Experimental investigation of intermediate-dissipation range energy spectra in shear turbulence

TL;DR

This study experimentally investigates the energy spectra in the intermediate dissipation range of shear turbulence at high Reynolds numbers, revealing a universal stretched-exponential form with Reynolds-number invariant scaling.

Contribution

It provides the first experimental evidence of a universal stretched-exponential energy spectrum in the intermediate dissipation range of high-Re shear turbulence.

Findings

Spectra collapse onto a universal stretched-exponential form with exponent ~0.5.

Reynolds-number invariance of the spectral shape supports universal scaling.

High-resolution measurements resolved small scales up to high wave numbers.

Abstract

The shape of the turbulent energy spectrum in the dissipation range, where viscous effects dominate, remains an open question despite decades of work. We report an experimental investigation of intermediate dissipation range energy spectra in turbulent shear layers at Taylor-scale Reynolds numbers, $Re_\lambda$, ranging from approximately 450 to 1500, which are among the highest achieved in shear flow experiments that resolved small scales. We generated turbulent shear layers in a wind tunnel and measured using nanoscale hot-wire probes with a sensing length $l_w \approx (0.2-0.5)\eta$ that was smaller than the Kolmogorov scale $\eta$ at all $Re_\lambda$. The measurements resolved wavenumbers up to $k_{max} \eta$ $\approx 17$ at the lowest $Re_\lambda$ and $k_{max} \eta$ $\approx 1$ at the highest $Re_\lambda$, where $k_{max}$ is the highest resolved wave number. In the range $0.1 \lesssim k \eta \lesssim 0.5$, the spectra collapse onto a universal stretched-exponential form, $E(k\eta) \sim $ exp$(-k\eta)^{\gamma} $, with $\gamma \approx 0.5$ independent of $Re_\lambda$. This value of stretching exponent, $\gamma$, is consistent with recent empirical and computational studies. The Reynolds-number invariance of $\gamma$ is strong evidence for universal scaling in the intermediate dissipation range of high-Reynolds-number shear turbulence.