Underwater mobile acoustic sensor networks are promising tools for the exploration of the oceans. These networks require new robust solutions for fundamental issues such as: localization service for data tagging and networking protocols for communication. All these tasks are closely related with connectivity, coverage and deployment of the network. A realistic mobility model that can capture the physical movement of the sensor nodes with ocean currents gives better understanding on the above problems. In this paper, we propose a novel physically-inspired mobility model which is representative of underwater environments. We study how the model affects a range-based localization protocol, and its impact on the coverage and connectivity of the network under different deployment scenarios.