Compute the velocity scale


INTERFACE:

   subroutine wscale(Bfsfc,u_taus,d,wm,ws)
DESCRIPTION:

This routine computes the turbulent velocity scale for momentum and tracer as a function of the turbulent friction velocity, $ u_*$, the "limited" distance, $ d_$lim, and the total buoyancy flux, $ B_f$, according to

$\displaystyle w_\phi = \dfrac{\kappa u_*}{\Phi_\phi (\zeta)} \quad .$ (227)

In this equation, $ \Phi_\phi$ is a non-dimensional function of the stability parameter $ \zeta=d_$lim$ /L$, using the Monin-Obukhov length,

$\displaystyle L = \dfrac{u_*^3}{\kappa B_f} \quad .$ (228)

In stable situations, $ B_f \ge 0$, the length scale $ d_$lim is just the distance from the surface or bottom, $ d$. Then, the non-dimensional function is of the form

$\displaystyle \Phi_\phi = 1 + \zeta \; , \quad$ (229)

and identical for momentum, heat, and tracers.

In unstable situations, $ B_f < 0$, the scale $ d_$lim corresponds to the distance from surface or bottom only until it reaches the end of the surface (or bottom) layer at $ d=\epsilon h$. Then it stays constant at this maximum value.

The different functional forms of $ \Phi_\phi(\zeta)$ for unstable flows are discussed in Large et al. (1994).


USES:

   IMPLICIT NONE
INPUT PARAMETERS:
 
   buoyancy flux (m^2/s^3)
   REALTYPE, intent(in)                :: Bfsfc
 
   friction velocity (m/s)
   REALTYPE, intent(in)                :: u_taus
 
   (limited) distance (m)
   REALTYPE, intent(in)                :: d
OUTPUT PARAMETERS:
 
   velocity scale (m/s)
   for momentum and tracer
   REALTYPE, intent(out)               :: wm, ws
REVISION HISTORY:
   Original author(s): Lars Umlauf

Karsten Bolding 2012-12-28