Scalar probability density function and fine structure in uniformly sheared turbulence

Abstract

This study is an experimental investigation of the probability density function (p.d.f.) and the fine structure of temperature fluctuations in uniformly sheared turbulence with a passively introduced uniform mean temperature gradient. The shear parameter was relatively large, resulting in vigorous turbulence production and a total mean strain up to 23. The turbulence Reynolds number was up to 253. The scalar fluctuations grew in a self-similar fashion and at the same exponential rate as the turbulence stresses, in conformity with predictions based on an analytical solution of the scalar variance equation. Analytical considerations as well as measurements demonstrate that the scalar p.d.f. is essentially Gaussian and that the scalar–velocity joint p.d.f. is essentially jointly Gaussian, with the conditional expectations of the velocity fluctuations linearly dependent on the scalar value. Joint statistics of the scalar and its dissipation rate indicate a statistical independence of the two parameters. The fine structure of the scalar was invoked from statistics of derivatives and differences of the scalar, in both the streamwise and transverse directions. Probability density functions of scalar derivatives and differences in the dissipative and the inertial ranges were strongly non-Gaussian and skewed, displaying flared, asymmetric tails. All measurements point to a highly intermittent scalar fine structure, even more intermittent than the fine structure of the turbulent velocity.