High-resolution satellite imagery is indispensable for tracking the genesis, intensification, and trajectory of tropical cyclones (TCs). However, existing deep learning-based super-resolution (SR) methods often treat satellite image sequences as generic videos, neglecting the underlying atmospheric physical laws governing cloud motion. To address this, we propose a Physics Encoded Spatial and Temporal Generative Adversarial Network (PESTGAN) for TC image super-resolution. Specifically, we design a disentangled generator architecture incorporating a PhyCell module, which approximates the vorticity equation via constrained convolutions and encodes the resulting approximate physical dynamics as implicit latent representations to separate physical dynamics from visual textures. Furthermore, a dual-discriminator framework is introduced, employing a temporal discriminator to enforce motion consistency alongside spatial realism. Experiments on the Digital Typhoon dataset for 4$\times$ upscaling demonstrate that PESTGAN establishes a better performance in structural fidelity and perceptual quality. While maintaining competitive pixel-wise accuracy compared to existing approaches, our method significantly excels in reconstructing meteorologically plausible cloud structures with superior physical fidelity.