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  • $\begingroup$ Exclusions -> None? $\endgroup$ Commented Jan 17 at 13:46
  • $\begingroup$ @cvgmt I did try that, it doesn't fix the branch cuts completely, in fact it actually didn't appear to make a difference at all. It also doesn't fix the slight shift of the aerofoil that I assume is due to the branch cuts. Originally I tried to take an approach similar to Alex where I have to include the sign of the functions but it (I) failed miserably $\endgroup$ Commented Jan 17 at 13:50
  • $\begingroup$ @Kendall: Regarding the first plot of streamFunction[z]: Am I to understand you are trying to avoid the default branch-cuts of the associated square root function of zTransform? If so, perhaps an analytically-continuous version of $\sqrt{1/4 z^2-a^2}$ can be used in your functions. I can look into it if this is something you'd be interested in. $\endgroup$ Commented Jan 17 at 16:01
  • $\begingroup$ @josh yes I am trying to avoid the branch cuts in general on either the z-plane or Z-plane. Your suggestion has made me think that perhaps there is a convenient transformation (such as z = 2acosh(w) ) that can enable me to avoid the root completely. I haven't made functions analytically continuous before, but it doesn't appear to be too difficult. Thank you for the suggestion. $\endgroup$ Commented Jan 18 at 8:32
  • $\begingroup$ @Kendall: I noticed your plot is in the range $|z|<3$. However, the function $\sqrt{1/4 z^2-1}$ fully-ramifies at its singular points $\pm 2$ so we cannot construct a single-valued analytic sheet which includes either of these points. However we can for $|z|<2$ which would then produce analytically continuous contours in this range. If this is something you wish to pursue. I can show you how if you wish. $\endgroup$ Commented Jan 18 at 15:34