Water in a glass settles down, but before that, vortices go through a stage where energy losses spike. Physicists seek early signs of this stage to predict flow behavior — from the atmosphere to pipelines. In a new study, they test one such sign: the curvature spectrum of vortex lines, that is, how twisted small and large eddies are.

The researchers took several initial velocity fields, from the symmetric Taylor–Green vortex to a random set of waves, and numerically simulated their decay. In all cases, the peak of the curvature spectrum reached its maximum before the peak of energy dissipation, which in turn preceded the peak of energy transfer across scales. This sequence held when there was a sufficient gap between large and small vortices, but broke down when the gap was small.

The practical takeaway: the curvature spectrum can reveal the approach of strong dissipation in advance, like feeling the steering wheel shiver before a car loses traction. This is useful for monitoring turbulent flows where anticipating sudden changes is crucial.