WVBottomFrictionLinear

Apply linear drag at the bottom boundary.

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Declaration

WVBottomFrictionLinear < WVForcing

Overview

The parameter \(r\) is an inverse time scale in \(\mathrm{s^{-1}}\). For a three-dimensional transform, the bottom tendency is scaled by the bottom quadrature weight z_int(1) so its vertically integrated effect does not change with vertical resolution:

\[r_\mathrm{scaled}=\frac{L_z}{z_\mathrm{int}(1)}r.\]

A barotropic transform has no vertical quadrature and uses \(r_\mathrm{scaled}=r\).

Comparing this with quadratic drag gives the characteristic relation \(L_z r=C_d\lvert\mathbf{u}\rvert\).

For both nonhydrostatic and hydrostatic transforms linear bottom drag

\[\begin{align} \mathcal{S}_u &= -r_\mathrm{scaled} u(x,y,-D) \\ \mathcal{S}_v &= -r_\mathrm{scaled} v(x,y,-D) \\ \mathcal{S}_w &= 0 \\ \mathcal{S}_\eta &= 0 \end{align}\]

and for quasigeostrophic transforms,

\[\begin{align} \mathcal{S}_\mathrm{qgpv} &= -r_\mathrm{scaled}\zeta(x,y,-D) \end{align}\]

where \(\zeta = \partial_x v - \partial_y u\).

Example

wvt = WVTransformConstantStratification([40e3,30e3,2e3],[8,6,5],N0=5.2e-3,latitude=45,isHydrostatic=true);
wvt.addForcing(WVBottomFrictionLinear(wvt,r=1/(200*86400)));

Topics

• Create the forcing
  • WVBottomFrictionLinear Create linear bottom friction for a transform.
• Inspect forcing configuration
  • r Configured linear drag rate in \(\mathrm{s^{-1}}\).
• Inspect forcing or damping scales
  • r_scaled Drag rate applied at the bottom grid point in \(\mathrm{s^{-1}}\).

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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