Numerical reproduction of the spiral wave visualized experimentally in a wide-gap spherical Couette flow

Abstract

Spherical Couette flow experiments were conducted according to the work of Egbers and Rath [Acta Mech. 111, 125–140 (1995)]. While the value of the critical Reynolds number obtained by the previous experiments was in good agreement with the numerical prediction, it has remained a question why a spiral wave bifurcating over the critical Reynolds number can be visualized even by a classical flow visualization technique like the mixing of a small amount of aluminum flakes to the working fluid. In the present study, through visualization using aluminum flakes drifting on a horizontal plane illuminated by a laser sheet, the flow was identified as a spiral wave with azimuthal wavenumber m = 3, using the experimentally obtained and numerically deduced comparison between phase velocities. By solving the equation of motion for the infinitesimal planar particles advecting in the flow field of the spiral wave, a visual distribution of reflected light was virtually reproduced, which is in good agreement with the experimentally obtained picture.