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In this paper, we examine the coupling between odor dynamics and vortex dynamics around undulating bodies, with a focus on bio-inspired propulsion mechanisms. Utilizing computational fluid dynamics simulations with an in-house immersed boundary method solver, we investigate how different waveform patterns, specifically carangiform and anguilliform, influence the dispersion of chemical cues in both water and air environments. Our findings reveal that vortex dynamics significantly impact the overall trajectory of odor spots, although the alignment between odor spots and coherent flow structures is not always precise. We also evaluate the relative contributions of diffusion and convection in odor transport, showing that convection dominates in water, driven by higher Schmidt numbers, while diffusion plays a more prominent role alongside convection in air. Additionally, the anguilliform waveform generally produces stronger and farther-reaching chemical cues compared to carangiform swimmers. The critical roles of Strouhal number and Reynolds number in determining the efficiency of odor dispersion are also explained, offering insights that could enhance the design of more efficient, adaptive, and intelligent autonomous underwater vehicles by integrating sensory and hydrodynamic principles inspired by fish locomotion.