Figure 2

Flow patterns by Lagrangian Coherent Structures.

(a) The black water of the Rio Negro meets the muddy water of the Rio Solimoẽs outside Manaus, Brazil. The border separating flows of different origins (colored line) is, by definition, a Lagrangian Coherent Structure (LCS). The LCS persists for several kilometers and grows increasingly uneven and complex as eddies contribute to mixing of the two flows. Image modified from an original by NASA Earth Observatory, with permission⁴². (b) Water tank experiment with LCS analysis of vortex rings. As water is injected from a nozzle into a tank, a symmetrical vortex ring forms (left), detaches and evolves (middle), then gradually breaks down into more complex flow patterns (right). (c) LCS showing vortex ring formation during filling of the LV. Healthy control (top), patient with ischemic cardiomyopathy (middle) and non-ischemic dilated cardiomyopathy (bottom). After the formative phase, the vortex ring evolved close to the endocardial border (red dotted line) in the control, gaining additional complexity compared to the water tank model. In the patients, vortex ring formation occurred without an obvious connection to the endocardium and the vortex ring moved along the inferior LV wall towards the apex. LV, left ventricle; RV, right ventricle; LA, left atrium; Ao, aorta; *, vortex core.