Diffusion

The unit models the longitudinal dispersion of any transported water quality variable in 1D Water Quality Solver.

Description

The transport and dispersion of water quality variables is governed by the mass balance equation. One term of the equation represents the effective longitudinal dispersion. The amount of dispersion is governed by the longitudinal dispersion coefficient D. 1D Water Quality Solver offers three ways of calculating the longitudinal dispersion coefficient. Different methods of calculating the longitudinal dispersion coefficient may be applied to different parts of the river system.

The longitudinal dispersion may be set to a constant value, D₀, irrespective of discharge or shear velocity, which is applied at all nodes throughout the model. This is set by using the keyword CONSTANT. Alternatively the constant value may be allowed to vary within the model area, in which case the keyword VARIABLE is used.

For estuary networks the longitudinal dispersion coefficient may be considered to vary with the tidal discharge and/or the longitudinal salinity gradient (mainly applicable to large delta systems). In these cases the keyword ESTUARY is used. The longitudinal dispersion coefficient is represented by a three part empirical function (see equation below). The size of the coefficient is governed by three empirical constants D₀, D₁ and D₂. D₀ is a constant term which is used to prevent unrealistically low values of dispersion from arising. D₁ is a term which is used to represent the amount of dispersion caused by tidal mixing in the estuary. D₂ is the term used to determine the effect of salinity gradient on dispersion.

For river applications the longitudinal dispersion is related to the shear velocity (see below). In these cases the keyword RIVER is used.

It is possible that user may wish to have varying values of ESTUARY or RIVER dispersion coefficients throughout the model. The user may even wish to mix the dispersion type. In these cases the keyword DYNAMIC should be used. This keyword enables the user to set individual values of D₀, D₁ and D₂ and diffusion type at each model node.

Equations

For estuary networks the dispersion coefficient has the form:

                    (1)

Where:
D₀, D₁ and D₂= Empirical constants (m²/s)
Q = Discharge (m³/s)
U0= Peak velocity at the seaward boundary (m/s)
A0= Representative cross-sectional area at the seaward boundary (m²)
S0= Representative salinity at the seaward boundary (ppt)
L0= Representative limit of saline intrusion from the seaward boundary (m²).

For river applications the dispersion coefficient has the form:

                    (2)

Where:
u_* = Shear velocity (m/s)
f = Colebrook-White friction factor
u = Mean flow velocity (m/s)
b = Channel width/breadth (m)
D₁ = Empirical diffusion coefficient