Errors in the Measurement of Turbulence Upstream of an Axisymmetric Body

John C. Wyngaard National Center for Atmospheric Research, Boulder, CO 80307

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Larry Rockwell National Center for Atmospheric Research, Boulder, CO 80307

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Carl A. Friehe University of California, Irvine, Irvine, CA 92717

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Abstract

We use a Taylor series expansion technique to calculate the effects of mean-flow distortion on turbulence measurements ahead of an axisymmetric body. The approach is valid when the integral scale of the turbulence is large compared to the maximum body diameter, which is usually the case for energy-containing turbulence statistics measured ahead of aircraft and the towed bodies used in oceanography. Using a 5:1 ellipsoid as a representative body, we show the nature of the attenuation and crosstalk error terms which the flow distortion induces in the measured turbulence components. The contours of the resulting errors in velocity covariances measured ahead of the ellipsoid and a paraboloid of revolution reveal that, in general, the errors in turbulent Roynolds stress can be the most severe. For sufficiently small distortion effects, which typically means more than one diameter away from the nose, the distortion matrix can easily be inverted analytically, giving explicit expressions for the true covariances in terms of the measured ones. We assess the effects of averaging measurements taken in different directions along the same path, as is sometimes done with aircraft data, and of nonzero angle of attack.

Abstract

We use a Taylor series expansion technique to calculate the effects of mean-flow distortion on turbulence measurements ahead of an axisymmetric body. The approach is valid when the integral scale of the turbulence is large compared to the maximum body diameter, which is usually the case for energy-containing turbulence statistics measured ahead of aircraft and the towed bodies used in oceanography. Using a 5:1 ellipsoid as a representative body, we show the nature of the attenuation and crosstalk error terms which the flow distortion induces in the measured turbulence components. The contours of the resulting errors in velocity covariances measured ahead of the ellipsoid and a paraboloid of revolution reveal that, in general, the errors in turbulent Roynolds stress can be the most severe. For sufficiently small distortion effects, which typically means more than one diameter away from the nose, the distortion matrix can easily be inverted analytically, giving explicit expressions for the true covariances in terms of the measured ones. We assess the effects of averaging measurements taken in different directions along the same path, as is sometimes done with aircraft data, and of nonzero angle of attack.

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