Effective drag in rotating, poorly conducting plasma turbulence

Abstract

Despite the increasing sophistication of numerical models of hot Jupiter atmospheres, the large time-scale separation required in simulating the wide range in electrical conductivity between the dayside and nightside has made it difficult to run fully consistent magnetohydrodynamic (MHD) models. This has led to many studies that resort to drag parametrizations of MHD. In this study, we revisit the question of the Lorentz force as an effective drag by running a series of direct numerical simulations of a weakly rotating, poorly conducting flow in the presence of a misaligned, strong background magnetic field. We find that the drag parametrization fails once the time-scale associated with the Lorentz force becomes shorter than the dynamical time-scale in the system, beyond which the effective drag coefficient remains roughly constant, despite orders-of-magnitude variation in the Lorentz (magnetic) time-scale. We offer an improvement to the drag parametrization by considering the relevant asymptotic limit of low conductivity and strong background magnetic field, known as the quasi-static MHD approximation of the Lorentz force. This approximation removes the fast time-scale associated with magnetic diffusion, but retains a more complex version of the Lorentz force, which could be utilized in future numerical models of hot Jupiter atmospheric circulation.

Main text 9 pages, total 11 pages, 4 figures, 1 table. v2: corrections and changes made based on referee reports. Published in The Astrophysical Journal

References in corpus (17)

• Inflating Hot Jupiters With Ohmic Dissipation
• Multi-Wavelength Constraints on the Day-Night Circulation Patterns of HD 189733b
• Atmospheric Circulation of Hot Jupiters: A Shallow Three-Dimensional Model
• Atmospheric Dynamics of Hot Exoplanets
• Atmospheric Dynamics of Short-period Extra Solar Gas Giant Planets I: Dependence of Night-Side Temperature on Opacity
• The 4.5 $\mu$m full-orbit phase curve of the hot Jupiter HD 209458b
• Magnetic Effects in Hot Jupiter Atmospheres
• Climate of an Ultra hot Jupiter: Spectroscopic phase curve of WASP-18b with HST/WFC3
• Estimating the magnetic field strength in hot Jupiters
• Exploring the Effects of Active Magnetic Drag in a GCM of the Ultra-Hot Jupiter WASP-76b
• Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence
• Shallow-water Magnetohydrodynamics for Westward Hotspots on Hot Jupiters
• Electrodynamics on extrasolar giant planets
• Dimensional transition of energy cascades in stably stratified thin fluid layers
• On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence
• Turbulent cascade, bottleneck and thermalized spectrum in hyperviscous flows
• Observational Consequences of Shallow-water Magnetohydrodynamics on Hot Jupiters

Cited by in corpus (1)

• Inflated hot Jupiters: Inferring average atmospheric velocity via Ohmic models coupled with internal dynamo evolution