  Capacity scaling laws are analyzed in an underwater acoustic network with $n$
regularly located nodes on a square. A narrow-band model is assumed where the
carrier frequency is allowed to scale as a function of $n$. In the network, we
characterize an attenuation parameter that depends on the frequency scaling as
well as the transmission distance. A cut-set upper bound on the throughput
scaling is then derived in extended networks. Our result indicates that the
upper bound is inversely proportional to the attenuation parameter, thus
resulting in a highly power-limited network. Interestingly, it is seen that
unlike the case of wireless radio networks, our upper bound is intrinsically
related to the attenuation parameter but not the spreading factor. Furthermore,
we describe an achievable scheme based on the simple nearest neighbor multi-hop
(MH) transmission. It is shown under extended networks that the MH scheme is
order-optimal as the attenuation parameter scales exponentially with $\sqrt{n}$
(or faster). Finally, these scaling results are extended to a random network
realization.
