On the reflection of Alfvén waves and its implication for Earth's core modeling

Abstract

Alfvén waves propagate in electrically conducting fluids in the presence of a magnetic field. Their reflection properties depend on the ratio between the kinematic viscosity and the magnetic diffusivity of the fluid, also known as the magnetic Prandtl number Pm. In the special case Pm=1, there is no reflection on an insulating, no-slip boundary, and the wave energy is entirely dissipated in the boundary layer. We investigate the consequences of this remarkable behaviour for the numerical modeling of torsional Alfvén waves (also known as torsional oscillations), which represent a special class of Alfvén waves, in rapidly rotating spherical shells. They consist of geostrophic motions and are thought to exist in the fluid cores of planets with internal magnetic field. In the geophysical limit Pm << 1, these waves are reflected at the core equator, where they are entirely absorbed for Pm=1. Our numerical calculations show that the reflection coefficient at the equator of these waves remains below 0.2 for Pm > 0.3, which is the range of values for which geodynamo numerical models operate. As a result, geodynamo models with no-slip boundary conditions cannot exhibit torsional oscillation normal modes.

12 pages

References in corpus (6)

• Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations
• Axial invariance of rapidly varying diffusionless motions in the Earth's core interior
• Parameter dependences of convection driven dynamos in rotating spherical fluid shells
• Longer lifespan for many solutions of the Kirchhoff equation
• Visco-magnetic torque at the core mantle boundary
• Experimental evidence of Alfvén wave propagation in a Gallium alloy

Cited by in corpus (11)

• Turbulent geodynamo simulations: a leap towards Earth's core
• Shell Models of Magnetohydrodynamic Turbulence
• Planetary gyre, time-dependent eddies, torsional waves, and equatorial jets at the Earth's core surface
• Dynamo-based limit to the extent of a stable layer atop Earth's core
• Electrical conductivity of the lowermost mantle explains absorption of core torsional waves at the equator
• The interplay of fast waves and slow convection in geodynamo simulations nearing Earth's core conditions
• The dynamics and excitation of torsional waves in geodynamo simulations
• Evolution of a magnetic field in a differentially rotating radiative zone
• Three-dimensional solutions for the geostrophic flow in the Earth's core
• Lorentz force mediation of turbulent dynamo transitions
• Anelastic torsional oscillations in Jupiter's metallic hydrogen region