(omega-user-vertmix)=

# Vertical Mixing Coefficients

The vertical mixing module in OMEGA handles the parameterization of unresolved vertical mixing
processes in the ocean. It calculates vertical diffusivity and viscosity coefficients that
determine how properties (like momentum, heat, salt, and biogeochemical tracers) mix vertically
in the ocean model. Currently, there is one primary operational vertical mixing option, `PP`,
which can superimpose three different mixing processes within the water column: (1) a constant
background mixing value, (2) a convective instability mixing value, and (3) a Richardson number
dependent shear mixing value based upon Pacanowski and Philander (1981). These are describe a bit
more in detail below. The second vertical mixing option, `KPP`, is not yet functional, but will be added soon.

The user-configurable options are: `VertMixType` (choose either `PP` or `KPP`), as well as the following parameters in the yaml configuration file for each mixing process within the `PP` option:

```yaml
VertMix:
  Background:
    Viscosity: 1.0e-4    # Background vertical viscosity (m²/s)
    Diffusivity: 1.0e-5  # Background vertical diffusivity (m²/s)
  Convective:
    Enable: true         # Enables the convective-induced mixing option
    Diffusivity: 1.0     # Convective mixing coefficient (m²/s)
    TriggerBVF: -1e-4    # Brunt-Vaisala frequency threshold
  Shear:
    Enable: true         # Enables the shear-induced mixing option
    NuZero: 1.0e-2       # Base viscosity coefficient
    Alpha: 5.0           # Stability parameter
    Exponent: 2          # Richardson number exponent
```

## Vertical Mixing Processes/Types

### 1. Background Mixing

A constant background mixing value that represents small-scale mixing processes not explicitly resolved by the model. Typically, this is chosen to represent low values of vertical mixing
happening in the ocean's stratified interior.

### 2. Convective Mixing

Enhanced convective adjustment mixing that occurs in statically unstable regions of the water column to parameterize convection and homogenize properties. In OMEGA this is mixing is defaulted to occur when the Brunt Vaisala Frequency is less than 0.0 (unstable), and is off when equal to (neutral) or greater than (stable) 0.0.

$$
\kappa =
\begin{cases}
\kappa_{b} + \kappa_{conv} \quad \text{ if } N^2 < N^2_{crit}\\
\kappa_{b} \quad \text{ if } N^2 \geq N^2_{crit}
\end{cases}
$$

### 3. Shear Mixing

Mixing induced by vertical velocity shear, implemented using the Pacanowski-Philander scheme, through the gradient Richardson number (ratio of buoyancy to shear).

$$
\nu = \frac{\nu_o}{(1+\alpha Ri)^n} + \nu_b\,,
$$

$$
\kappa = \frac{\nu}{(1+\alpha Ri)} + \kappa_b\,.
$$

where $Ri$ is defined as:

$$
Ri = \frac{N^2}{\left|\frac{\partial \mathbf{U}}{\partial z}\right|^2}\,,
$$