Pseudo-Visualization and Analysis of Phase in Two-Dimensional Flow Using Aluminum Flake Tracers

The flow within a concentric double spherical shell, characterized by a stationary outer sphere and a rotation of the inner sphere at a constant angular velocity, is recognized as spherical Couette flow (SCF). Egbers and Rath [Acta Mech. vol.111, 125-140 (1995)] experimentally confirmed the emergence of a phase extending from the poles to the equatorial plane, commonly referred to as a spiral state. Meanwhile, Yoshikawa et al. [Phys. Fluids vol.35, 034110 (2023)] successfully identified the phase in the early stages of the SCF transition by using a working fluid suspended with aluminum flakes as tracer particles. In this study, we emulated their visualization experiment as a simplified two-dimensional model, yielding notable outcomes. Our findings demonstrate the feasibility of measuring the phase velocity ω of the flow field through flake visualization on a plane parallel to the equator and determining the wavenumber associated with the observed phase in the spiral states.