Long Time Correlations in Lagrangian Dynamics: A Key to Intermittency in Turbulence

N. Mordant, J. Delour, E. Léveque, A. Arnéodo, J.-F. Pinton
2002 Physical Review Letters  
New aspects of turbulence are uncovered if one considers flow motion from the perspective of a fluid particle (known as the Lagrangian approach) rather than in terms of a velocity field (the Eulerian viewpoint). Using a new experimental technique, based on the scattering of ultrasounds, we have obtained a direct measurement of particle velocities, resolved at all scales, in a fully turbulent flow. It enables us to approach intermittency in turbulence from a dynamical point of view and to
more » ... the Lagrangian velocity fluctuations in the framework of random walks. We find experimentally that the elementary steps in the 'walk' have random uncorrelated directions but a magnitude that is extremely long-range correlated in time. Theoretically, we study a Langevin equation that incorporates these features and we show that the resulting dynamics accounts for the observed one- and two-point statistical properties of the Lagrangian velocity fluctuations. Our approach connects the intermittent statistical nature of turbulence to the dynamics of the flow.
doi:10.1103/physrevlett.89.254502 pmid:12484891 fatcat:kfilqlzukjejliwe5cwerbryxu