Relative dispersion in fully developed turbulence: Lagrangian statistics in synthetic flows

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Abstract
The eect of Eulerian intermittency on the Lagrangian statistics of relative dis- persion in fully developed turbulence is investigated. A scaling range spanning many decades is achieved by generating a multi-ane synthetic velocity eld with prescribed intermittency features. The scaling laws for the Lagrangian statistics are found to depend on intermittency in agreement with a multifractal description. As a consequence of the Kolmogorov law, the Richardson law for the variance of pair separation is not aected by intermittency corrections. Understanding the statistics of particle pairs dispersion in turbulent velocity elds is of great interest for both theoretical and practical implications. Since fully developed turbulence displays well-known, non-trivial universal features in the Eulerian statistics of velocity dier- ences (1, 2), it represents a starting point for the investigation of the general problem of the relationship between Eulerian and Lagrangian characteristics. Since the pioneering work by Richardson (3), many eorts have been done to conrm exper- imentally (1) or numerically (4-6) his law. Most of the previous works concerning the validation of the Richardson law have been focused mainly on the numerical prefactor (Richardson constant (1)). Also theoretically there are very few attempts to investigate possible corrections stemming from Eulerian intermittency (7-9). This is quite surprising compared with the enormous amount of literature concerning the intermittency correction for the Eulerian statistics (2, 10). The main obstacle to a deeper investigation of relative dispersion is essentially the lack of sucient statistics due to tech- nical diculties in laboratory experiments and to moderate inertial range achieved in direct numerical simulations.
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