Mean flow and Convective instability analysis of the BEK and related rotating boundary layer flows subject to a uniform static magnetic field

Abstract

This study examines the convective instability of the hydromagnetic Bödewadt, Ekman, and von Kármán (BEK) rotating system under the low magnetic Reynolds number approximation. The computations for the mean flow are carried out for different magnetic parameters using MATLAB for several flows of the BEK family. The equations for the linear instability are derived and then solved through the Chebyshev-spectral method for both Type-I (Inviscid) and Type-II (viscous) modes. It is observed that the Rossby number, the Reynolds number, and the magnetic parameter characterize the stability of the hydromagnetic BEK flows. The Reynolds number is based on the dimensionless radial location at the disk while the Rossby number is the ratio of the difference between the angular speeds of fluid and disk and the angular speed of the disk. The magnetic number is the ratio of magnetic field strength and the system rotation rate. The analysis reveals a stabilizing effect of the magnetic parameter on the Type-I modes for Rossby numbers in the range [−1,1]. Further, the Type-II modes disappear upon elevating the magnetic parameter in the aforementioned range of the Rossby number. The growth rates, |αi|, also diminish upon increasing the magnetic parameter. The computations for mean flow reveal that the radial wall shear stress diminishes upon elevating the strength of the applied magnetic field. However, a reverse trend is noted for the azimuthal wall shear stress which indicates an increase in the torque on the disk with enhancing the intensity of the magnetic field.