The twinkling of stars, or scintillation, occurs because the optical path length of the atmosphere varies in both space and time due to turbulence.
This means that when the wavefront from a distant star enters a telescope, it is distorted from the flat wavefront expected for an object at infinity.
Because the fundamental Fourier mode of this wavefront varies in time, the average position of the PSF on the retina of a human observer also changes in time; the star appears to shake back and forth. (By this I mean that the wavefront at the telescope may be considered a superposition of plane waves. One particular plane wave is the strongest, or is the median; that is the one I mean by "fundamental Fourier mode". I'm not sure if I'm using exactly the right term. When I worked with an adaptive optics team one summer, we had a "tip-tilt mirror" specifically to correct for this mode, and then the deformable mirror corrected for higher-order aberrations. )
That much makes sense to me. However, I have read on Wikipedia that this is not the dominant effect in what we observe as scintillation. Instead, the overall apparent brightness of the star varies.
I presume this has essentially the same physical origin. The wavefront is complicated and dynamic, and so interference effects sometimes reduce and sometimes increase the brightness. What are the details of how this works? How can one work out that this effect should occur? Perhaps a specific example of what a wavefront might do and how this would result in varying brightness would be helpful.