Enhanced magnetostrophic waves with magnetic field orthogonal to the rotation axis

TL;DR

This paper analytically and numerically investigates magnetostrophic waves in a rotating, magnetized fluid, revealing that orthogonal magnetic fields enhance wave propagation and may explain long-period oscillations in Earth's outer core.

Contribution

It provides the first analytical solution for magnetostrophic waves with magnetic fields orthogonal to rotation, validating it with numerical methods and exploring their implications for Earth's core dynamics.

Findings

Magnetostrophic waves travel faster when magnetic field is orthogonal to rotation.

Wave vectors perpendicular to the rotation axis propagate as inertial-Alfvén waves.

Enhanced wave propagation may explain centuries-long oscillations in Earth's outer core.

Abstract

We consider an isolated Gaussian velocity vortex perturbation in an otherwise quiescent, electrically conducting, and rotating fluid permeated by a uniform magnetic field $\bf{B}$. Studies suggest a presence of strong azimuthal wave motions on the timescale of centuries within the Earth's liquid outer core at higher latitudes. To understand these long-period oscillations, we focus on magnetostrophic waves, a slow component of magnetic-Coriolis waves with $\bf{B}$ orthogonally aligned with the rotation vector $\bf{\Omega}$, which replicate the field lines in the azimuthal direction. We present an analytical solution to the magnetic-Coriolis wave equation in Cartesian coordinates. Later, with numerical solution, we validate our analytical estimates and show that magnetostrophic waves travel relatively faster along the magnetic field when $\bf{B} \perp \bf{\Omega}$ compared with the case when both are aligned. The study confirms that with a magnetic field $\bf{B}$ orthogonally aligned to the rotation vector $\bf{\Omega}$, wave vectors satisfying the condition $\bf{\Omega}\cdot\bf{k} \approx 0$, travel with Alfv\'en velocities along the magnetic field lines as a component of inertial-Alfv\'en waves. The timescales on which Alfv\'en waves travel are relatively short, and it is also less likely that inertial-Alfv\'en waves will be sustained inside the core at higher latitudes \citep{Davidson2017}. This study shows that, excluding the inertial-Alfv\'en waves contribution ($k_z\neq 0$), there exists intensified magnetostrophic wave propagation when $\bf{B} \perp \bf{\Omega}$, which can explain the strong periodic oscillations on the time scales of centuries along the azimuthal field at higher latitudes. Results show persistence of the magnetostrophic waves despite the lower Lehnert number $Le$, suggesting the plausible existence of a low-intensity azimuthal magnetic field in the Earth's core.