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The butterfly effect is today commonly identified with the sensitivedependence of deterministic chaotic systems upon initial conditions. However,this is only one facet of the notion of unpredictability pioneered by Lorenz,who actually predicted that multiscale fluid flows could spontaneously losetheir deterministic nature and become intrinsically random. This effect, whichis radically different from chaos, have remained out of reach for detailedphysical observations. Here, we substantiate this scenario by showing that itis inherent to the elementary Kelvin--Helmholtz hydrodynamical instability ofan initially singular shear layer. We moreover provide evidence that theresulting macroscopic flow displays universal statistical properties that aretriggered by, but independent of specific physical properties at micro-scales.This spontaneous stochasticity is interpreted as an Eulerian counterpart toRichardson's relative dispersion of Lagrangian particles, giving substance tothe intrinsic nature of randomness in turbulence.

From the butterfly effect to intrinsic randomness: the spontaneous growth of singular shear flows