Direct, high resolution, four-dimensional measurements of the fine scale structure of Sc≫1 molecular mixing in turbulent flows

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Abstract
Results from highly resolved, four‐dimensional measurements of the fine structure of the fully space‐ and time‐varying Sc≫1 conserved scalar field and the associated scalar energy dissipation rate field in a turbulent flow are presented. The resolution achieved in all three spatial dimensions and in time reaches down to the local strain‐limited molecular diffusion scale in the flow, allowing all three components of the instantaneous scalar gradient vector field ∇ζ(x,t) and their time evolution at every point in the data space to be directly evaluated. Results are presented in the form of fine structure maps of the instantaneous dissipation field loge ∇ζ⋅∇ζ(x,t) in several spatially adjacent data planes within an individual three‐dimensional spatial data volume, as well as in several temporally successive data planes from a sequence of such three‐dimensional data volumes. The degree of anisotopy in the underlying scalar gradient field is characterized in terms of the joint distribution β(ϑ,φ) of spherical orientation angles. The probability density of true scalar energy dissipation rates is presented and compared with the distributions that would result from lower‐dimensional measurements of the scalar gradient vector. From this the ‘‘spottiness’’ of the scalar dissipation field is directly quantified by determining the true fraction of the total dissipation that occurs in any given volume fraction of the flow