  In the recent paper [1] it was shown that for paraxial propagation of scalar
waves, the transverse linear momentum and orbital angular momentum (OAM) are
related to the wave coherence function. Although both of these quantities are
conserved during free-space propagation, they fluctuate for beam propagation in
a random inhomogeneous medium. We hereby present an extension of this theory to
the case of OAM fluctuations of a spherical wave intercepted by a finite
aperture. A complete asymptotic theory for the aperture-averaged OAM variance
is developed for both weak and strong fluctuation conditions, based on the
asymptotic expansions of the Feynman path-integral solution for the
fourth-order coherence function of a spherical wave propagating through a
random inhomogeneous medium. We show that"square root" law, and that the
weak/strong fluctuation conditions for the aperture-averaged OAM are not
defined by the values of the scintillation index of the incident wave.
