  By tracking tracer particles at high speeds and for long times, we study the
geometric statistics of Lagrangian trajectories in an intensely turbulent
laboratory flow. In particular, we consider the distinction between the
displacement of particles from their initial positions and the total distance
they travel. The difference of these two quantities shows power-law scaling in
the inertial range. By comparing them with simulations of a chaotic but
non-turbulent flow and a Lagrangian Stochastic model, we suggest that our
results are a signature of turbulence.
