We propose an algorithm for coherent detection of OFDM signals over underwater acoustic channels in the presence of Doppler distortions. The algorithm uses multiple FFT demodulators, each operating on a different (partial) segment of the incoming OFDM block. The segments corresponding to several adjacent carriers and multiple receiving elements are adaptively combined to reduce the inter-carrier interference. The combiner weights are computed recursively across carriers, using a stochastic gradient algorithm. The information contained in the combiner weights is also used to predict the Doppler shifts for the next incoming block, thus enhancing the accuracy of adaptive channel tracking. Synthetic and experimental data from a recent experiment conducted over a mobile acoustic channel in the 10 – 15 kHz band, show that partial FFT demodulation with enhanced channel tracking provides a significant gain in performance over a conventional coherent detector, and increases the bandwidth efficiency.