This paper is concerned with the analysis of 2D fluid motion from numerical images. The interpretation of such deformable flow fields can be derived from the characterization of linear motion models provided that first order approximations are considered in an adequate neighborhood of so-called singular points where the velocity becomes null. However, locating such points, delimiting this neighborhood, and estimating the associated 2D affine motion model, are intricate difficult problems. We explicitly address these three joint problems according to a statistical adaptive approach. In the fluid mechanics images we are dealing with, the motion model can be directly inferred from a single image, since the visualized form accounts for the underlying motion. We have developed an original method which relies on an orthogonality constraint between the spatial image gradient field and the motion model velocity field, while explicitly formalizing and handling both model and measurement noises. This method has been validated on several real fluid flow images.