On the strength of the nonlinearity in isotropic turbulence

Turbulence governed by the Navier-Stokes equations shows a tendency to evolve towards a state in which the nonlinearity is diminished. In fully developed turbulence this tendency can be measured by comparing the variance of the nonlinear term to the variance of the same quantity measured in a Gaussian field with the same energy distribution. In order to study this phenomenon at high Reynolds numbers, a version of the Direct Interaction Approximation is used to obtain a closed expression for the statistical average of the mean-square nonlinearity. The wavenumber spectrum of the mean-square nonlinear term is evaluated and its scaling in the inertial range is investigated as a function of the Reynolds number. Its scaling is dominated by the sweeping by the energetic scales, but this sweeping is weaker than predicted by a random sweeping estimate. At inertial range scales, the depletion of nonlinearity as a function of the wavenumber is observed to be constant. At large it is observed that the mean-square nonlinearity is larger than its Gaussian estimate, which is shown to be related to the non-Gaussianity of the Reynolds-stress fluctuations at these scales.Comment: Accepted for publication in J. Fluid Mec

On the scaling of temperature fluctuations induced by frictional heating

The temperature fluctuations generated by viscous dissipation in an isotropic turbulent flow are studied using direct numerical simulation. It is shown that their scaling with Reynolds number is at odds with predictions from recent investigations. The origin of the discrepancy is traced back to the anomalous scaling of the dissipation rate fluctuations. Phenomenological arguments are presented which explain the observed results. The study shows that previously proposed models underpredict the variance of frictional temperature fluctuations by a factor proportional to the square of the Taylor-scale Reynolds number

Reynolds number effect on the velocity increment skewness in isotropic turbulence

Second and third order longitudinal structure functions and wavenumber spectra of isotropic turbulence are computed using the EDQNM model and compared to results of the multifractal formalism. At the highest Reynolds number available in windtunnel experiments, $R_\lambda=2500$, both the multifractal model and EDQNM give power-law corrections to the inertial range scaling of the velocity increment skewness. For EDQNM, this correction is a finite Reynolds number effect, whereas for the multifractal formalism it is an intermittency correction that persists at any high Reynolds number. Furthermore, the two approaches yield realistic behavior of second and third order statistics of the velocity fluctuations in the dissipative and near-dissipative ranges. Similarities and differences are highlighted, in particular the Reynolds number dependence

Career and Technical Education Teachers’ Perspectives of Evidence-Based Grading

As education leans into competency-based assessment methods, Evidenced-Based Grading (EBG) presents as a potential effective option for Career and Technical Education (CTE) teachers. In this study we use a basic qualitative design to explore CTE teachers’ perceptions of assessment, student growth, and implementation of an Evidenced-Based Grading system. Eight teachers in a Career-Tech Center in Michigan participated in the study, with each completing one semi-structured, in-depth interview about their perceptions of EBG, and data were analyzed following an inductive coding process with open and axial coding. Member checking, audit trails, and peer debriefs were utilized to enhance trustworthiness of findings. In this article we present themes that emerged from the in-depth interviews, as well as a discussion of implications for practice and recommendations for future research