The vertical friction


   subroutine friction(kappa,avmolu,tx,ty)

This subroutine updates the bottom roughness

$\displaystyle z_0^b = 0.1 \frac{\nu}{u_*^b} + 0.03 h_0^b + z_a \quad .$ (23)

The first term on the right hand side of (23) represents the limit for hydraulically smooth surfaces, the second term the limit for completely rough surfaces. Note that the third term, $ z_a$, is the contribution of suspended sediments to the roughness length, see Smith and McLean (1977). It is updated during calls to the sediment-routines.

The law-of-the-wall relations are used to compute the friction velocity

$\displaystyle u_*^b = r \sqrt{U_1^2 + V_1^2} \; , \quad$ (24)

where $ U_1$ and $ V_1$ are the components of the mean velocity at the center of the lowest cell. We used the abbreviation

$\displaystyle r=\frac{\kappa}{\ln \left( \frac{0.5h_1+z_0^b}{z^b_0} \right)} \; , \quad$ (25)

where $ \kappa$ is the von Kármán constant and the index `1' indicates values at the center of the first grid box at the bottom (version 1). Another expression for $ r$ can be derived using the mean value of the velocity in the lowest grid box, and not its value in the middle of the box (version 2). Also this method is supported in friction() and can be activated by uncommenting one line in the code.

If no breaking surface waves are considered, the law of the wall also holds at the surface. The surface roughness length may be calculated according to the Charnock (1955) formula,

$\displaystyle z_0^s=\alpha \frac{(u_*^s)^2}{g} \quad .$ (26)

The model constant $ \alpha$ is read in as charnock_val from the meanflow namelist.


   use meanflow,      only: h,z0b,h0b,MaxItz0b,z0s,za
   use meanflow,      only: u,v,rho,gravity
   use meanflow,      only: u_taub,u_taus,drag,taub
   use meanflow,      only: charnock,charnock_val,z0s_min
   REALTYPE, intent(in)                :: kappa,avmolu,tx,ty
   Original author(s): Hans Burchard & Karsten Bolding

Karsten Bolding 2012-12-28