The model of Mellor and Yamada (1982)

The pressure-strain model of Mellor and Yamada (1982) is expressed in terms of $q^2=2k$ and the dissipation length scale $l=q^3/(B_1 \epsilon)$, where $B_1$ is a model constant. The time scale ratio in this model is set to $r=c_b=B_1/B_2$. Using these expression, their model can be re-written as

$$\Phi_{ij} = - \dfrac{B_1}{3 A_1} \epsilon b_{ij} + 4 C_1 k S_{ij} \; , \quad$$ (93)

which, by comparison with (51), yields $c_1 = B_1 / (3 A_1)$ and $c_2 = 4 C_1$. All other parameters are zero.

Similarly, the pressure-scrambling model of Mellor and Yamada (1982) (using the extensions suggested by Kantha and Clayson (1994) and Kantha (2003)) reads

$$\Phi^b_i = - \dfrac{B_1}{6 A_2} \dfrac{\epsilon}{k} {\langle u'_i... ... S_{ij} + W_{ij} ) {\langle u'_j b' \rangle} - 2 C_3 k_b \delta_{i3} \; , \quad$$ (94)

which can be compared to (57) to obtain $c_{b1} = B_1 / (6 A_2)$ and $c_{b2} = C_2$, $c_{b3} = C_2$, $c_{b5} = C_3$. All other parameters are zero.

Several parameter sets suggested for this model are compiled in table 4

Table 4: Some parameter sets for the model of Mellor and Yamada (1982)

	$A_1$	$A_2$	$B_1$	$B_2$	$C_1$	$C_2$	$C_3$
MY82	$0.92$	$0.74$	$16.55$	$10.1$	$0.08$	0	0
KC94	$0.92$	$0.74$	$16.55$	$10.1$	$0.08$	$0.7$	$0.2$
K03	$0.58$	$0.62$	$16.55$	$11.6$	$0.038$	$0.7$	$0.2$