On the rheoscopic measurement of turbulent decay in wall-bounded flows

TL;DR

This work investigates what rheoscopic flow visualization actually measures in wall-bounded turbulence during quench-induced relaminarisation by directly comparing it with PIV data in a plane Couette–Poiseuille flow. Using two image-processing approaches to extract turbulent regions from visualization frames and velocity-thresholded/kinetic-energy metrics from PIV, the authors show that the decay time of the visualization-derived turbulent fraction corresponds to the decay of streamwise velocity fluctuations (streaks) and is longer than the spanwise roll decay. The findings clarify the physical meaning of rheoscopic decay times, demonstrate the robustness of visualization-based diagnostics, and suggest that rheoscopic methods effectively capture streak persistence during relaminarisation. The results support using rheoscopic visualization as a reliable complementary tool for studying streak-dominated dynamics in wall-bounded turbulence and for identifying weak shear regions that may elude velocity-based detection.

Abstract

Quench experiments where the flow passes from a fully turbulent state to a laminar state by an abrupt decrease in the flow Reynolds number ($Re$) have been extensively studied in the literature to quantify the turbulent-laminar transition process in wall-bounded flows. Measurements have been classically made using rheoscopic fluid visualisations, which make turbulent coherent structures easily identifiable, allowing for quantification of the evolution of a turbulent fraction -- the percentage of a given observation window where turbulence is deemed active by the presence of coherent structures, such as streamwise vortices called rolls, and modulations of the streamwise velocity fluctuations called streaks. Decay characteristic times of these structures have therefore been extensively measured. However, owing to the nature of visualization based techniques, only a single decay time is typically extracted, whereas measurements of the velocity field can reveal distinct decay times associated with different velocity or kinetic energy components. As a result, the physical meaning of the decay time inferred from visualization alone is not straightforward. The goal of the present paper is to perform such a comparison quantitatively, using particle image velocimetry (PIV) measurements and rheoscopic fluid visualisations in the same setup: a Couette-Poiseuille experiment. We observe via PIV different characteristic times of decay for streamwise (streaks) and spanwise (rolls) velocity fluctuations. We show that the characteristic time of decay of the turbulent fraction observed by visualisation is close to the decay of the streaks.

Figures (9)

• Figure 1: Schematic of the plane Couette–Poiseuille flow channel equipped for (a) 2D2C Particle Image Velocimetry (PIV) and (b) flow visualization measurements with LED light band and anisotropic light-reflecting aluminium particles.
• Figure 2: Illustration of image processing steps proposed by Sano_NP_2016 for a sample flow visualization image taken shortly after the quench at $t^* = 62$ for $Re_f = 500$: (a) Raw grayscale image, (b) intensity-normalized image to enhance contrast, (c) binary image obtained via intensity fluctuation thresholding.
• Figure 3: Illustration of the image-processing procedure following Bottin_thesis_1998 applied to a sample flow-visualization frame taken shortly after the quench at $t^* = 62$ for $Re_f = 500$: (a) Raw grayscale image; (b) morphological opening followed by gradient filtering; (c) thresholded binary field; and (d) image erosion and dilation.
• Figure 4: Comparison of the temporal evolution of the turbulent fraction of quench experiments obtained flow visualization and PIV velocity field results. (a) $Re_f = 300$, (b) $Re_f = 500$. The gold solid line $F_t^S$ represents flow visualization analyzed using the image processing method in Section \ref{['subsec:MethodSano']}. The green solid line $F_t^B$ shows an alternative flow visualization result processed following the method in Section \ref{['subsec:MethodBottin']}. The blue solid line corresponds to $F_x$, obtained by thresholding the streamwise velocity field with $|u_x| > 0.1U_{\text{belt}}$, while the red solid line corresponds to $F_z$, obtained by thresholding the spanwise velocity field with $|u_z| > 0.05U_{\text{belt}}$. The horizontal black dashed line indicates the reference level $F = 0.15$.
• Figure 5: Binary flow fields for the quench case at $Re_f = 500$. Top row: fully turbulent initial state at $Re_i = 1000$ ($t<0$ in Fig. \ref{['fig:turb_frac_evolution']}b). Bottom row: post-quench state when the turbulent fraction reaches its peak. Panels (a,d) show velocity-thresholded fields ($\lvert u_x\rvert \ge 0.1\,U_{\mathrm{belt}}$) from PIV measurements, (b,e) intensity-variation thresholding, and (c,f) image morphological processing.