Fingering convection (otherwise known as thermohaline convection) is an
instability that occurs in stellar radiative interiors in the presence of
unstable compositional gradients. Numerical simulations have been used in order
to estimate the efficiency of mixing induced by this instability. However,
fully three-dimensional (3D) computations in the parameter regime appropriate
for stellar astrophysics (i.e. low Prandtl number) are prohibitively expensive.
This raises the question of whether two-dimensional (2D) simulations could be
used instead to achieve the same goals. In this work, we address this issue by
comparing the outcome of 2D and 3D simulations of fingering convection at low
Prandtl number. We find that 2D simulations are never appropriate. However, we
also find that the required 3D computational domain does not have to be very
wide: the third dimension need only contain a minimum of two wavelengths of the
fastest-growing linearly unstable mode to capture the essentially 3D dynamics
of small-scale fingering. Narrow domains, however, should still be used with
caution since they could limit the subsequent development of any large-scale
dynamics typically associated with fingering convection.Comment: Submitted to Ap
