Spectral Coherence and the Statistical Significance of Turbulent Flux Computations

The squared spectral coherence, a frequency-domain analog of the squared correlation coefficient, identifies the frequencies at which two variables most strongly covary. A simple coherence significance test designed to determine whether coherence peaks exceed critical values expected from chance random number correlations is described. This significance test determines the probability with which coherence peaks are likely to arise out of random turbulence. A statistically significant coherence peak also indicates the likely presence of a significant turbulent flux. The test is illustrated using sonic anemometer–thermometer data acquired in an urban setting and over a salt playa. Successful application of this coherence significance test requires selection of a properly sized data record and a Fourier transform with appropriate windowing. The sampling period should be sufficiently long to span major flux-generating scales of motion up to the cross-spectral gap but not so long that extraneous larger scale motions are included. A record length and transform size that yield equivalent degrees of freedom in the range between 10 and 100 produces the most consistent and reliable significance test results.

Well Resolved Wall Pressure Measurements in a High Reynolds Number Turbulent Boundary Layer

In order to better understand boundary layer turbulence at high Reynolds number, the fluctuating wall pressure was measured within the turbulent boundary layer that forms over the salt playa of Utah’s west desert. Pressure measurements simultaneously acquired from an array of nine microphones were analyzed and interpreted. The wall pressure intensity was computed and compared with low Reynolds number data. This analysis indicated that the variance in wall pressure increases logarithmically with Reynolds number. Computed autocorrelations provide evidence for a hierarchy of surface pressure producing scales. Space-time correlations are used to compute broadband convection velocities. The convection velocity data indicate an increasing value for larger sensor separations. To the author’s knowledge, the pressure measurements are the highest Reynolds number, well resolved measurements of fluctuating surface pressure to date.