Experimental measurement of large scale velocity fluctuations in a turbulent flow*

We design an experiment to study the large scale velocity fluctuations of a three dimensional turbulent flow to test the two existing theoretical predictions; one by Saffman and the other by Batchelor, for the mean wavenumber energy spectrum. Using an innovative modification of the 3D scanning PIV technique, we achieve a measure of the three dimensional two point velocity correlation function in a turbulent flow. We report the observation of the Saffman spectrum over a wide range of Reynolds numbers studied in the experiment. Our observation implies a thermalization of the large scale fluctuations in a turbulent flow. These experimental results show that the large scale fluctuations may be described by equilibrium statistical mechanics, contrary to the direct cascade of energy. We will eventually discuss how our experimental observation may open the door for the statistical description of the large scale dynamics of turbulence.