Unveiling the structure of a free Stewartson-Shercliff layer in liquid-metal Taylor-Couette flow

Free flow shear layers are ubiquitous in nature, arising in planetary interiors, stellar convection zones, and accretion disks where localized differential rotation exists in the absence of solid boundaries. These layers play a critical role in magnetohydrodynamics (MHD) and are essential for enabling instabilities such as the magnetorotational instability (MRI), a key mechanism for angular momentum transport in astrophysical systems. In this work, we create and fully characterize a magnetized free shear layer—known as the Stewartson-Shercliff layer (SSL)—in a liquid-metal Taylor-Couette flow using GaInSn under a strong axial magnetic field. The SSL forms naturally at the junction between split endcap rings and extends axially through the differentially rotating bulk flow via magnetic coupling. We derive a set of governing equations for the SSL, yielding analytical solutions for the velocity and magnetic field profiles therein. These solutions show excellent agreement with both numerical simulations and experimental measurements using ultrasound Doppler velocimetry. Simulations further reveal that magnetic induction within the SSL generates an azimuthal magnetic field exceeding the applied field, indicating a strong Omega effect. These findings provide a comprehensive understanding of free shear layers in MHD and have broad implications for modeling astrophysical and geophysical flows.