Transport by meridional circulations in solar-type stars

TL;DR

This study uses local 3D simulations to investigate meridional flow transport in solar-type stars, revealing that laminar models accurately predict flow behavior and that previous simulations underestimated this transport.

Contribution

It demonstrates that laminar, balanced models correctly describe meridional flow behavior and introduces the concept of flow burrowing, which was not observed in earlier simulations.

Findings

Mean flow behavior aligns with laminar model predictions

Flow burrowing occurs when Eddington-Sweet timescale is shorter than viscous diffusion timescale

Previous simulations underestimated meridional flow transport

Abstract

Transport by meridional flows has significant consequences for stellar evolution, but is difficult to capture in global-scale numerical simulations because of the wide range of timescales involved. Stellar evolution models therefore usually adopt parameterizations for such transport based on idealized laminar or mean-field models. Unfortunately, recent attempts to model this transport in global simulations have produced results that are not consistent with any of these idealized models. In an effort to explain the discrepancies between global simulations and idealized models, we here use three-dimensional local Cartesian simulations of compressible convection to study the efficiency of transport by meridional flows below a convection zone in several parameter regimes of relevance to the Sun and solar-type stars. In these local simulations we are able to establish the correct ordering of dynamical timescales, although the separation of the timescales remains unrealistic. We find that, even though the generation of internal waves by convective overshoot produces a high degree of time dependence in the meridional flow field, the mean flow has the qualitative behavior predicted by laminar, "balanced" models. In particular, we observe a progressive deepening, or "burrowing", of the mean circulation if the local Eddington-Sweet timescale is shorter than the viscous diffusion timescale. Such burrowing is a robust prediction of laminar models in this parameter regime, but has never been observed in any previous numerical simulation. We argue that previous simulations therefore underestimate the transport by meridional flows.