WVBottomFrictionQuadratic

Quadratic bottom friction

Declaration 

WVBottomFrictionQuadratic < WVForcing

Overview

Applies quadratic bottom friction to the flow, i.e., \(\frac{du}{dt} = -(Cd/dz)*|u|*u\). Cd is unitless, and dz is (approximately) the size of the grid spacing at the bottom boundary.

To compare with linear bottom friction where \(\frac{du}{dt} = -r*u\), note that \(-(Lz/dz)*r = -(Cd/dz)*|u|\) and you will find a characteristic velocity \(|u|\) of about 11.5 cm/s for Cd=0.002 and r=1/(200 days). If Cd=0.001, then the damping time scale has to double to 1/(400 days) for and equivalent characteristic velocity.

For barotropic QG we want the scaling to work out similarly, but now have \(-r = -(Cd/D)*|u|\) where \(D\) works out to be Lz. Thus, we will scale the barotropic QG quadratic bottom drag by 4000 m, to match typical oceanic scales.

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