In order to obtain insight into a complex vector field, it is often necessary to construct a hierarchical representation of the field. One way to construct such a hierarchy is based on grouping vectors together using certain similarity criteria. In this paper, we present a study of a 2D vector field clustering technique that is based on piecewise linear vector field approximations and an extension of a data clustering method called Normalized Cut (NC). Specifically, two steps are taken to implement the extended NC method. First, a similarity measurement for vector data is defined. Second, an eigenproblem solver is used to find the eigenvector used for partitioning. After the constructio n of first-level clusters, we can obtain a finer-level clustering by recursively applying the same procedure to intermediate clusters. The resulting clusters capture the features around the critical points.