Multifractal dimension of Lagrangian turbulence

We report experimental measurements of the Lagrangian multifractal dimension spectrum in an intensely turbulent laboratory water flow by the optical tracking of tracer particles. The Legendre transform of the measured spectrum is compared with measurements of the scaling exponents of the Lagrangian velocity structure functions, and excellent agreement between the two measurements is found, in support of the multifractal picture of turbulence. These measurements are compared with three model dimension spectra. When the nonexistence of structure functions of order less than -1 is accounted for, the models are shown to agree well with the measured spectrum.