A geometric invariant for the study of planar curves and its application to spiral tip meander

Abstract

Planar curves with periodically varying curvature arise in the natural sciences as the result of a wide variety of periodic processes. The total curvature of a periodic arc in such curves constrains their symmetry. It is shown how the total curvature can be computed without reparameterizing the curve to unit speed. The use of the total curvature of the periodic arcs is demonstrated through a series of four examples from various branches of science. Insights gained from these examples are applied to improve the modeling of spiral wave meander.