WVHorizontalDamping

Horizontal laplacian damping with 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 for direct comparison between the models. This should probably be used in combination with WVVerticalScalarDiffusivity. In general, you should be using the WVAdaptiveDamping.

The specific form of the forcing is given by

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

which is just your standard Laplacian viscosity, \(\nu\), and diffusivity, \(\kappa\), in the horizontal. This should be combined with WVVerticalScalarDiffusivity for a complete closure. For help choosing appropriate values, see the notes in WVAdaptiveDamping.

Usage

Assuming there is a WVTransform instance wvt, to add this forcing,

wvt.addForcing(WVHorizontalDamping(wvt,nu=1e-4, kappa=1e-6));

Notes

This is currently implemented in the spatial domain, an is thus highly un-optimized.

Topics

• Initialization
  • WVHorizontalDamping initialize the WVHorizontalDamping
• Properties
  • kappa horizontal diffusivity
  • nu horizontal viscosity
• CAAnnotatedClass requirement
  • classRequiredPropertyNames Returns the required property names for the class

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