WVVerticalDiffusivity

Apply vertical diffusivity to the thermodynamic field.

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Declaration

WVVerticalDiffusivity < WVForcing

Overview

This forcing applies a vertical diffusivity with fixed \(\kappa_z\) to the thermodynamic equation.

The specific form of the forcing is given by

\[\begin{align} \mathcal{S}_u &= 0 \\ \mathcal{S}_v &= 0 \\ \mathcal{S}_w &= 0 \\ \mathcal{S}_\eta &= \kappa_z \frac{\partial^2 \eta}{\partial z^2} - \kappa_z \frac{\partial}{\partial z} \ln N^2 \end{align}\]

The horizontally uniform \(-\kappa_z\partial_z\ln N^2\) source projects onto the mean-density-anomaly component. Set shouldForceMeanDensityAnomaly=false to omit this source. The option has no effect for constant stratification because the gradient is zero, and it does not modify the wave modes.

For WVTransformStratifiedQG, the QGPV definition

\[q=\partial_xv-\partial_yu-f\partial_z\eta\]

maps the displacement source \(\mathcal{S}_\eta=\kappa_z\partial_{zz}\eta\) to

\[\mathcal{S}_q=-f\partial_z\mathcal{S}_\eta =-f\kappa_z\partial_{zzz}\eta.\]

Stratified QG contains only nonzero-horizontal-wavenumber geostrophic modes, not a mean-density-anomaly component. Consequently, shouldForceMeanDensityAnomaly does not alter its QGPV pathway.

Example

wvt = WVTransformConstantStratification([40e3,30e3,2e3],[8,6,5],N0=5.2e-3,latitude=45,isHydrostatic=true);
wvt.addForcing(WVVerticalDiffusivity(wvt,kappa_z=1e-6));

Notes

This is currently implemented in the spatial domain. It applies to wave-bearing three-dimensional transforms and has a separate QGPV pathway for stratified QG. It is not compatible with barotropic QG, which has no vertical structure.

Topics

• Create the forcing
  • WVVerticalDiffusivity Create vertical diffusivity for a three-dimensional transform.
• Inspect forcing configuration
  • kappa_z Configured vertical diffusivity in \(\mathrm{m^{2}\,s^{-1}}\).
  • shouldForceMeanDensityAnomaly Whether to include the mean-density-anomaly source.

Developer Topics

These items document internal implementation details and are not part of the primary public API.

• Forcing persistence
  • classRequiredPropertyNames Returns the required property names for the class
• Forcing internals
  • dLnN2 Precomputed vertical logarithmic stratification gradient.

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