This paper presents a new turbo decision feedback equalizer and decoder (TDFED) for the orthogonal time-frequency space (OTFS) system of underwater mobile acoustic communications where the communication channel suffers from severe multipath and Doppler effects simultaneously. The proposed TDFED employs a set of feedforward and feedback filters in the time domain instead of the common approach that employs a normalized least mean square equalizer in the delay-Doppler domain. The receiver also utilizes low-complexity improved proportionate normalized least mean square channel estimation in the delay-Doppler domain. Practical OTFS modulation schemes are designed for acoustic transmission at a center frequency of 115 kHz and a symbol rate of 11.5 ksps (kilo-symbols-per-second). Several lake experiments in mobile communication scenarios are conducted to evaluate the proposed OTFS in comparison to the single-carrier coherent modulation (SCCM) and the orthogonal frequency division modulation (OFDM) schemes. The experimental results demonstrate that the proposed OTFS receiver effectively reduces the accuracy requirements of the Doppler compensation algorithm compared to the SCCM and OFDM schemes. The proposed TDFED algorithm achieves a much better bit error rate against long-multipath fading and severe Doppler shift than the existing delay-Doppler domain equalizers.