The orbital angular momentum (OAM) of vortex beams has important application prospects in free-space optical communications. During the propagation of vortex beams, atmospheric turbulence can affect the accurate detection of OAM modes. We propose and demonstrate the accurate detection of OAM modes using a shear interferometer and residual network model (ResNet-50) under different atmospheric turbulence conditions. We first derive the optical field intensity distribution of OAM beams after passing them through a shearing interferometer. We then introduce atmospheric turbulence theory and a residual network model suitable for the proposed physical model. Finally, we investigate the effects of training sample size on OAM recognition accuracy and OAM recognition accuracy under different turbulence intensity conditions. Results show that during the propagation of OAM beams, within the range of topological charge l of －4―4 and under weak atmospheric turbulence simulated by computers at Cn2=5×10^-16 m^-2/3, the OAM recognition accuracy is 100%. Under strong atmospheric turbulence simulated at Cn2=5×10^-14 m^-2/3, the OAM recognition accuracy is 92%.