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^{1}, H. Q. Danh

^{1}and R. A. Antonia

^{1}

### Abstract

Simultaneous measurements have been made of all three components of the fluctuating temperature dissipation in the inner region of a fully developed turbulent boundary layer at a moderate Reynolds number. Measurements are made with a four‐wire arrangement which consists of two parallel vertical wires mounted a small distance upstream of two parallel horizontal wires. Each of the four wires is operated at very low current by a contant current anemometer and is sensitive to only the temperature fluctuation Θ. The separation between wires in each parallel pair is kept small, so that the differences between the outputs of each pair are reasonable approximations to ∂Θ/∂*z* and ∂Θ/Λ*y*, the temperature derivatives in the transverse and vertical directions, respectively. The streamwise derivative ∂Θ/Λ*x* was obtained from the time derivative, through use of Taylor’s hypothesis. Mean square and spectral density measurements show that in the inner region local isotropy is not closely approximated [(∂Θ/∂*z*)^{2}≳ (∂Θ/∂*y*)^{2}≳ (∂Θ/∂*x*)^{2}] and (∂Θ/∂*x*)^{2} is richer in high frequency content than the other two components or the sum. The probability density of the sum χ[= (∂Θ/∂*x*)^{2}+(∂Θ/∂*y*)^{2}+(∂Θ/∂*z*)^{2}] has a lower skewness and flatness factor and is more closely log‐normal than the probability densities of the individual components. This is true regardless of whether χ and its components are unaveraged or locally averaged over a linear dimension *r*, in the Obukhov–Kolmogoroff sense. The variance σ^{2} of the logarithm of the locally averaged χ is proportional to log *r* over a wide range of *r* (*r* _{max}/*r* _{min}≃30), in contrast to the individual components where this ratio may be as small as 3. The value of the Kolmogoroff constant μ determined from the slope of σ^{2} vs log *r* is about 0.35. This is consistent with the slope of the spectral density of χ and is also in agreement with previous best estimates of μ obtained at high Reynolds numbers. Using only one component of χ, the evaluation of μ either from the slope of the spectral density or from the slope of σ^{2} vs log *r* seems to be highly ambiguous and can lead to erroneous results.

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