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This paper proposes a new approach, coupling physical models and image estimation techniques, for modelling the movement of fluids. The fluid flow is characterized by turbulent movement and dynamically changing patterns which poses challenges to existing optical flow estimation methods. The proposed methodology, which relies on Navier-Stokes equations, is used for processing fluid optical flow by using a succession of stages such as advection, diffusion and mass conservation. A robust diffusion step jointly considering the local data geometry and its statistics is embedded in the proposed framework. The diffusion kernel is Gaussian with the covariance matrix defined by the local second derivatives. Such an anisotropic kernel is able to implicitly detect changes in the vector field orientation and to diffuse accordingly. A new approach is developed for detecting fluid flow structures such as vortices. The proposed methodology is applied on artificially generated vector fields as well as on various image sequences.