WVNonlinearAdvection

Add nonlinear advection to the model equations.

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Declaration

WVNonlinearAdvection < WVForcing

Overview

The nonlinear terms are evaluated in physical space and added to the momentum, thermodynamic, or quasigeostrophic potential-vorticity (QGPV) equation appropriate to the transform.

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,

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

where \(q\) is QGPV.

Notes

Every supported transform installs this forcing by default. A nonlinear WVModel evaluates it automatically. Analytical linear evolution does not evaluate nonlinear forcing, so the object does not need to be removed when using linear evolution.

Example

wvt = WVTransformConstantStratification([40e3,30e3,2e3],[8,6,5],N0=5.2e-3,latitude=45,isHydrostatic=true);
nonlinearAdvection = wvt.forcingWithName("nonlinear advection");

Topics

• Create the forcing
  • WVNonlinearAdvection Create nonlinear advection for a transform.

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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