Corrections to SA implementation

[rois1995]

Proposed Changes

The CRot value was set to 1.0 for the HLPW5 but the standard value is 2.0 as suggested in TMR. Plus, there may be some inconsistencies with the negative branch of SA when used with the R variant. $\hat{S}$ should be used in the computation of the production term when $\hat{\nu}>0$. When $\hat{\nu}<0$, instead, the vorticity $\Omega$ should be used together with the $c_{t3}$ constant. Citing TMR:

"This model is the same as the "standard" version (SA), except that the (SA-R) production term becomes:

$c_{b1}(1-f_{t2})[\hat{S}+C_{rot}min(0,S-\Omega)]\hat{\nu}$

...

However, a negative production term is not acceptable for the negative branch ($\hat{\nu} < 0$) of the (SA-neg) model. If coding (SA-neg-R), a possible C0 continuous production term in the negative (SA-neg-R) branch is the following:

$c_{b1}(1-c_{t3})[\hat{\Omega}+C_{rot}min(0,S-\Omega)]\hat{\nu}$

"

I don't understand if the second production term has to be used everytime SA-neg is considered or only at the points where $\hat{\nu}<0$.

If it is already taken into account, then I'll modify the PR.

Related Work

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[rois1995]

I think no more changes are needed. All of the test cases remain the same since probably the Rotation correction wasn't used.

The only major corrections are the following:

• CRot now is set to 2.0 as in TMR
• The computation of $\hat{S}$ is performed before the the Rotation correction is applied, not after.

[bigfooted]

No regression tests are affected, so we have no test that uses this model? Can you add a test for this as well?