Based on the geometrical optics approximation, we analyze the effects of non-Kolmogorov turbulence on the spiral spectrum of the orbital angular momentum (OAM) of Airy–Schell beams. Our numerical results of Airy–Schell beams on the horizontal path show that the beam spreading due to diffraction is smaller for shorter wavelengths, a smaller OAM quantum number, a larger radius of the main ring, and a higher arbitrary transverse scale in weak turbulence. The oscillation frequency of the mode probability density of Airy–Schell beams in the radial direction is much lower than that of Hankel–Bessel beams. The mode probability densities of Airy–Schell and Hankel–Bessel beams are remarkably dependent on the wavelength and OAM quantum number. In order to improve the mode probability density, Airy–Schell beams with shorter wavelengths and lower OAM quantum numbers may be the better choice, which is diametrically opposite to Hankel–Bessel beams. Our research provides a reasonable basis for selecting light sources and precise tracking.