WVHorizontalDamping

Apply horizontal Laplacian viscosity and diffusivity.

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Declaration

WVHorizontalDamping < WVForcing

Overview

The damping is a simple horizontal Laplacian, designed to mimic the HorizontalScalarDiffusivity in Oceananigans to allow direct comparison between the models. It applies to wave-bearing three-dimensional transforms and is intended for use with WVVerticalDamping. For an automatically scaled closure, use WVAdaptiveDamping.

The specific form of the forcing is given by

\[\begin{align} \mathcal{S}_u &= \nu \left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) u \\ \mathcal{S}_v &= \nu \left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) v \\ \mathcal{S}_w &= \nu \left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) w \\ \mathcal{S}_\eta &= \kappa \left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \eta \end{align}\]

These are horizontal Laplacian viscosity, \(\nu\), and diffusivity, \(\kappa\). Combine this closure with WVVerticalDamping to damp vertical 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(WVHorizontalDamping(wvt,nu=1e-4,kappa=1e-6));

Notes

This closure is evaluated in the spatial domain.

The configured viscosity and diffusivity are preserved when the forcing is copied to a transform with a different resolution.

Topics

• Create the forcing
  • WVHorizontalDamping Create horizontal Laplacian damping for a transform.
• Inspect forcing configuration
  • nu Horizontal momentum viscosity in \(\mathrm{m^{2}\,s^{-1}}\).
  • kappa Horizontal 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

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