Counterintuitive recorder fingerings I understand the basic principle of recorder's sound production. The frequency of the basic sound wave is reversely proportional to the effective length of the air column. One can shorten the air column by opening the holes, which is pretty straightforward for the "open fingerings" (the ones with an unbroken line of upper holes closed and lower holes open).
I also understand some of the "cross fingerings" e.g the D♯ on alto, (using this table: http://recorder-fingerings.com/en/F.php?t=aBar.2A.2g) is like an E but with some lower holes covered, so the effective length of the air column reaches a little below the one for E.
Also, I understand that by leaking the thumbhole one suppresses the basic wavelength and allows for the second harmonic to dominate (thus raising the sound octave higher)
There are however some fingerings that are counterintuitive for me in the upper part of the basic register. Namely: F, F♯, G, G♯, The strangest is that the for F♯ one covers fewer holes than for G♯. What is the physical explanation for these fingerings?
 A: Carse 2002 Musical Wind Instruments (pgs. 27 - 28) and Benade 1990 Fundamentals of Musical Acoustics: Second, Revised Edition (pgs. 460 - 463) both describe the finger placement you mention for F# as forkfingering, i.e.:

"...when the hole immediately below the one which is sounding is closed by a finger, the pitch of the sounding hole is lowered approximately a semitone."


The simple description of this phenomenon is that the single open hole is too small to act as a high-pass filter and 'cut off' the vibrating air column.
Benade explains this empirically by setting up a model woodwind instrument with bore radius $a$, tone hole radius $b$, and tone hole spacing $2s$.  When all the tone holes are open, he defines the cutoff frequency of the instrument as:
$$f_c = \frac{0.110 \ b \ c}{a}  \sqrt{\frac{1}{s \ t_e}}$$
Where $c$ is the speed of sound in free space, and $t_e$ is "the length of a cylindrical plug of air whose inertia is identical with that of the air which flows in and out through an actual hole drilled through a wall of thickness $t$".  Benade suggests $t_e \simeq (t + 1.5 b)$.
All of this is to suggest that for $f < f_c$, we can define a length correction $C$:
$$C = s \ \biggr (\sqrt{1 + 2 \frac{t_e \ a^2}{s \ b^2}} - 1 \biggr ) $$
The author paraphrases this quite nicely:

...an increase of interhole spacing $2s$ produced by fork-fingering will increase $C$ (and so flatten the note) simply because $s$ multiplies everything else in the formula. However $C$ does not increase quite in simple proportion to $s$; the diluting effect of the factor $\frac{1}{s}$ under the square root sign somewhat lessens the change in $C$...  In any event, we find that closing the hole always increases $C$ somewhat. and so flattens the note.

(Emphasis included in original document.)
