Temperature dissipation fluctuations in a turbulent boundary layer

Abstract

All three components of the dissipation rate of the fluctuating temperature ϑ are measured simultaneously in the inner region of a fully developed turbulent boundary layer at a moderate Reynolds number. Measurements are made with a probe of four cold wires consisting of two closely spaced parallel vertical wires mounted a small distance upstream of two closely spaced parallel horizontal wires. In the inner region of the layer, local isotropy is not closely approximated (∂ϑ/∂z)2〉 (∂ϑ/∂y)2〉 (∂ϑ/∂x)2. The spectral density of the sum χ[= (∂ϑ/∂x)2+(∂ϑ/∂y)2+ (∂ϑ/∂z)2] is similar in shape to that of (∂ϑ/∂y)2 or (∂ϑ/∂z)2 but not as rich in high frequency content as that of (∂ϑ/∂x)2. The probability density of χ has a lower skewness and flatness factor and is more closely log-normal than those of the individual components. This is true regardless of whether χ and its components are unaveraged or locally averaged over a linear dimension r. When averaging is applied, departures from log-normality are diminished but do not disappear entirely. The variance σ2 of the logarithm of the locally averaged χ is proportional to ln r over a wide range of r (rmax/rmin≃30), in contrast to the individual components where this ratio may be as small as 2. The value of the Kolmogoroff constant μϑ determined from the slope of σ vs ln 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 μϑ (and μ) obtained at high Reynolds numbers.