We have developed an adaptive sampling algorithm for an Explorer autonomous underwater vehicle (AUV) to conduct in-situ analysis of acoustic measurements to perform autonomous oil plume detection and tracking. The methodology of the tracking phase involves ongoing analysis of the detected plume, assessing target validity and proximity for AUV decision-making for plume mapping. We previously introduced the bumblebee flight path, a new biomimetic search pattern designed to maximize the spatial coverage in the oil plume detection phase. This paper focuses on a new tracking strategy as the key adaptive stage in our plume delineation. For initial development we used a 360-degree scanning sonar sensor model. Simulations were done with different plume models to assess the performance of the developed adaptive sampling algorithm. A convergence study demonstrated that the algorithm could successfully track the boundary of a non-regular shaped/patchy oil plume at up to a 0.05Hz sampling frequency. A sensitivity study identified the correlations between plume feature complexity and the anticipated range of acoustic measurement update delays. The decision-making architecture consists of three separate components which implements either proximity or boundary following control and contributes to the final decision on the next desired heading of the vehicle. A weight ratio, that determined the relative allocation of each component, was varied to study its impact on the tracking performance of the AUV. The novelty of our approach is in addressing the discontinuous and patchy nature of realistic oil plumes. Our sampling algorithm and its performance in simulations is a significant step beyond the practical limitations of existing gradient-following methods because it accounts for the oil patches and droplets which gradient-following algorithms do not.