We provide evidence that the small-scale statistics of the acceleration of
a test particle in high-Reynolds number Lagrangian turbulence is correctly
described by Tsallis statistics, with entropic index q = 3/2. We present th
eoretical arguments why Tsallis statistics can naturally arise in Lagrangia
n turbulence and why at the smallest scales q = 3/2 is relevant. A generali
zed Heisenberg-Yaglom formula is derived from the nonextensive model. (C) 2
001 Elsevier Science B.V. All rights reserved.