WVNonlinearAdvection

The advective flux, \(\mathbf{u}\cdot \nabla \mathbf{u}\) and \(\mathbf{u}\cdot \nabla \eta\)

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Declaration

WVNonlinearAdvection < WVForcing

Overview

The nonlinear advection forcing adds the nonlinear terms to the momentum and thermodynamic equation.

The nonlinear terms are all computed in the spatial domain.

For nonhydrostatic transforms,

\[\begin{align} \mathcal{S}_u &= - \left( u \partial_x u + v \partial_y u + w \partial_z u \right) \\ \mathcal{S}_v &= - \left( u \partial_x v + v \partial_y v + w \partial_z v \right) \\ \mathcal{S}_w &= - \left( u \partial_x w + v \partial_y w + w \partial_z w \right) \\ \mathcal{S}_\eta &= - \left( u \partial_x \eta + v \partial_y \eta + w \left(\partial_z \eta +\eta \partial_z \ln N^2 \right) \right) \end{align}\]

for hydrostatic transforms,

\[\begin{align} \mathcal{S}_u &= - \left( u \partial_x u + v \partial_y u + w \partial_z u \right) \\ \mathcal{S}_v &= - \left( u \partial_x v + v \partial_y v + w \partial_z v \right) \\ \mathcal{S}_\eta &= - \left( u \partial_x \eta + v \partial_y \eta + w \left(\partial_z \eta +\eta \partial_z \ln N^2 \right) \right) \end{align}\]

and for quasigeostrophic transforms,

\[\begin{align} \mathcal{S}_\textrm{qgpv} &= - \left( u \partial_x q + v \partial_y q \right) \end{align}\]

where \(q\) is the qgpv.

Notes

This is the only forcing added to the transforms by default. You must explicitly remove it if you want to consider linear flows.

Topics

• Initialization
  • WVNonlinearAdvection initialize the WVNonlinearAdvection nonlinear flux
• Properties
  • dLnN2 variable stratification factor
• CAAnnotatedClass requirement
  • classRequiredPropertyNames Returns the required property names for the class

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