Modes and instabilities in magnetized spherical Couette flow

Abstract

Several teams have reported peculiar frequency spectra for flows in a spherical shell. To address their origin, we perform numerical simulations of the spherical Couette flow in a dipolar magnetic field, in the configuration of the DTS experiment. The frequency spectra computed from time-series of the induced magnetic field display similar bumpy spectra, where each bump corresponds to a given azimuthal mode number m. The bumps show up at moderate Reynolds number (2 600) if the time-series are long enough (>300 rotations of the inner sphere). We present a new method that permits to retrieve the dominant frequencies for individual mode numbers m, and to extract the modal structure of the full non-linear flow. The maps of the energy of the fluctuations and the spatio-temporal evolution of the velocity field suggest that fluctuations originate in the outer boundary layer. The threshold of instability if found at Re_c = 1 860. The fluctuations result from two coupled instabilities: high latitude Bödewadt-type boundary layer instability, and secondary non-axisymmetric instability of a centripetal jet forming at the equator of the outer sphere. We explore the variation of the magnetic and kinetic energies with the input parameters, and show that a modified Elsasser number controls their evolution. We can thus compare with experimental determinations of these energies and find a good agreement. Because of the dipolar nature of the imposed magnetic field, the energy of magnetic fluctuations is much larger near the inner sphere, but their origin lies in velocity fluctuations that initiate in the outer boundary layer.

23 pages

References in corpus (13)

• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• Experimental observation and characterization of the magnetorotational instability
• Constraints on Deep-seated Zonal Winds Inside Jupiter and Saturn
• Axial invariance of rapidly varying diffusionless motions in the Earth's core interior
• Observation of magnetocoriolis waves in a liquid metal Taylor-Couette experiment
• Rapidly rotating spherical Couette flow in a dipolar magnetic field: an experimental study of the mean axisymmetric flow
• Observation of a Free-Shercliff-Layer Instability in Cylindrical Geometry
• On the excitation of inertial modes in an experimental spherical Couette flow
• Zonal shear and super-rotation in a magnetized spherical Couette flow experiment
• Modes and instabilities in magnetized spherical Couette flow
• Spherical Couette flow in a dipolar magnetic field
• A note on "Constraints on deep-seated zonal winds inside Jupiter and Saturn"
• Magneto--Coriolis waves in a spherical Couette flow experiment

Cited by in corpus (15)

• Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations
• Modes and instabilities in magnetized spherical Couette flow
• Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment
• Modulated rotating waves in the magnetized spherical Couette system
• Chaotic wave dynamics in weakly magnetised spherical Couette flows
• A systematic bias in the calculation of spectral density from a 3D spatial grid
• Experimental investigation of the return flow instability in magnetic spherical Couette flow
• Dynamic Domains of DTS: Simulations of a Spherical Magnetized Couette Flow
• Continuation and stability of rotating waves in the magnetized spherical Couette system: Secondary transitions and multistability
• Four-frequency solution in a magnetohydrodynamic Couette flow as a consequence of azimuthal symmetry breaking
• Magnetic induction maps in a magnetized spherical Couette flow experiment
• Magnetic induction and diffusion mechanisms in a liquid sodium spherical Couette experiment
• Transition to turbulence in the wide-gap spherical Couette system
• Shercliff layers in strongly magnetic cylindrical Taylor-Couette flow
• Tidally synchronized solar dynamo: a rebuttal