flowline

Flowline is a term used in geography, hydrology, and mathematics to denote a line that follows the direction of flow in a field. In geographic contexts, a flowline represents the path water would take across the landscape, tracing overland flow toward streams and drainage networks. Flowlines are often derived from digital elevation models by applying flow-direction and flow-accumulation algorithms; the resulting network helps delineate watersheds, model runoff, and characterize river channels.

In mathematics and physics, a flowline (often called an integral curve) is a trajectory of a point under a vector field. If a velocity field v(x) is defined, a flowline γ(t) satisfies γ'(t) = v(γ(t)). Flowlines describe the time evolution of particles in a flow and are central to dynamical systems and fluid dynamics. In steady flows, flowlines are aligned with streamlines, which reflect instantaneous motion directions.

Flowlines are related to, but not identical with, other representations such as streamlines, pathlines, and drainage networks. The term emphasizes the directional paths of transport and can be used to visualize motion in both landscapes and vector fields.