Velocity Derivatives in Turbulent Boundary Layers. Part II: Statistical Properties

Abstract

An experiment was performed using Dual-plane-SPIV in the LMFL boundary layer facility to determine all of the derivative moments needed to estimate the average dissipation rate of the turbulent kinetic energy, $\varepsilon$, and its Reynolds stress counterpart the dissipation tensor, $\varepsilon_{ij}$. For this experiment, the Reynolds number was $Re_\theta = 7500$ or $Re_\tau = 2300$. Part I of this contribution \cite{stanislas20} presented in short the experiment and discussed in detail the dissipation profile and all twelve derivative moments required to compute it. The data were compared to a channel flow DNS at approximately the same Reynolds number and to previous results. They were also used to evaluate recent theoretical results for the overlap region. In this Part II the experimental and DNS results are used to evaluate the assumptions of `local isotropy', `local axisymmetry', and `local homogeneity'. They are extended to include the full dissipation tensor, $\varepsilon_{ij}$ and the `pseudo-dissipation tensor', $\mathcal{D}_{ij}$ and explain the strong anisotropy of the dissipation tensors observed. Two important results of the present study are that {\it local isotropy} is never valid inside the outer limit of the overlap region, $y/\delta_{99} \approx 0.1$; and that the assumptions of {\it local axisymmetry} and {\it local homogeneity} fail inside of $y^+ =100$. The implications of {\it homogeneity in planes parallel to the wall} is introduced to partially explain observations throughout the wall layer. The dissipation characteristics in this very near wall region show that $\varepsilon_{ij}$ is close to but different from $\mathcal{D}_{ij}$ .