The vertical friction

INTERFACE:

   subroutine friction(kappa,avmolu,tx,ty)

DESCRIPTION:

This subroutine updates the bottom roughness

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

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

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

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

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

USES:

   use meanflow,      only: h,z0b,h0b,MaxItz0b,z0s,za
   use meanflow,      only: u,v,gravity
   use meanflow,      only: u_taub,u_taus,drag
   use meanflow,      only: charnock,charnock_val,z0s_min
 
   IMPLICIT NONE

INPUT PARAMETERS:

   REALTYPE, intent(in)                :: kappa,avmolu,tx,ty

REVISION HISTORY:

   Original author(s): Hans Burchard & Karsten Bolding
   $Log: friction.F90,v $
   Revision 1.10  2006-11-20 17:28:58  kbk
   [Cc]harnok -> [Cc]harnock - A. Jenkins
   Revision 1.9  2006-11-20 17:26:15  kbk
   [Cc]harnok -> [Cc]harnock - A. Jenkins
   Revision 1.8  2005/08/11 12:31:54  lars
   corrected error in documentation. Thanks to Patrizio Mariani
   Revision 1.7  2005/06/27 13:44:07  kbk
   modified + removed traling blanks
   Revision 1.6  2004/08/18 12:33:30  lars
   updated documentation
   Revision 1.5  2004/01/13 08:39:49  lars
   included roughness due to suspended sediments
   Revision 1.4  2003/03/28 09:20:35  kbk
   added new copyright to files
   Revision 1.3  2003/03/28 08:56:56  kbk
   removed tabs
   Revision 1.2  2003/03/10 08:50:06  gotm
   Improved documentation and cleaned up code
   Revision 1.1.1.1  2001/02/12 15:55:57  gotm
   initial import into CVS