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Lagrangian velocity and energy statistics are studied in inhomogeneous turbulence. A Rλ = 285 flow between two oscillating grids, with regions of nearly homogeneous and highly inhomogeneous turbulence, is studied. Large data sets of three-dimensional tracer particle velocities have been collected using stereoscopic high speed cameras with real-time image compression technology. Lagrangian structure functions conditioned on the instantaneous large scale velocity are measured in both homogeneous and inhomogeneous regions of the flow to assess the effects of the large scales on the small scales in turbulence. At all scales, the structure functions depend strongly on the large scale velocity, the dependence showing clear signatures of inhomogeneity near the oscillating grids. But even in the homogeneous region in the center, a strong dependence on the large scale velocity remains at all scales. The conditional structure function measurements are powerful tools in assessing the effects of inhomogeneity and intermittency of the large scales on the small scales in turbulence. There is a bias present in the measurement of Lagrangian structure functions at all timescales due to the finiteness of the measurement volume. A method we developed to estimate such bias for different timescales in our data is described. Our method gives an extrapolation based on the structure functions for different artificial volumes, revealing the estimates of errors at different timescales. Analysis of structure functions is limited to the timescales whose errors do not exceed 17%. Components of the turbulent kinetic energy budget are estimated to identify the chief agents of turbulent energy transport using Lagrangian energy measurements. Our estimation of the terms in the turbulent energy equation identifies pressure transport as being significant, along with the velocity transport term, in turbulent energy transport. These energy measurements provide a basis for further studying Lagrangian and Eulerian energy transport in turbulent systems. Lastly, we study the average decay of the kinetic energy of a particle as it enters a measurement volume in the shape of a slab or a cube. We see that the bias due to trajectory length affects the energy measurement. When this sample bias is removed, particles lose two-thirds of their energy during their residence time.

Experimental Study of Lagrangian Velocity and Energy Statistics in Inhomogeneous Turbulence