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تسجيل مستخدم جديدVelocity Derivatives in Turbulent Boundary Layers. Part II: Statistical Properties
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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 $mathcal{D}_{ij}$ .
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An experiment was performed using SPIV in the LMFL boundary layer facility to determine all the derivative moments needed to estimate the average dissipation rate of the turbulence kinetic energy, $varepsilon = 2 u langle s_{ij}s_{ij} rangle$ where
$s_{ij}$ is the fluctuating strain-rate and $langle~rangle$ denotes ensemble averages. Also measured were all the moments of the full average deformation rate tensor, as well as all of the first, second and third fluctuating velocity moments except those involving pressure. The Reynolds number was $Re_theta = 7500$ or $Re_tau = 2300$. The results are presented in three separate papers. This first paper (Part I) presents the measured average dissipation, $varepsilon$ and the derivative moments comprising it. It compares the results to the earlier measurements of cite{balint91,honkan97} at lower Reynolds numbers and a new results from a plane channel flow DNS at comparable Reynolds number. It then uses the results to extend and evaluate the theoretical predictions of cite{george97b,wosnik00} for all quantities in the overlap region. Of special interest is the prediction that $varepsilon^+ propto {y^+}^{-1}$ for streamwise homogeneous flows and a nearly indistinguishable power law, $varepsilon propto {y^+}^{gamma-1}$, for boundary layers. In spite of the modest Reynolds number, the predictions seem to be correct. It also predicts and confirms that the transport moment contribution to the energy balance in the overlap region, $partial langle - pv /rho - q^2 v/2 rangle/ partial y$ behaves similarly. An immediate consequence is that the usual eddy viscosity model for these terms cannot be correct. The second paper, Part II, examines in detail the statistical character of the velocity derivatives. The details of the SPIV methodology is in Part III, since it will primarily be of interest to experimentalists.
An SPIV experiment using two orthogonal planes simultaneously was performed in the LML boundary layer facility to specifically measure all of the derivative moments needed to estimate the dissipation rate of the Turbulence Kinetic Energy. The Reynold
s number was $Re_theta = 7500$ or $Re_tau = 2300$. A detailed analysis of the errors in derivative measurements was carried out, as well as applying and using consistency checks derived from the continuity equation. The random noise error was quantified, and used to ``de-noise the derivative moments. A comparison with a DNS channel flow at comparable Reynolds number demonstrated the capability of the technique. The results were further validated using the recent theory developed by George and Stanislas 2020. The resulting data have been extensively used in parts I and II of the present contribution to study near wall dissipation. An important result of the present work is the provision of reliable rules for an accurate assessment of the dissipation in future PIV experiments.
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