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Providing an efficient communication for the underwater wireless sensor networks is a significant problem due to the unique characteristics of such environments. Radio signal cannot propagate well in deep water, and we have to replace this with the acoustic channel. This replacement results in many issues like high latency due to less propagation speeds, low bandwidths and high error probability. In addition, new features like node mobility with water currents and 3-dimensional space brings additional challenges to the underwater sensor network (UWSN) protocol design. Many routing protocols have been proposed for such environments but most of them considered that the complete dimensional location of all the sensor nodes is already known through a localization process, which itself is a challenging task in UWSNs. In this paper, we propose a novel routing protocol, called Hop-by-Hop Dynamic Addressing Based (H2-DAB), in order to provide scalable and time efficient routing. Our routing protocol will take advantage of the multiple-sink architecture of the underwater wireless sensor networks. The novelty of H2-DAB is that, it does not require any dimensional location information, or any extra specialized hardware compared to many other routing protocols in the same area. Our results show that H2-DAB effectively achieves the goals of higher data deliveries with optimal delays and energy consumptions.