Velocity derivatives in a high Reynolds number turbulent boundary layer. Part I: Dissipation and Energy Balance

TL;DR

This study measures velocity derivatives and energy dissipation in a high Reynolds number turbulent boundary layer using SPIV, comparing results with theoretical models and lower Reynolds number data to evaluate turbulence predictions.

Contribution

It provides new experimental measurements of dissipation and derivative moments at high Reynolds numbers, extending and testing turbulence theories in boundary layers.

Findings

Dissipation rate and derivative moments are measured at high Reynolds number.

Results support theoretical predictions of dissipation behavior in boundary layers.

Transport contributions to energy balance challenge traditional eddy viscosity models.

Abstract

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, $\varepsilon = 2 \nu \langle s_{ij}s_{ij} \rangle$ 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.