The small-scale structure of passive scalar mixing in turbulent boundary layers

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Dasi, Lakshmi
Webster, Donald R.
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The objective is to contribute to several issues regarding the traditional view of the local structure of passive scalar fields: (1) probability density function (PDF) of the scalar concentration and scalar gradient, (2) the scalar power spectrum, (3) the structure functions, and (4) correlation functions and multi-point correlators. In addition, the research provides a geometric description of two-dimensional transects of the passive scalar iso-surfaces using the tools of fractal geometry. The local structure is analyzed as a function of large-scale anisotropy, intermittency factor, Reynolds number, and initial condition of the scalar injection. Experiments were performed in the bed boundary layer produced by a uniform depth open channel flow of water in a tilting flume for Re_lamda = 63, 94, and 120. A small nozzle iso-kinetically delivers a passive scalar of high Schmidt number ( Sc = 1000) at mid-depth to generate the turbulent scalar field. Three nozzle diameters are used to study the effects of the injection length scale. High-resolution planar laser induced fluorescence (PLIF) technique is used to measure the scalar field. The local structure far from isotropic and is influenced even at the smallest scales by large-scale anisotropy, initial injection length scale and the Reynolds number of the flow. The PDF of the scalar fluctuations is non-Gaussian and dependent on large-scale anisotropy. The PDF of scalar gradients show the influence of large-scale anisotropy on the structure at the smallest scales. The spectrum of the scalar field deviates from the in the inertial convection regime and is dependent on large-scale anisotropy, external intermittency, and low Reynolds number. There is no evidence of Batchelors k^-1 scaling law. The scaling exponents of the even-ordered structure functions appear to be inversely correlated with the kurtosis of the scalar fluctuations. The fractal geometry of the two dimensional transects of passive scalar iso-surfaces is scale dependent. The fractal dimension is 1.0 at the smallest length scale and increases in a universal manner in the viscous-convective regime. The coverage length underestimate reflects this universal behavior with practical significance. The lacunarity function shows that the instantaneous scalar field is most in-homogenous around the Kolmogorov scale.
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