A detailed comparison between data from experimental measurements and numerical simulations of Lagrangian velocity structure functions in turbulence is presented. Experimental data, at Reynolds number ranging from R? = 350 to R? = 815, are obtained in a swirling water flow between counter-rotating baffled disks. Direct numerical simulations (DNS) data, up to R? = 284, are obtained from a statistically homogeneous and isotropic turbulent flow.

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We investigate the uniform convergence of Lagrange interpolation at the zeros of the orthogonal polynomials with respect to a Freud-type weight in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with re- spect to the given constraints well approximates a given function. This procedure was, at ¯rst, successfully introduced for the polynomial inter- polation with constraints on bounded intervals [1].