The Interaction between Shear and Fingering (Thermohaline) Convection

Abstract

Fingering convection is a turbulent mixing process that can occur in stellar radiative regions whenever the mean molecular weight increases with radius. In some cases, it can have a significant observable impact on stellar structure and evolution. The efficiency of mixing by fingering convection as a standalone process has been studied by Brown et al. (2013), but other processes such as rotation, magnetic fields and shear can affect it. In this paper, we present a first study of the effect of shear on fingering (thermohaline) convection in astrophysics. Using Direct Numerical Simulations we find that a moderate amount of shear (that is not intrinsically shear-unstable) always decreases the mixing efficiency of fingering convection, as a result of the tilt it imparts to the fingering structures. We propose a simple analytical extension of the Brown et al. (2013) model in the presence of shear that satisfactorily explains the numerically-derived turbulent compositional mixing coefficient for moderate shearing rates, and can trivially be implemented in stellar evolution codes. We also measure from the numerical simulations a turbulent viscosity, and find that the latter is strongly tied to the turbulent compositional mixing coefficient. Observational implications and caveats of the model are discussed.

Instability driven by settling and evaporation in a shear flow: a model for asperitas clouds

“…Equations II.11-II.15 are specialised to two dimensions by setting v ≡ 0, and ∂/∂y ≡ 0. We find, in general agree-ment with previous work on related systems, that the introduction of shear smooths out small-scale perturbations [17,18]. We also find that increasing droplet sizes, corresponding here to lower F r −2 and larger τ s,0 , supports larger lobe sizes.…”

“…We therefore begin our investigations with 2D simulations. The application of shear sets a preferred horizontal direction and, as discussion in Section I, is known to cause the formation of salt sheets parallel to the direction of the shear flow ( [16][17][18][19]22]) in thermohaline and settling-driven convection. In the 2D simulations, this leads to a planar interface.…”

“…The difference is that in the typical DD system, none of the scalar components undergoes settling. Both DD and settling driven instabilities have been studied in the presence of a horizontal shear flow [16][17][18][19]. In general, due to the imposed homogeneity in the direction of flow, shear stabilizes the fingering instabilities that occur at the interface, while modes in the direction perpendicular to the shear are unaffected.…”

Idealised 3D simulations of diabatically forced Ledoux convection

“…The Riemann solver employed was similar to the Harten-Lax-van Leer-Contact (HLLC) type, known to be necessary for capturing this type of instability; however, as the spatial reconstruction and time integration is first order, the degree of dissipation in the model may simply be too great for the instability to establish. This is, however, purely speculative and we leave further discussion of the role of shear to a future publication in which the general case of shear in 3D simulations will be studied (see also Garaud & Brummell 2015;Garaud et al 2019).…”

Modeling coexisting GSF and shear instabilities in rotating stars

“…However, this general practice is considered heretical by most fluid dynamicists, as there is a wealth of evidence showing that doing this often gives nonsensical results. For example, adding shear to convection or fingering convection can reduce mixing considerably (Garaud et al 2019;Blass et al 2021) instead of increasing it.…”