Calculation of the vertical shear

INTERFACE:

   subroutine shear(nlev,cnpar)

DESCRIPTION:

The (square of the) shear frequency is defined as

$$M^2 = \left( \dfrac{\partial {U}}{\partial {z}} \right)^2 + \left( \dfrac{\partial {V}}{\partial {z}} \right)^2 \quad .$$ (36)

It is an important parameter in almost all turbulence models. The $U$- and $V$-contributions to $M^2$ are computed using a new scheme which guarantees conservation of kinetic energy for the convertion from mean to turbulent kinetic energy, see Burchard (2002a). With this method, the discretisation of the $U$-contribution can be written as

$$\left( \dfrac{\partial {U}}{\partial {z}} \right)^2 \approx \frac{(\bar U_{j+1}-\bar U_j) (\tilde U_{j+1}-\tilde U_j)}{(z_{j+1}-z_j)^2}$$ (37)

where $\tilde U_j=\frac12(\hat U_j+U_j)$. The $V$-contribution is computed analogously. The shear obtained from (37) plus the $V$-contribution is then used for the computation of the turbulence shear production, see equation (146).

USES:

   use meanflow,   only: h,u,v,uo,vo
   use meanflow,   only: SS,SSU,SSV
 
   IMPLICIT NONE

INPUT PARAMETERS:

 
   number of vertical layers
   integer,  intent(in)                :: nlev
 
   numerical "implicitness" parameter
   REALTYPE, intent(in)                :: cnpar

REVISION HISTORY:

   Original author(s): Lars Umlauf
   $Log: shear.F90,v $
   Revision 1.1  2005-06-27 10:54:33  kbk
   new files needed