WVBottomFrictionQuadratic

Apply quadratic drag at the bottom boundary.

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Declaration

WVBottomFrictionQuadratic < WVForcing

Overview

The dimensionless drag coefficient \(C_d\) is divided by the bottom quadrature weight for a three-dimensional transform:

\[c_d=\frac{C_d}{z_\mathrm{int}(1)}.\]

Barotropic QG uses a fixed 4000 m reference depth, \(c_d=C_d/(4000\,\mathrm{m})\). Comparing quadratic and linear drag gives the characteristic relation \(L_z r=C_d\lvert\mathbf{u}\rvert\).

Using the notation that

\[|\mathbf{u}(x,y,-D)| = \sqrt{u^2(x,y,-D) + v^2(x,y,-D)}\]

is the magnitude of the total velocity at the bottom boundary. For hydrostatic and nonhydrostatic transforms,

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

and for quasigeostrophic transforms,

\[\begin{align} \mathcal{S}_\mathrm{qgpv} &= -c_d \left[ \partial_x \left( |\mathbf{u}|v \right) - \partial_y \left( |\mathbf{u}|u \right) \right]_{z=-D} \end{align}\]

Example

wvt = WVTransformConstantStratification([40e3,30e3,2e3],[8,6,5],N0=5.2e-3,latitude=45,isHydrostatic=true);
wvt.addForcing(WVBottomFrictionQuadratic(wvt,Cd=0.001));

Topics

• Create the forcing
  • WVBottomFrictionQuadratic Create quadratic bottom friction for a transform.
• Inspect forcing configuration
  • Cd Configured dimensionless quadratic drag coefficient.
• Inspect forcing or damping scales
  • cd Drag coefficient applied at the bottom in \(\mathrm{m^{-1}}\).

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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