On inertial-range scaling laws

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's $k^{-5/3}$ scaling is derived for the energy inertial range. A related modification is found to Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at the injection wavenumber. The significance of these corrections is illustrated with steady-state energy spectra from recent high-resolution closure computations. Implications for conventional numerical simulations are discussed. These results underscore the asymptotic nature of inertial-range scaling laws.Comment: 16 pages, postscript (uncompressed, not encoded

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program

A small-scale turbulence model

A model for the small-scale structure of turbulence is reformulated in such a way that it may be conveniently computed. The model is an ensemble of randomly oriented structured two dimensional vortices stretched by an axially symmetric strain flow. The energy spectrum of the resulting flow may be expressed as a time integral involving only the enstrophy spectrum of the time evolving two-dimensional cross section flow, which may be obtained numerically. Examples are given in which a k(exp -5/3) spectrum is obtained by this method without using large wave number asymptotic analysis. The k(exp -5/3) inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the two-dimensional enstrophy spectrum. The results are insensitive to time dependence of the strain-rate, including even intermittent on-or-off strains

Optimal Lp-Metric for Minimizing Powered Deviations in Regression

Minimizations by least squares or by least absolute deviations are well known criteria in regression modeling. In this work the criterion of generalized mean by powered deviations is suggested. If the parameter of the generalized mean equals one or two, the fitting corresponds to the least absolute or the least squared deviations, respectively. Varying the power parameter yields an optimum value for the objective with a minimum possible residual error. Estimation of a most favorable value of the generalized mean parameter shows that it almost does not depend on data. The optimal power always occurs to be close to 1.7, so these powered deviations should be used for a better regression fit