WVVerticalDamping

Apply vertical Laplacian viscosity and diffusivity.

---

Declaration

WVVerticalDamping < WVForcing

Overview

The damping is designed to mimic the VerticalScalarDiffusivity in Oceananigans to allow for direct comparison between the models. This applies to wave-bearing three-dimensional transforms and is intended for use with WVHorizontalDamping. For an automatically scaled closure, use WVAdaptiveDamping.

The specific form of the forcing is given by

\[\begin{align} \mathcal{S}_u &= \nu \frac{\partial^2 u}{\partial z^2} \\ \mathcal{S}_v &= \nu \frac{\partial^2 v }{\partial z^2} \\ \mathcal{S}_w &= \nu \frac{\partial^2 w}{\partial z^2} \\ \mathcal{S}_\eta &= \kappa \frac{\partial^2 \eta}{\partial z^2} - \kappa \frac{\partial}{\partial z} \ln N^2 \end{align}\]

Here \(\nu\) is the vertical viscosity and \(\kappa\) is the vertical diffusivity. Combine this closure with WVHorizontalDamping to damp horizontal gradients as well. For guidance on automatically scaled coefficients, see WVAdaptiveDamping.

Example

wvt = WVTransformConstantStratification([40e3,30e3,2e3],[8,6,5],N0=5.2e-3,latitude=45,isHydrostatic=true);
wvt.addForcing(WVVerticalDamping(wvt,nu=5e-4,kappa=1e-6));

Notes

This closure is evaluated in the spatial domain.

For constant stratification, \(\partial_z \ln N^2=0\) and the stratification-gradient correction vanishes. The configured viscosity and diffusivity are preserved when the forcing is copied to a transform with a different resolution.

Topics

• Create the forcing
  • WVVerticalDamping Create vertical Laplacian damping for a transform.
• Inspect forcing configuration
  • nu Vertical momentum viscosity in \(\mathrm{m^{2}\,s^{-1}}\).
  • kappa Vertical displacement diffusivity in \(\mathrm{m^{2}\,s^{-1}}\).

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.

---