Calculation of the vertical shear


   subroutine shear(nlev,cnpar)

The (square of the) shear frequency is defined as

$\displaystyle M^2 = \left( \dfrac{\partial {U}}{\partial {z}} \right)^2 + \left( \dfrac{\partial {V}}{\partial {z}} \right)^2 \quad .$ (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 conversion from mean to turbulent kinetic energy, see Burchard (2002a). The shear is calculated by dividing the energy-consistent form of the shear production (see equation (14) by Burchard (2002a), but note the typo in that equation) by the eddy viscosity. The correct form of the right hand side of equation (14) of Burchard (2002a) should be:

\begin{displaymath}\begin{array}{rcl} \displaystyle \left(D_{kin} \right)_j & = ...
... \ & = & \displaystyle P_{j+1/2}^l + P_{j-1/2}^u, \end{array}\end{displaymath} (37)

with the mean kinetic energy dissipation, $ \left(D_{kin} \right)_j$. The two terms on the right hand side are the contribution of energy dissipation from below the interface at $ j+1/2$ and the contribution from above the interface at $ j-1/2$. With (37), an energy-conserving discretisation of the shear production at $ j+1/2$ should be

$\displaystyle P_{j+1/2} = P_{j+1/2}^l + P_{j+1/2}^u,$ (38)

such that a consistent discretisation of the square of the shear in $ x$-direction should be

\begin{displaymath}\begin{array}{rcl} \displaystyle \left( \dfrac{\partial {U}}{...
...}-U_j\right)} {(z_{j+3/2}-z_{j+1/2})(z_{j+1}-z_j)}. \end{array}\end{displaymath} (39)

The $ V$-contribution is computed analogously. The shear obtained from (39) plus the $ V$-contribution is then used for the computation of the turbulence shear production, see equation (148).


   use meanflow,   only: h,u,v,uo,vo
   use meanflow,   only: SS,SSU,SSV
   number of vertical layers
   integer,  intent(in)                :: nlev
   numerical "implicitness" parameter
   REALTYPE, intent(in)                :: cnpar
   Original author(s): Lars Umlauf

Karsten Bolding 2012-12-28