Utilizing synthetically generated random variates and laboratory measurements, we document the inherent limitations of the conventional structure function approach in limited sample size settings. We demonstrate that an alternative approach, based on the principle of maximum likelihood, can provide nearly unbiased structure function estimates with far less uncertainty under such unfavorable conditions. The superiority of this approach over the conventional approach does not diminish even in the case of strongly correlated samples. Two entirely different types of probability distributions, which have been reported in the turbulence literature, are found to be compatible with the proposed approach.@en

In this study, we explore several integral and outer length scales of turbulence which can be formulated by using the dissipation of temperature fluctuations (χ) and other relevant variables. Our analyses directly lead to simple yet non-trivial parameterizations for both spatially-averaged χ¯ and the structure parameter of temperature (CT2). For our purposes, we make use of high-fidelity data from direct numerical simulations of stratified channel flows.@en

We analyzed several multiyear wind speed datasets from 4 different geographical locations. The probability density functions of wind ramps from all these sites revealed remarkably similar shapes. The tails of the probability density functions are much heavier than a Gaussian distribution, and they also systematically depend on time increments. Quite interestingly, from a purely statistical standpoint, the characteristics of the extreme ramp‐up and ramp‐down events are found to be almost identical. With the aid of extreme value theory, we describe several other inherent features of extreme wind ramps in this paper.@en