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Abstract

We use silicon strip detectors (originally developed for the CLEO III high energy
particle physics experiment) to measure fluid particle trajectories in turbulence
with temporal resolution of up to 70,000 frames per second. This high frame rate allows
the Kolmogorov time scale of a turbulent water flow to be fully resolved for 140 <=
R_lambda <= 970. Particle trajectories exhibiting accelerations up to 16,000 m\s^2
(40 times the rms value) are routinely observed. The probability density function
of the acceleration is found to have Reynolds number dependent stretched exponential
tails. The moments of the acceleration distribution are calculated. The scaling of
the acceleration component variance with the energy dissipation is found to be consistent
with the results for low Reynolds number direct numerical simulations, and with the
K41 based Heisenberg-Yaglom prediction for R_lambda >= 500. The acceleration flatness
is found to increase with Reynolds number, and to exceed 60 at R_lambda = 970. The
coupling of the acceleration to the large scale anisotropy is found to be large at
low Reynolds number and to decrease as the Reynolds number increases, but to persist
at all Reynolds numbers measured. The dependence of the acceleration variance on the
size and density of the tracer particles is measured. The autocorrelation function
of an acceleration component is measured, and is found to scale with the Kolmogorov
time tau_eta.

The advection of a passive substance by a turbulent flow is important in many natural and engineering settings. The concentration of such a substance can exhibit complex dynamic behaviour that shows many phenomenological parallels with the behaviour of the turbulent velocity field. Yet the statistical properties of this so-called 'passive scalar' turbulence are decoupled from those of the underlying velocity field. Passive scalar turbulence has recently yielded to mathematical analysis, and such progress may ultimately lead to a better understanding of the still intractable problem of fluid turbulence itself.