6.5 Vertical Mixing

6.5.1 Command Status

Required.

6.5.2 Description

Vertical turbulent mixing of momentum is modelled using the Vertical Mixing Model command. The available models are presented in Table 6.3 and the associated commands are presented in Table 6.4.

Both the \(k-\epsilon\) and \(k-\omega\) models can be optionally extended using the Second Order Vertical Mixing Model, Vertical Mixing Length Scale Limiter, and Internal Wave Mixing Model commands. Regardless of the model chosen, vertical turbulent mixing calculations are undertaken at the time interval specified by Turbulence Update dt, in seconds. Further information on the science of each model is provided in Appendix B.10.

Table 6.3: Vertical Mixing Model Implementations

Model Implementation	Description
Constant	Spatially constant vertical mixing value.
Parametric	Parametric mixing model
K-Epsilon	k-\(\epsilon\) mixing model after Launder & Spalding (1974)
K-Omega	k-\(\omega\) mixing model after Wilcox (1988)

Table 6.4: Vertical Mixing Model Commands

Command	Description
Vertical Mixing Model	Conditional - Required for 3D HD simulations. Selects the momentum mixing model for vertical subgrid scale turbulent mixing.
Vertical Mixing Parameters	Conditional. Sets the input parameters for the selected vertical mixing model.
Global Vertical Eddy Viscosity Limits	Optional - Sets a minimum and maximum limit on computed eddy viscosity.
Turbulence Update dt	Optional - Sets the update timestep for the K-Epsilon and K-Omega vertical mixing models.
Global Minimum Vertical TKE	Optional - A user-specified minimum limit on the calculated turbulent kinetic energy.
Global Minimum Vertical EPS	Optional - A user-specified minimum limit on the calculated turbulent dissipation rate.
Second Order Vertical Mixing Model	Optional - Second order vertical turbulence closure method.
Second Order Vertical Mixing Model Parameter Group	Optional - Suite of parameters for use in the second order turbulence closure method.
Vertical Mixing Length Scale Limiter	Optional - Turbulent length scale limter for K-Epsilon and K-Omega vertical mixing models.
Internal Wave Mixing Model	Optional - Account for vertical mixing below the thermocline or halocline associated with internal waves.
Internal Wave Mixing Model Parameters	Optional - Sets the input parameters for the selected internal wave mixing model.

6.5.3 Constant

This model sets a single value for the vertical eddy viscosity.

! Vertical Mixing Model Commands
Vertical Mixing Model == Constant ! {Constant} | Parametric | K-Epsilon | K-Omega
Vertical Mixing Parameters == 1E-06 ! {0.0} Vertical eddy viscosity (and diffusivity) (m²/s)

6.5.4 Parametric

This model uses a parametric description to compute eddy viscosity (see Appendix B.10.1.1). Global upper and lower limits can be applied to constrain the calculation.

! Vertical Mixing Model Commands
Vertical Mixing Model == Parametric ! {Constant} | Parametric | K-Epsilon | K-Omega
Vertical Mixing Parameters == 0.41, 0.41 ! {0.41} Parametric model coefficient 1, {0.41} Parametric model coefficient 2
Global Vertical Eddy Viscosity Limits == 1.0e-4, 1.0 ! {0.0} Minimum eddy viscosity (m^2/s), {99999.} Maximum eddy viscosity (m^2/s)

6.5.5 K-Epsilon

This model follows Launder & Spalding (1974) to estimate vertical eddy viscosity (see Appendix B.10.1.2). Global upper and lower limits can be applied to constrain the calculation. Minimum turbulent kinetic energy (TKE) and turbulent kinetic energy dissipation rates (EPS) can also be set.

Three extension options are available for the \(k-\epsilon\) mixing model. The associated commands are presented in Section 6.5.7.

! Vertical Mixing Model Commands
Vertical Mixing Model == K-Epsilon ! {Constant} | Parametric | K-Epsilon | K-Omega
Vertical Mixing Parameters == 1.44, 1.92, 0.09, 1.0, 1.3, 1.0, 0.0 ! {1.44} C_1e, {1.92} C_2e, {0.09} Cmu, {1.0} sigma_k, {1.3} sigma_omega, {1.0} C_3omega+, {0.0} C_3omega-

! Vertical Mixing Limits
Global Vertical Eddy Viscosity Limits == 1.0e-4, 1.0 ! {0.0} Minimum eddy viscosity (m^2/s), {99999.} Maximum eddy viscosity (m^2/s)
Global Minimum Vertical TKE == 1.e-10 ! {1E-10 m^2/s2} Minimum turbulent kinetic energy
Global Minimum Vertical EPS == 1.e-14 ! {1E-14 m^2/s3} Minimum dissipation rate

6.5.6 K-Omega

This model follows Wilcox (1988) to estimate vertical eddy viscosity (see Appendix B.10.1.3). Global upper and lower limits can be applied to constrain the calculation. Minimum turbulent kinetic energy (TKE) and turbulent kinetic energy dissipation rates (EPS) can also be set.

Three extension options are available for the \(k-\omega\) mixing model. The associated commands are presented in Section 6.5.7.

! Vertical Mixing Model Commands
Vertical Mixing Model == K-Omega ! {Constant} | Parametric | K-Epsilon | K-Omega
Vertical Mixing Parameters == 0.55555, 0.075, 0.0768, 2.0, 2.0, 0.0, -0.637117 ! {5/9} alpha, {3/40} beta, {0.09} Cmu, {2.} sigma_k, {2.} sigma_omega, {0.} C_3omega+, {0.} C_3omega-

! Vertical Mixing Limits
Global Vertical Eddy Viscosity Limits == 1.0e-4, 1.0 ! {0.0} Minimum eddy viscosity (m^2/s), {99999.} Maximum eddy viscosity (m^2/s)
Global Minimum Vertical TKE == 1.e-10 ! {1E-10 m^2/s2} Minimum turbulent kinetic energy
Global Minimum Vertical EPS == 1.e-14 ! {1E-14 m^2/s3} Minimum dissipation rate

6.5.7 K-Epsilon and K-Omega Extension Options

Three extension options are available to both the \(k-\epsilon\) and \(k-\omega\) turbulence models.

6.5.7.1 Second Order Model

The Second Order Model (see Appendix B.10.1.4) is used to optionally extend the \(k-\epsilon\) or \(k-\omega\) Vertical Mixing Model. A parameter group is required in conjunction with this command.

! Enable second-order algebraic formulation for Cmu
Second Order Vertical Mixing Model == Algebraic
! Specify parameter group ID for second-order model (No default)
Second Order Vertical Mixing Model Parameter Group == GL78

6.5.7.2 Lengthscale Limiter

The Lengthscale Limiter (see Appendix B.10.1.5) is used to optionally extend the \(k-\epsilon\) or \(k-\omega\) Vertical Mixing Model.

! Apply Galperin et al. (1988) length scale limiter using C_Gapl
Vertical Mixing Length Scale Limiter == 0.53 ! <C_Gapl> {0.53}

6.5.7.3 Internal Wave Mixing Model

The Internal Wave Mixing Model (see Appendix B.10.1.6) is used to optionally extend the \(k-\epsilon\) or \(k-\omega\) Vertical Mixing Model. The default parameters can also be overridden.

! Activate the internal wave mixing model (Kantha and Clayson, 1994)
Internal Wave Mixing Model == ON ! {OFF}

! Optional override of model parameters == k_lim,iw, R_i,cr, nu_t,shear, nu_t,R, nu_h,R
Internal Wave Mixing Model Parameters == 1.0e-6, 0.7, 5.0e-3, 1.0e-4, 5.0e-5