7.5 Horizontal Mixing
7.5.2 Description
Salinity, temperature and tracers undergo horizontal mixing in addition to advection. The horizontal scalar mixing models available to support this simulation are described here. Vertical scalar mixing models are described in Chapter 6.5. The horizontal mixing approach is selected using the
Other than ‘None’, all models involve a method to specify or compute a horizontal scalar diffusivity (‘scalar diffusivity’ is sometimes referred to in the literature as ‘eddy diffusivity’. This is different again to ‘eddy viscosity’ which refers to the turbulent diffusion of momentum). This diffusivity has units of m\(^2\)/s and is the turbulent equivalent of laminar (molecular) diffusivity. It is applied as a multiplicative factor to the diffusive terms in the scalar conservation equations (see Appendix B.3). In all models other than ‘None’, computed scalar diffusivity can also be optionally limited between a user defined minimum and maximum using the
Supported horizontal mixing implementations are summarised in Table 7.7, with links to the relevant implementation sections below. Commands are listed in Table 7.8.
| Model Implementation | Description |
|---|---|
| None | Scalar mixing disabled. |
| Constant | Scalar diffusivity set to a spatially constant value. |
| Elder | Scalar diffusivity computed using Elder relations. |
| Smagorinsky | Scalar diffusivity computed using Smagorinsky formulation. |
| Warmup | Scalar diffusivity computed to maximum stable values for warmup/interpolation workflows. |
| Command | Description |
|---|---|
| Scalar Mixing Model | Conditional - Required for the AD simulation class. Selects the horizontal scalar mixing model implementation. |
| Global Horizontal Scalar Diffusivity | Conditional - Required when using the Constant, Smagorinsky or Elder Scalar Mixing Model implementations. Specifies model coefficients or diffusivity values for applicable mixing models. |
| Global Horizontal Scalar Diffusivity Limits | Optional - Applies global minimum and maximum limits to computed scalar diffusivity. |
7.5.3 None
This model is the default and excludes the simulation of scalar mixing. It is the same as setting \(K^{AD}_d\) to zero.
This model might be used where large cell sizes are present to reduce numerical diffusion or for analytical model testing. It is not typically recommended for project or research work.
7.5.4 Constant
This model sets a constant scalar diffusivity.
This model might be used in relatively simple and low gradient systems such as shallow lakes or the coastal ocean. If this model is deployed, then the constant scalar diffusivity is also required using the
7.5.5 Elder
This model sets the scalar diffusivity using the Elder relations (see Equation (B.105)).
This model should only be used in two dimensional simulations. If this model is deployed, then specification of longitudinal \(C^{AD}_{Eld-L}\) and transverse \(C^{AD}_{Eld-T}\) coefficients is also required using the
7.5.6 Smagorinsky
This model sets the scalar diffusivity using the Smagorinsky relation (see Equation (B.106)).
This model can be used in two and three dimensional simulations. If this model is deployed, then specification of the Smagorinsky coefficient \(C^{AD}_{Smg}\) is also required using the
7.5.7 Warmup
This model automatically computes the scalar diffusivity to be the maximum allowable under CFL conditions.
This model can be used in two and three dimensional simulations to distribute spatially localised initial conditions across a wider computational domain. It enforces smooth interpolation between point or polygon based boundary conditions for subsequent saving of a restart file. These boundary conditions are type CP (Section 7.11.9.2) and CP_POLY (7.11.9.3) for points and polygons, respectively. The warmup horizontal scalar diffusivity model is not intended for use in calibration or production simulations.