Based on a method of inductive inference known as the principle of maximum entropy, a time-varying underwater acoustic channel model is derived. The resulting model is proved to be consistent so that it only relies on the available knowledge of the environment to model. While requiring only a few parameters (e.g. channel average power and Doppler spread), it is shown through fading statistics and bit error rates measurements that accurate channel impulse responses can be obtained for communication applications. The Matlab code of the proposed model is available at http://perso.telecombretagne.eu/fxsocheleau/software.