A current-aided inertial navigation framework is proposed for small autonomous underwater vehicles in longduration operations (> 1 hour), where neither frequent surfacing nor consistent bottom-tracking are available. We instantiate this concept through mid-depth, underwater navigation. This strategy mitigates dead-reckoning uncertainty of a traditional inertial navigation system by comparing the estimate of local, ambient flow velocity with preloaded ocean current maps. The proposed navigation system is implemented through a marginalized particle filter where the vehicle's states are sequentially tracked along with sensor bias and local turbulence that is not resolved by general flow prediction. The performance of the proposed approach is first analyzed through Monte Carlo simulations in two artificial background flow fields, resembling real-world ocean circulation patterns, superposed with smaller-scale, turbulent components with Kolmogorov energy spectrum. The current-aided navigation scheme significantly improves the dead-reckoning performance of the vehicle even when unresolved, small-scale flow perturbations are present. For a 6-hour navigation with an automotive-grade inertial navigation system, the currentaided navigation scheme results in positioning estimates with under 3% uncertainty per distance traveled (UDT) in a turbulent, double-gyre flow field, and under 7.3% UDT in a turbulent, meandering jet flow field. Further evaluation with field test data and actual ocean simulation analysis demonstrates consistent performance for a 6-hour mission, positioning result with under 25% UDT for a 24-hour navigation when provided direct heading measurements, and terminal positioning estimate with 16% UDT at the cost of increased uncertainty at an early stage of the navigation.