Channel estimation is critical to achieve high data rate acoustic communications in the ocean. Channel estimates are often utilized to address the distortions induced by multipath propagation in various communication receivers. Therefore, accurate channel estimation is often the prerequisite for reliable coherent acoustic communications. Many efforts have been devoted to either characterizing the acoustic channel or developing high-performance channel estimation algorithms. However, limited work has been directed to investigate effect of channel fluctuations on estimation performance. Here we seek to quantify the impact of channel fluctuations on least squares channel estimators. A new metric, channel variation ratio, is used to describe the rate of fluctuations in the acoustic impulse responses. We investigate the relationship between the mean squared error (MSE) of the channel estimates and the channel variation ratio. We show the new metric can be used to predict channel estimation MSE for least squares channel estimators. Numeric results also show that there exists an optimal channel length with the minimum estimation error for fluctuating acoustic channels. Both computer simulations and experimental data have been used to validate the findings. [Work supported by the National Science Foundation CNS# 1704076.]