Thu September 26th 2013
Seminar Turbulent super-dipersion as a ballistic cascade
Mickaël Bourgoin


Since the pioneering work of Richardson [1] in the 1920s, later refined by Batchelor and Obukhov in the 1950s [2], it is predicted that the rate of separation of pairs of fluid elements in turbulent flows with initial separation D0 at inertial scales, grows ballistically first (Batchelor regime), before undergoing a transition toward a super-diffusive regime where the mean-square separation grows as t^3 (Richardson regime). The mechanism at the origin of such a rapid dispersion remains however unclear, and experimental observation of the Richardson regime remains a challenge.

I will briefly review in this presentation recent experimental measurements of turbulent relative dispersion and propose a new simple physical phenomenology for the Richardson superdiffusivity in turbulence. This phenomenology seems to elucidate several aspects of turbulent dispersion: (i) it gives a simple physical explanation of the origin of the super diffusive t^3 Richardson regime as a cascade of scale-dependent ballistic regimes, (ii) it is consistent with most recent numerical simulations for pair dispersion, (iii) it shows that the Richardson constant is directly related to the Kolmogorov constant, and therefore should not be considered as an independent universal constant and (iv) it also possibly gives a simple physical interpretation of the non-Fickian scale-dependent diffusivity coefficient as originally proposed by Richardson.

[1] Lewis F Richardson. Atmospheric Diffusion Shown on a Distance-Neighbour Graph. Proceedings of the Royal So- ciety of London, Series A, 110(756):709–737, 1926.

[2] G K Batchelor. The application of the similarity theory of turbulence to atmospheric diffusion. Quarterly Journal of the Royal Meteorological Sociey, 76(328):133–146, 1950.
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The 10th Complex Motion in Fluids 2021
Max Planck Gesellschaft
Centre for Scientific Computing