Canuto et al. (2001) and Cheng et al. (2002) use a model
that is virtually identical to the traditional model of
Launder et al. (1975) and Gibson and Launder (1978). The values
of their model parameters and their notation, however, are somewhat
different.
Looking for conversion relations, it should be noted that the
anisotropy tensor
CCHD used by Canuto et al. (2001)
is twice the tensor defined in (52),
CCHD. Also the dissipative time scale
CCHD of
Canuto et al. (2001) is twice the time scal defined in (56),
CCHD. If one further notes that the turbulent
heat flux
is related to the buoyancy flux
according to
, relations between the
model parameters can be found.
With these relations, equation (10a) of Canuto et al. (2001) can be
rewritten as

(89) 
The returntoisotropy part of the pressurestrain model
of Canuto et al. (2001) reads

(90) 
from which, by comparing with (51), it follows that
and , and hence from (65)
. Thus, adopting the relations
,
,
, ,
and
, (89) corresponds exactly
to (59),
Similarly, equation (10a) of Cheng et al. (2002) can be reexpressed
in the form

(91) 
The somewhat simpler model of Canuto et al. (2001) adopts the
equilibrium assumption
(72), and replaces the last term in (91) by
and, assuming
constant , identifies
. The time scale
ratio is computed in equation (20a) of Canuto et al. (2001).
The returntoisotropy part of this model (see equation (6c) of
Cheng et al. (2002)) reads

(92) 
from which follows, by comparison with (57) and (65), that
. Comparing (91) with
(63) one finds, by inspection, the relations
,
,
,
,
and
. Some parameter sets for this model are compiled in table 3.
Karsten Bolding
20120124