In this work, we introduce a method to detect moving objects in an image sequence, which is degraded from atmospheric turbulence and is taken from a non-stationary platform. For the purposes of this study, objects whose motion is on the same scale of the motion induced by atmospheric turbulence are examined. In addition, the problem of detecting moving objects from a non-stationary platform and detecting moving objects in atmospheric turbulence has been studied in literature, but the coupled problem is scarcely explored. Here, an optical flow-based approach is considered to remove flows corresponding to camera motion and atmospheric turbulence, leaving only the flow corresponding to moving objects. Our procedure first creates a model and compensates for camera motion. Next, a spatial-temporal cartoon+texture inspired decomposition is made on the motion-compensated flow field in order to separate flows corresponding to atmospheric turbulence and object motion. In the decomposition, the oscillatory (texture) component from the decomposition is assumed to correspond to the motion created by atmospheric turbulence, while the remaining geometric (cartoon) component is assumed to contain primarily moving objects. The geometric component is then processed with a detection and tracking method through the use of adaptive thresholding and Kalman filtering. The efficacy of the proposed method is demonstrated on an open source real-world dataset as well as a turbulence-simulated dataset.