We introduce stochastic models for flow fields with parameters that dictate the scale-dependent (self-similar) character of the field and control the balance between its rotational vs compressive behaviour. The development of our models is motivated by the availability of imaging modalities that measure flow vector fields (flow-sensitive MRI and Doppler ultrasound). To study such data, we formulate estimators of the model parameters, and use them to quantify the Hurst exponent and directional properties of synthetic and real-world flow fields (measured by means of phase-contrast MRI) in 3D.