Effective drag in rotating, poorly conducting plasma turbulence

TL;DR

This paper investigates the effectiveness of drag parametrizations in modeling magnetic effects in poorly conducting, rotating plasma turbulence, proposing an improved approximation suitable for hot Jupiter atmospheres.

Contribution

It demonstrates the limitations of traditional drag parametrizations and introduces a quasi-static MHD approximation for better modeling magnetic influences in planetary atmospheres.

Findings

Drag parametrization fails when Lorentz force time-scale is short.

Effective drag coefficient remains constant despite magnetic time-scale variations.

Quasi-static MHD approximation captures complex Lorentz force effects.

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.