Statistics of filtered velocity in grid and wake turbulence

Abstract

Data on spatially filtered turbulence are commonly needed for a priori sub-grid model studies and for a posteriori testing of large eddy simulation (LES) codes. In this paper, hot-wire anemometry is used to record very long records of such data, required for good convergence of high-order statistics. An array consisting of four X-wire probes placed transversal to the flow direction is built. Unlike previous single-probe hot-wire measurements, which only allowed stream-wise filtering using Taylor’s hypothesis, the array permits cross-stream filtering as well. Measurements which are spatially filtered at a length-scale Δ pertaining to the inertial-range of turbulence are performed in grid and wake turbulence. The data can be used directly to compare with results from LES. From the data, fundamental differences between filtered and unfiltered velocity fields are examined through probability density functions and the scaling behavior of high-order structure functions. A comparative study of probability density functions of filtered and unfiltered velocity increments shows that the tails of the distributions are affected by the filtering even at scales much larger than the filter scale. Significant differences are also observed in regard to the scaling of structure functions. It is shown that extended self-similarity, a recent technique for measuring inertial range scaling exponents, yields questionable results when applied to structure functions of filtered velocity.