Revisiting visualization of spiral states in a wide-gap spherical Couette flow

Abstract

A pioneering study conducted by Egbers and Rath [Acta Mech. 111 pp. 125--140 (1995)] experimentally captured spiral waves to elucidate the transition in the wide-gap spherical Couette flow. However, the physical field quantities of the spiral waves corresponding to light patterns of various intensities, as obtained in the experiment, remain unclear, and we have yet to move beyond the understanding that the reflected light from shear-sensitive flake tracers responds to a flow that appears at the transition. In this study, the experiment to visualize spiral waves using aluminum flakes, as performed by Egbers and Rath, was numerically reproduced by solving the translational and rotational motions of the particles in a spiral wave. First, the spiral wave in a spherical Couette flow with an aspect ratio $\eta=1/2$ was numerically calculated using the Newton--Raphson method. Subsequently, the image that was numerically reproduced from the spiral wave was compared with an experimentally visualized image. The torque acting on the inner sphere and the phase angular velocity of the spiral waves with various wavenumbers were provided. Attempts have been made to determine the instantaneous physical quantity to which the light and dark patterns obtained in the visualization corresponded, and the orientation motion of the flakes developed in the advective history of the flow is essential to yield favorable results. Exploring the correlation between flow visualization results and shear structures may provide a new avenue for quantitatively estimating spatial structures and time scales in complex and quickly time-varying flow fields, such as turbulence.