In this paper we investigate the use of Kriging method in order to reconstruct and enhance the resolution of mixed convection data. Direct numerical solutions are performed for mixed convection in a two-dimensional partially open rectangular cavity with a flush-mounted discrete heat source on a heat conducting vertical board. An external airflow enters the cavity through an opening in the left vertical wall and exits from the opposite opening in the right vertical wall. Kriging is a statistical tool useful in many disciplines such as geology, thermo-fluid systems, process engineering, environment and medicine. Kriging is used to estimate unknown values from data observed at known locations. A variogram is usually constructed to account for the spatial variation of known data. Kriging gives an unbias estimate for the unknown value using a weighted linear combination of the available data. In this paper, we investigate the capabilities of Kriging procedure for transitional mixed convection flows. Particularly, the effect of various types of variograms (e.g. polynomial, exponential and spherical functions, etc.) on the effectiveness of the Kriging procedure has been studied in detail. The use of Kriging for the resolution enhancement and for the reconstruction of large missing zone (black zone) is investigated. It is found that the gappy data for both periodic and non-periodic (quasi-periodic) flows can be remarkably recovered by the method. While we apply the method for DNS data in order to assess its effectiveness, the method should be particularly very useful for experimental data, where some enhancement/smoothing is generally required.

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We study spectra and high-order structure functions in anisotropic wind tunnel turbulence, which is generated using an active grid. In the first experiment, we impose homogeneous shear turbulence with a constant gradient of the mean flow and (approximately) homogeneous turbulent fluctuations. We measure mixed structure functions of order 2, 3, 4, 6, and 10 using an array of two-component hotwires. These structure functions, which vanish for isotropic turbulence, display scaling with scaling exponents that highlight intermittency: the return to isotropy at small scales of large fluctuations is much slower than expected on the basis of a simple Kolmogorov-like scaling argument [J. L. Lumley, “Similarity and the turbulent energy spectrum,” Phys. Fluids 10, 855 (1967)]. In the second experiment, we impose anisotropy in otherwise homogeneous turbulence through the time modulation of the active grid. This is done by driving the grid using signals from a turbulence (shell) model, which acts as a convenient turbulent random signal generator. In this way, different statistical properties of different velocity components could be imposed. Similar to the first experiment, our interest is in the return to isotropy of the small-scale turbulent fluctuations, which is quantified using second-order quantities such as spectra and correlation functions. Also, in this case, the strongly anisotropic correlations induced by the forcing at large scales tend to return to isotropy at small, inertial-range scales, but with the imprint of large-scale anisotropy retained.

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