  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.
