Statistics of incremental averages of passive scalar fluctuations
Résumé
Whereas statistical moments of differences of turbulent quantities measured over a given separation (viz., structure functions) have been extensively studied, statistics of incremental sums (or equivalently averages, e.g., Σθ≡[θ(x+r)+θ(x)]/2) of the same quantities have only been the subject of recent research. The present work investigates incremental averages of a turbulent passive scalar (temperature), measured in nearly homogeneous, and isotropic (passive and active), grid-generated turbulence, for turbulent Reynolds numbers in the range 94≤Rλ(≡urmsλ/ν)≤582. The scalar field is generated by the action of the turbulent velocity field against an imposed mean temperature gradient. Following the approach of Mouri and Hori [Phys. Fluids 22, 115110 (2010)] for the velocity field, we examine statistics of incremental averages of the passive scalar field as a function of separation (viz., incremental average structure functions) for different Reynolds numbers, comparing them with both the results of Mouri and Hori, as well as the corresponding incremental average structure functions for the velocity field for the flows studied herein. While the statistics of Σθ are primarily large-scale quantities, and would therefore be expected to be flow dependent, they exhibit certain similarities to the statistics of incremental averages of velocity (Σuα), measured both in the flow under consideration as well as the different classes of flows studied by Mouri and Hori. Finally, we derive a scale-dependent evolution equation for the incremental average of the scalar field fluctuations, Σθ. We discuss its relationship to Yaglom's four-thirds law for differences in passive scalar fluctuations and compare the results with the experimental data.