Underwater acoustic communication is a key point for performance improvement in an autonomous underwater vehicle (AUV) swarm. The communication process is essential for improving the AUVs localization accuracy for navigation and is a convenient way for sharing information among the AUVs in a network. The objective of this work, which was developed in the COMET and NEMOSENS projects, is to address the communication process required in a mobile underwater wireless network, with a focus on the proposal of an adaptive physical layer methodology. We discuss about the employed channel access method, the frame structure, and we propose the usage of an adaptive guard interval in order to ameliorate the network usage rate. We explain the physical layer aspect of the communication: the data processing at the transmitter and receiver side. In addition to that, we propose the usage of smart communications among AUVs. We design a method for adapting some physical layer parameters. The proposed approach relies only on the knowledge of the transmission geometry, and it optimizes the number of subcarriers and the cyclic-prefix length of the Orthogonal Frequency-Division Multiplexing (OFDM) system. The obtained results show a performance improvement in terms of bit-error rate when compared with the case of random parameters selection. These results corroborate the benefits of our adaptive parameters approach.