I mean, that portion of water moving with the ship due to its surge longitudinal acceleration. I need it to solve the ship motion dynamics longitudinally.
I ended up answering this question with the paper "Identification of hydrodynamic damping derivatives – a pragmatic approach", published in the Proceedings of the International Conference on Marine Simulation and Ship Manoeuvrability (MARSIM’03) by P. Oltmann. The semi-empirical equation given by him calculates the longitudinal added mass of water as a function of the ship displacement and hull block coefficient.