Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F. Toschi

Intermittency K41 Kolmogorov (1941) Landau’s objection - fluctuating energy dissipation Kolmogorov’s refined hypothesis (1962) Random beta model Multifractal model Eulerian velocity structure function

Multifractal formalism (1) Frisch (1995)

Multifractal formalism (2) Eulerian reference frame Lagrangian reference frame - time scale of eddy of scale r - velocity difference at scale r Fractal dimension Superposition of contributions from eddies of all sizes Contributions from eddies smaller than scale r are uncorrelated Fluctuating Universal

Acceleration in multifractal framework Acceleration Fluctuating Kolmogorov scale

Acceleration pdf (1) Pdf of acceleration Probabililty of observing h in Pdf of large scale velocity

Acceleration pdf (2) Multifractal K41 (h=1/3, D(h) = 3) No additional free parameters D(h) derived from She-Leveque model

Direct numerical simulation Homogeneous isotropic turbulence cubic lattice Taylor-scale Reynolds number Two million Lagrangian particles Sampling rate

Acceleration pdf (3) K41 prediction Multifractal prediction

Conditional acceleration variance Acceleration variance conditional on velocity Lagrangian stochastic models

Conditional acceleration variance Multifractal prediction B.L. Sawford et al., Phys. Fluids 15, 3478 (2003).

Lagrangian structure functions Multifractal prediction for the Lagrangian structure functions where Same D(h) as in Eulerian model

Lagrangian structure functions P=8 P=6 P=4 Plotted using Extended Self Similarity Bottleneck at Multifractal Lagrangian exponents

Conclusions Acceleration exhibits fluctuations up to Multifractal formalism captures this behaviour with no additional free parameters Conditional acceleration variance Velocity structure functions only for Read more in Physical Review Letters vol. 93, no.6 p