WVBottomFrictionLinear

Linear bottom friction

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Declaration

WVBottomFrictionLinear < WVForcing

Overview

Applies linear bottom friction to the flow, i.e., \(\frac{du}{dt} = -r \cdot u(x,y,-D)\). The parameter \(r\) has units of \(s^{-1}\) and thus can be set as an inverse time scale.

The linear bottom friction is scaled such that we actually apply, \(\frac{du}{dt} = -\frac{L_z}{dz} r \cdot u(x,y,-D)\) and the volume integrated effect of friction remains the same regardless of resolution. \(L_z\) is the total domain depth and \(dz\) is the spacing at the bottom grid point.

To compare with quadratic bottom friction where \(\frac{du}{dt} = -\frac{C_d}{dz} \lvert \mathbf{u} \rvert\), note that \(- \frac{L_z}{dz} r = -\frac{C_d}{dz} \lvert \mathbf{u} \rvert\) and you will find a characteristic velocity \(\lvert\mathbf{u}\rvert\) of about 10 cm/s for \(C_d=0.002\).

For both nonhydrostatic and hydrostatic transforms linear bottom drag

\[\begin{align} \mathcal{S}_u &= -\frac{L_z}{dz} r \cdot u(x,y,-D) \\ \mathcal{S}_v &= -\frac{L_z}{dz} r \cdot v(x,y,-D) \\ \mathcal{S}_w &= 0 \\ \mathcal{S}_\eta &= 0 \end{align}\]

and for quasigeostrophic transforms,

\[\begin{align} \mathcal{S}_\textrm{qgpv} &= -\frac{L_z}{dz} r \cdot \zeta(x,y,-D) \end{align}\]

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

Usage

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

wvt.addForcing(WVBottomFrictionLinear(r=1/(200*86400)));

Topics

• Initialization
  • WVBottomFrictionLinear initialize the WVBottomFrictionLinear
• Properties
  • r bottom friction, \(s^{-1}\)
  • r_scaled scaled bottom friction, \(\frac{Lz}{dz} r\) with units \(s^{-1}\)
• CAAnnotatedClass requirement
  • classRequiredPropertyNames Returns the required property names for the class

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