Do STRIDE/RDCON Δ' values require manual nondimensionalization for comparison against PEST3?

[d-burg]

@zrwang2015 @aglasser17 I'm trying to understand whether STRIDE & RDCON raw $\Delta'$ values need to be multiplied by $\psi^{2\mu}$ for comparison against PEST3, and for further stability analysis (e.g. taking $\Delta' - \Delta_{crit}$). In Fig. 6 of Wang, Glasser, Brennan et al. 2020, were the raw RDCON $\Delta'$ values externally multiplied by $\psi^{2\mu}$?

Thank you for your help.

[matt-pharr]

@d-burg I have been thinking about this for a while and I think it was necessary not to compare between STRIDE/RDCON vs PEST3 but because they were comparing different rational surfaces.

$$ \Delta' \equiv \lim_{ \epsilon \to 0 } \frac{{\Psi'_{r}(r_{s}+\epsilon)-\Psi'_{r}(r_{s}-\epsilon)}}{\Psi_{r}(r_{s})} $$

so $\Delta'$ is a dimensionless quantity that is dependent on the flux, and its derivative at a rational surface, and the first order asymptotic terms of solutions $\Psi$ at rational surfaces go like $\psi^{-2\sqrt{ D_{I} }}$ (See the paragraph after eq. 50 in Glasser "Direct criterion of Newcomb" 2016). Then, the derivative of this term would go like $\psi^{-1-2\sqrt{ D_{I} }}$ or $\psi^{2\mu}$ where $\mu = -\frac{1}{2} - \sqrt{D_{I}}$. Thus scaling by this quantity makes the $\Delta'$ values comparable at different rational surfaces. Would this make sense?