Sorry I can't help with the physics. One of my whistle teachers thinks
that instruments have souls of their own to account for the differences.
As for recorders, have you heard the FIRST Capercaillie album? Mark
Duff (a graduate of an Early Music School) rather disproves the notion
that recorders "can't substitute for a whistle, especially...in fast reels."
He is amazing. (He also uses some other early wind instruments to good
---Jim Ventola ([log in to unmask])