Ground based long-range passive imaging systems often suffer from degraded image quality due to a turbulent atmosphere. While methods exist for removing such turbulent distortions, many are limited to static sequences which cannot be extended to dynamic scenes. In addition, the physics of the turbulence is often not integrated into the image reconstruction algorithms, making the physics foundations of the methods weak. In this paper, we present a unified method for atmospheric turbulence mitigation in both static and dynamic sequences. We are able to achieve better results compared to existing methods by utilizing (i) a novel space-time non-local averaging method to construct a reliable reference frame, (ii) a geometric consistency and a sharpness metric to generate the lucky frame, (iii) a physics-constrained prior model of the point spread function for blind deconvolution. Experimental results based on synthetic and real long-range turbulence sequences validate the performance of the proposed method.