Orthogonal frequency division multiplexing (OFDM) implicitly assumes that the channel used for signal transmission is linear and time-invariant for the length of each OFDM symbol. This is necessary for the channel matrix to be diagonalizable via the DFT, under cyclic prefix. The underwater acoustic channel is highly time-variant due to platform motion and environmental fluctuations. As a result, the application of standard OFDM leads to communication algorithms that break down when the transmitter or receiver are mobile. Several modifications to standard OFDM have been suggested and tested in the field. These have demonstrated that OFDM can perform reasonably well when the Doppler spread is minor. Unfortunately, Doppler can be highly time-varying in practice, with different wave propagation paths experiencing different amounts of Doppler. In this paper, we simulate various scenarios of platform mobility such as a receiver moving at constant speed or acceleration, a transmitter whose position is tracing out an oscillating pattern near a nominal transmission point, and basic multipath with significant Doppler spread. We compare the performance of published OFDM and single-carrier methods under these conditions. The single-carrier adaptive resampling equalizer presented here demonstrates significant improvement over OFDM in a variety of scenarios.