Weglinien
Weglinien refer to the pathlines of fluid motion: the trajectories followed by individual fluid particles as time advances within a velocity field. In mathematical terms, a Weglinie is the curve x(t) that satisfies the differential equation dx/dt = v(x(t), t) with an initial position x(t0) = x0. This concept is part of the Lagrangian description of fluid flow, contrasting with the Eulerian viewpoint that describes the velocity field v(x,t) at fixed points in space.
In steady (time-independent) flows, Weglinien coincide with streamlines, which are lines tangent to the velocity vector
Weglinien are commonly visualized by introducing tracer particles or dyes into the flow or by reconstructing
Applications of Weglinien span engineering and geophysical contexts, including the analysis of mixing and transport in