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

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

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


Karsten Bolding 2012-01-24