Generating photorealistic animations from a single still photo represents a significant advancement in multimedia editing and artistic creation. While existing AIGC methods have reached milestone successes, they often struggle with maintaining consistency with real-world physical laws, particularly in fluid dynamics. To address this issue, this paper introduces ANFluid, a physics solver and data-driven coupled framework that combines physics-aware simulation (PAS) and dual-flow texture learning (DFTL) to animate natural fluid photos effectively. The PAS component of ANFluid ensures that motion guides adhere to physical laws, and can be automatically tailored with specific numerical solver to meet the diversities of different fluid scenes. Concurrently, DFTL focuses on enhancing texture prediction. It employs bidirectional self-supervised optical flow estimation and multi-scale wrapping to strengthen dynamic relationships and elevate the overall animation quality. Notably, despite being built on a transformer architecture, the innovative encoder-decoder design in DFTL does not increase the parameter count but rather enhances inference efficiency. Extensive quantitative experiments have shown that our ANFluid surpasses most current methods on the Holynski and CLAW datasets. User studies further confirm that animations produced by ANFluid maintain better physical and content consistency with the real world and the original input, respectively. Moreover, ANFluid supports interactive editing during the simulation process, enriching the animation content and broadening its application potential.