Flowsurfaces

Flowsurfaces are a concept used in fluid dynamics and computational simulations. They represent a two-dimensional surface embedded within a three-dimensional flow field. The defining characteristic of a flowsurface is that it is constructed such that all fluid particles that start on the surface remain on the surface as the flow evolves over time. In essence, a flowsurface is a Lagrangian construct that moves and deforms with the fluid.

These surfaces are distinct from stream surfaces, which are defined by the instantaneous velocity vector field. While stream surfaces are instantaneous, flowsurfaces are inherently time-dependent and capture the history of the fluid's motion. They can be generated by following a specific initial two-dimensional manifold through the flow field.

Flowsurfaces find applications in analyzing and visualizing complex fluid flows. They can be used to track the transport of pollutants, understand mixing processes, or identify regions of coherent structures within turbulence. By following the evolution of a flowsurface, researchers can gain insights into the dynamics and transport properties of the fluid that might be difficult to discern from Eulerian velocity field data alone. Their construction and analysis often involve numerical methods to integrate the fluid particle trajectories.