### Compute special values of stability functions

INTERFACE:

   subroutine compute_cm0(turb_method,stab_method,scnd_method)

DESCRIPTION:

Computes the values of the stability function defined in (46) in the logarithmic boundary-layer, , and in shear-free, spatially decaying turbulence, sf (see section 4.7.4).

is the value of in unstratified equilibrium flows, i.e. in the logarithmic wall region. It can be obtained from the relation , according to (80) written in the form

 (122)

In unstratified flows, only depends on (see sections 4.24-4.26), and (122) is a polynomial equation for the value of in equilibrium. Its solution is

 (123)

where, according to (67) in equilibrium . The value of the stability function in equilibrium follows directly from (122),

 (124)

Note that according to (78).

Algebraic Stress Models exhibit an interesting behaviour in unstratified, shear-free turbulence. Clearly, in the absence of shear, these models predict isotropic turbulence, , according to (61). This is a direct consequence of the assumption (60), implying an infinitely small return-to-isotropy time scale. Formally, however, the limit of the stability function for follows from (76) and the definitions given in sections 4.24-4.26. The limiting value is

 sf (125)

where, according to (67), one has either or , see section 4.24 and section 4.26, respectively. The above limit corresponds to nearly isotropic turbulence supporting a very small momentum flux caused by a very small shear.

Note that sfsf according to (78).

USES:

   IMPLICIT NONE

INPUT PARAMETERS:
   integer, intent(in)                 :: turb_method
integer, intent(in)                 :: stab_method
integer, intent(in)                 :: scnd_method

REVISION HISTORY:
   Original author(s): Lars Umlauf


Karsten Bolding 2012-12-28