The connection between an 18th-century savant called Joseph-Louis Lagrange and the problem of landing safely at Hong Kong International Airport may not, at first, be obvious. But there is one. Hong Kong airport is notorious for rocky and sometimes aborted landings caused by the disturbed air flow from nearby mountains. Though laser technology is deployed alongside its runways to monitor changes in wind speed and thus forewarn pilots, that is often not enough. What is needed is a better understanding of the theory of the winds themselves.

And this is where Lagrange comes in. He was a pioneer of the study of moving fluids (among many other things), but his ideas outran the computational tools of his day. Only now, with supercomputers available to help with the calculations, is it possible to explore those ideas completely. What is emerging is a picture of fluid dynamics more subtle and more complex than anything dreamed of even a decade ago. The atmosphere and the ocean are, it seems, dominated by invisible barriers that have come to be known as Lagrangian coherent structures. They govern the movement of everything from the trajectories of aircraft to the distribution of pollution, the migration of jellyfish and the tracks taken by hurricanes. They are, as it were, the skeletons of the sea and the air.

To understand what a Lagrangian coherent structure is, it helps to imagine a crowd at a railway terminus, says Thomas Peacock of the Massachusetts Institute of Technology, who studies the structures. Some people will be arriving. Some will be leaving. And, whichever they are doing, they will be going to and from numerous different platforms. The result is chaos, but structured chaos. What emerges is a shifting pattern of borders between groups of people with different goals. These borders are Lagrangian coherent structures. They are intangible, immaterial and would be undetectable if the passengers stopped moving. But they are also real enough to be treated mathematically.

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