Conditions on feature lines of two-dimensional scalar fields and their application to planar fluid flows

We give a local algebraic condition on the coincidence of feature lines of contour curvature and slope (the latter is associated with ridges and valleys in a terrain map) for general two-dimensional scalar fields employing two newly derived feature lines. We also give a sufficient condition on the coincidence of feature lines using the reflection symmetries of the contour curves. We analyze the coincidence and separation of the different feature lines in symmetric and asymmetric terrain objects. Then, we apply the results for planar fluid flows, including simple ideal and viscous flows and a natural lake circulation. In the fluid dynamic examples, the stream function replaces the height field. The symmetry-breaking of the contour curves by boundary deformations and viscous dissipations are highlighted and discussed in each case. •Coincidence conditions on feature lines of two-dimensional scalar fields.•Application on idealized height fields with and without mirror symmetries.•Application on planar flows of ideal and real fluids.•Geometric and viscosus breaking of mirror symmetries and feature line separation.•Feature lines of a natural vortex pattern in a lake-flow.