Abstract: This paper presents Drawing with the Flow, a sketch-based interface for illustrating 2D vector fields. Drawing with the Flow explores the problem of making scientific visualization tools accessible to artists and illustrators, who have a finely tuned visual design sense, but do not typically have the programming or mathematical background required to work with modern visualization algorithms and tools. Using a sketch-based interface that is accessible to illustrations, Drawing with the Flow makes it possible for illustrators to explore new visual designs for streamline placement in order to create illustrations of 2D vector fields, such as simulated fluid flows. The interface includes a method for interpreting hand-drawn marks relative to an underlying vector field, utilizing an "ink-data settling" procedure to subtly maintain an image consistent with the underlying data. A variable-density interactive streamline seeding algorithm tied to sketch-based input is also introduced, and design lessons learned and limitations are discussed. Several example illustration results have been created during sessions ranging from five to twenty-five minutes. The results presented demonstrate different styles of illustration for describing simulated data for 2D flows past a cylinder and 2D flows that include several different types of critical points.