In this paper, a variational technique derived from optimal control theory is used in order to realize a dynamically consistent motion estimation of a whole fluid image sequence. The estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint evolution law. By combining physical conservation laws and image observations, a physically grounded temporal consistency is imposed, and the quality of the motion estimation is significantly improved. The method is validated on two synthetic image sequences provided by numerical simulation of fluid flows and on real world meteorological examples.