Analyzing fluid motion is essential in number of domains and can rarely be handled using generic computer vision techniques. In this particular application context, we address two distinct problems. First we describe a dedicated dense motion estimator. The approach relies on constraints issuing from fluid motion properties and allows us to recover dense motion fields of good quality. Secondly, we address the problem of analyzing such velocity fields. We present a kind of motionbased segmentation relying on an analytic representation of the motion field that permits to extract important quantities such as singularities, stream-functions or velocity potentials. The proposed method has the advantage to be robust, simple, and fast.