $$rea=1+0.38*coef\_a*coef\_b*h\_{fall}*(1-0.11*h\_{fall})*(1+0.046\*\overline T\_{water})$$   7:3.5.12

where $$rea$$ is the reaeration coefficient, $$coef\_a$$ is an empirical water quality factor, $$coef\_b$$ is an empirical dam aeration coefficient, $$h\_{fall}$$ is the height through which water falls (m), and $$\overline T\_{water}$$ is the average water temperature ($$\degree$$C).

The empirical water quality factor is assigned a value based on the condition of the stream:

            $$coef\_a$$ = 1.80 in clean water

            $$coef\_a$$ = 1.60 in slightly polluted water

            $$coef\_a$$ = 1.00 in moderately polluted water

            $$coef\_a$$ = 0.65 in grossly polluted water

The empirical dam aeration coefficient is assigned a value based on the type of structure:

            $$coef\_b$$ = 0.70 to 0.90 for flat broad crested weir

            $$coef\_b$$ = 1.05 for sharp crested weir with straight slope face

            $$coef\_b$$ = 0.80 for sharp crested weir with vertical face

            $$coef\_b$$ = 0.05 for sluice gates with submerged discharge

Table 7:3-5: SWAT+ input variables used in in-stream oxygen calculations.

| Variable Name  | Definition                                                                                    | File Name |
| -------------- | --------------------------------------------------------------------------------------------- | --------- |
| RK2            | $$\kappa\_{2,20}$$: Reaeration rate at    20$$\degree$$C (day$$^{-1}$$)                       | .swq      |
| AI3            | $$\alpha\_3$$: Rate of oxygen production per unit algal photosynthesis (mg O$$\_2$$/mg alg)   | .wwq      |
| AI4            | $$\alpha\_4$$: Rate of oxygen uptake per unit algal respiration (mg O$$\_2$$/mg alg)          | .wwq      |
| RHOQ           | $$\rho\_{a,20}$$: Local algal respiration rate at 20$$\degree$$C (day$$^{-1}$$)               | .wwq      |
| RK1            | $$\kappa\_{1,20}$$: CBOD deoxygenation rate at 20$$\degree$$C (day$$^{-1}$$)                  | .swq      |
| RK4            | $$\kappa\_{4,20}$$:Sediment oxygen demand rate at 20$$\degree$$C(mg   O$$\_2$$/(m$$^2$$.day)) | .swq      |
| AI5            | $$\alpha\_5$$: Rate of oxygen uptake per unit NH$$\_4^+$$ oxidation (mg O$$\_2$$/mg N)        | .wwq      |
| AI6            | $$\alpha\_6$$: Rate of oxygen uptake per unit NO$$\_2$$ oxidation (mg O$$\_2$$/mg N)          | .wwq      |
| AERATION\_COEF | $$rea$$: Reaeration coefficient                                                               | .fig      |