Scaling range of velocity and passive scalar spectra in grid turbulence

Isotropic velocity and scalar fluctuations are closely approximated by slightly stretching a heated grid flow through a short (1.36:1) contraction. The heating is such that temperature serves as a passive scalar, and the velocity/scalar time scale ratio is about one. At small values of Taylor microscale Reynolds number (10 < R λ < 102), the spectrum of the temperature fluctuations has a more discernible scaling range than the spectrum of the velocity fluctuations. The scaling-range exponent for the thermal spectrum, m θ, exhibits a power-law function of R λ and tends to the Kolmogorov value of 5/3 more rapidly than that for the velocity spectrum, m u . Both m θ and m u are closer to the Kolmogorov value with the contraction than with no contraction. The trends for the present measurements supplemented with previously published data for larger R λ (>102) indicate that, to obtain a 5/3 scaling range, R λ must exceed 103. The ratio (5/3 + m u )/m θ is approximately 2, in close conformity with the proposal of Danaila and Antonia [“Spectrum of a passive scalar in moderate Reynolds number homogeneous isotropic turbulence,” Phys. Fluids21, 111702 (2009)]