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A Super-Butterfly That's Even More Turbulent

Building upon a laboratory experiment, researchers from IRAMIS and LSCE have proposed a set of three "simple" equations to represent a very turbulent flow. These equations lead to an extremely chaotic behavior, which could be qualified as a "super-butterfly effect". Their results are a good starting point to describe complex atmospheric phenomenon, such as clouds or rainfalls.

Published on 29 January 2018

Understanding turbulence is a major concern for air and sea transport security as well as in meteorology. The movement of a fluid can be described by Navier-Stokes equations, whose solutions can be extremely complex when they describe dynamic phenomenon on several orders of magnitude of the spatial scale, from a few hundredths of a millimeter to several hundred meters.

In 1963, American meteorologist Edward Lorenz modeled atmospheric convection, without turbulence, by three determinist equations. This allowed him to highlight the butterfly effect for the first time, a sign of chaotic behavior illustrated by this question: "Can the flap of a butterfly's wings in Brazil set off a tornado in Texas?" However, for real flows that are highly turbulent, scientists were unable to find a model as simple as that of Lorentz.

To tackle this challenge, researchers from IRAMIS and LSCE performed a detailed analysis of a laboratory experiment, known as the von Karman experiment, in which a very turbulent flow is produced by two rotating turbines in a cylinder filled with water. They show that the dynamic of vortices can be described by a system of three equations, which are like those proposed by Lorentz, but this time stochastic.

So where was the difficultly hiding? So far, each vortex has been described separately. Yet small vortices can also be considered as a random component that can influence bigger vortices at any moment. This random component introduces a new uncertainty regarding the chaos discovered by Lorenz in the initial model, and reinforces the butterfly effect by one additional degree.

Such simplified models could be used to describe the dynamics of natural turbulent flows, such as clouds and rainfalls in meteorology. One can say that the climate butterfly hunting season is now open.

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