Stretch-minimising stream surfaces

We study the problem of finding stretch-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a stretch minimising manner, i.e., they move without stretching or shrinking, preserving the length of their arbitrary arc. In general fields, such curves may not exist. However, the divergence-free constraint gives rise to these ‘stretch-free’ curves that are locally arc-length preserving when infinitesimally propagated. Several families of stretch-free curves are identified and used as initial guesses for stream surface generation. These surfaces are subsequently globally optimised to obtain the best stretch-minimising stream surfaces in a given divergence-free vector field.