Small uncrewed underwater vehicles are proliferating and threaten maritime security, yet evade sonar and magnetic sensors built for larger submarines. Infrared thermal wakes, generated by hydrodynamic displacement that modulates the cold-skin layer, offer a non-acoustic, non-magnetic alternative even without cooling-water discharge. Existing studies, however, rely on idealized simulations that fail to capture real-world backgrounds, offering limited guidance for target-background discrimination. We establish AVP-IR-Wake, the first large-scale, real-world, physically diverse benchmark of 161,485 frames collected over three years. We show that thermal wakes are extended structures of discrete vortices, violating the compactness assumption of conventional targets. We reveal local indistinguishability: individual wake vortices are statistically identical to wind-induced background vortices in temporal, frequency, and sparse domains, sharing low-frequency information and long-range correlations. This challenges the assumptions of compact, transient, high-frequency targets in conventional detection. Yet we establish global morphological separability: although locally inseparable, the wake as a whole is organized by vehicle trajectory, whereas background clutter is organized by wind-driven thermal fronts. This explains why representative detectors fail and shows that reliable detection must shift from local feature extraction to global trajectory-constrained physical modeling. Because the cold-skin layer varies globally and seasonally, forecasting wake observability will require integrating physical oceanography and atmospheric science, linking underwater surveillance to the changing ocean surface.

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