Damping of magnetic-Coriolis waves with imposed magnetic field orthogonal to the axis of rotation

Abstract

Small-scale columnar structures (<10 km radius) in Earth's outer core result from inertial waves. In highly conducting fluid, magnetic field behaviour resembles stretched elastic strings and transmits disturbances as Alfvén waves. Magnetic-Coriolis waves occur in a rotating fluid with an imposed magnetic field with a low Lehnert number (Le << 1), exhibiting weakly modified inertial and magnetostrophic waves. With higher group velocity, the former traverses the outer core in months, while the latter takes centuries. Studies mainly focus on aligned rotation and magnetic fields, but changing the magnetic field direction alters magnetohydrodynamic flow. Hybrid inertial-Alfvén waves exist only when the magnetic field is perpendicular to the rotation axis. Strong magnetic dissipation leads to kinetic energy decay through Joule damping when the rotation vector is orthogonal to the magnetic field. In contrast, aligning these two vectors directs energy along the rotation axis, resulting in a slowdown of dissipation. This study investigates the evolution of an isolated vortex in a rotating fluid with an imposed uniform magnetic field under two different configurations. Using the initial velocity condition, the magnetic-Coriolis wave equation is solved by applying Fourier transforms over an infinite domain. The solution for velocity and magnetic fields is derived through both analytical and numerical solutions of inverse Fourier integrals. In the case of aligned rotation and imposed magnetic field, results match prior findings. Conversely, orthogonal alignment reveals distinct decay rates for weakly modified inertial and magnetostrophic waves, with the former decaying slowly and the latter decaying more rapidly. Specifically, weakly modified inertial waves' kinetic and magnetic energy decay as (t/tη)-0.6 and (t/tη)-1.5, respectively. The kinetic and magnetic energy of magnetostrophic waves decay as (t/tη)-6.0 and (t/tη)-4.0, respectively, where t/tη represents the normalized time with the dissipation time tη. The perpendicular configuration becomes significant considering Earth's core's dominating azimuthal magnetic field. The study shows a reduced initial phase for weakly modified inertial waves (reduction of ~11.5 years) and increased energy O(102-104 ) for magnetostrophic waves during the initial wave-dominated phase, suggesting slow magnetostrophic waves persist even with a small Lehnert number. This anticipates a lower intensity in the core's azimuthal magnetic field than the predictions based on aligned rotation and magnetic field.