Power spectrum of high Schmidt number scalar in a turbulent jet at a moderate Reynolds number

Abstract

The power spectrum of concentration fluctuation of high Schmidt number dye (${\rm Sc}\simeq 2.9\times 10^3$) was measured in a liquid-phase axisymmetric turbulent jet at the jet Reynolds number of $2.0\times 10^4$. We used the optical fiber LIF probe which has a spatial resolution of 2.8 $\mu$m and a working distance of 140 $\mu$m. It is confirmed that the probe can achieve high signal-to-noise ratio by using high concentration dye, which enabled us to examine the spectral shape almost up to the Batchelor scale for the present experimental condition. The measured power spectrum captures the transition from the inertial–convective range to the viscous–convective range at around $k\eta _K=0.03$ ($\eta _K$: Kolmogorov scale). The $k^{-1}$ scaling law for the power spectrum almost holds in the viscous–convective range. However, the spectrum does not perfectly follow the $k^{-1}$ scaling but has a small bump in the range. It is also shown that the small-scale concentration fluctuation largely contributes to the r.m.s value of concentration fluctuation.

Graphic abstract