In this paper, we apply a derived scalar field, called the φ field, to assist the visualization of various flow data. The value of the φ field at a spatio-temporal location is determined by the accumulated angle changes of the tangent directions along the integral curve starting from this location. Important properties of the φ field and its gradient magnitude |∇φ| field are studied. In particular, we show that the patterns in the derived φ field are generally aligned with the flow direction based on an inequality property. In addition, we compare the φ field with some other attribute fields and discuss its relation with a number of flow features, such as topology, LCS and cusp-like seeding structures. Furthermore, we introduce a unified framework for the computation of the φ field and its gradient field, and employ them to a number of flow visualization and exploration tasks, including integral curve filtering, seeds generation and flow domain segmentation. We show that these tasks can be conducted more efficiently based on the information encoded in the φ field and its gradient.