Commit 0335a833 authored by Jonathan Lambrechts's avatar Jonathan Lambrechts
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add bottom friction doc

parent 6dae3b12
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in 35 minutes and 3 seconds
We suppose a logarithmic profile :
u(z) = \frac{u^*}{\kappa}\,\ln\left({\frac z {z_0}}\right)
where $z=0$ at the bottom of the sea and $z=H$ at the surface.
The mean 2D value can be obtained :
u_{2d} = \frac 1 H \int_0^H u(z)\, dz = \frac{u^*}{\kappa}\left(\ln\left({\frac H {z_0}}\right)-1\right)
which gives
u^* = \frac{\kappa\,u_{2d}}{\ln\left({\frac H {z_0}}\right)-1}
u(z) = \frac{u_{2d}\ln\left({\frac z {z_0}}\right)}{\ln\left({\frac H {z_0}}\right)-1}
in the 3D model, the bottom drag is parametrized as
d = -\left(\frac \kappa {\ln\frac{z_{\text{bot}}}{z_0}}\right)^2
by inserting $u(z)$
d = -\left(\frac{\kappa}{\ln\frac{H}{z_0}-1}\right)^2|u_{\text{2d}}|\,u_{\text{2d}}
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