2D or not 2D: the effect of dimensionality on the dynamics of fingering convection at low Prandtl number

TL;DR

This study compares 2D and 3D simulations of fingering convection at low Prandtl numbers, concluding that 2D simulations are inadequate and that minimal 3D domain width is sufficient to capture key dynamics.

Contribution

It demonstrates that 2D simulations cannot reliably replicate 3D fingering convection at low Prandtl numbers and identifies the minimal 3D domain size needed for accurate modeling.

Findings

2D simulations are never appropriate for this phenomenon.

A 3D domain with only two wavelengths of the fastest-growing mode suffices.

Narrow 3D domains may limit large-scale dynamics development.

Abstract

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.