A novel inertial navigation system is proposed for small autonomous underwater vehicles in long-duration, large-scale operations where frequent surfacing and consistent bottom-locking are not desirable. This strategy utilizes the dynamics of the background flow to significantly mitigate the dead-reckoning error of an inertial navigation system. This is achieved by comparing the local ambient flow velocity against the velocity field prediction pre-calculated through solving the background flow dynamics. The vehicle's attitude and linear velocity are estimated along with the vehicle's position in order to obtain an in-situ estimation of the absolute background flow velocity. Estimation errors of the vehicle's location, attitude and linear velocity are mutually correlated through continuously incorporating relative flow velocity measurements into state estimation. The proposed navigation system is implemented as a marginalized sequential Monte Carlo estimator, where the vehicle's position is estimated through samples, and the vehicle's attitude and linear velocity are inferred by Gaussian filters. Opportunistic information fusion among neighboring vehicles are achieved using covariance intersection. The performance of the proposed navigation system is analyzed in simulation within a turbulent multi-gyre flow field.