Some open questions concerning the modelling of non-locality in Reynolds stress type models of stellar convection.

Abstract

We discuss some benefits and pitfalls when combining conceptually different types of closure approximations into complete Reynolds stress models of stellar convection.

Thermal Convection in Stars and in Their Atmosphere

“…Recalling the Reynolds stress models it might seem attractive to combine the closures suggested in [86,90] to a more general model (see [86]). However, the naive combination of "favourite closures" including those by [86,90] easily triggers instabilities as has been shown in [83] and confirmed by [98].…”

“…For deep convection zones with low radiative heat losses inside the convection zone, such as in our Sun, a comparison with numerical simulations for idealized microphysics reveals [83,84] that the models for the TOMs suggested in [74,78] cannot any more reproduce higher (third) order moments. Those cases of numerical simulations of compressible, vertically stratified convection for which they had been found to work, such as discussed in [77], had been characterized by small values of skewness of the vertical velocity and temperature fields.…”

“…At this level of complexity the model has been used in [76,77,82]. When compared to 3D hydrodynamical simulations it allows accurate predictions for cases with large radiative losses, as in sufficiently hot A type and DA type stars ( [83]), but not for solar-like convection.…”

“…Studies which show the substantial improvement of either some or all of Eq. ( 36)-( 42) when compared to previous models include a resolved numerical simulation of free oceanic convection, [95], the numerical simulation of deep, compressible convection with idealized microphysics, [81,83,84,96], the numerical simulation of solar granulation, [24,94,97], and granulation in a K-dwarf, [94], as well as in a DA white dwarf, [24], and again simulations of compressible convection with idealized microphysics, [98].…”

Convection Theory and Relevant Problems in Stellar Structure, Evolution, and Pulsational Stability I Convection Theory and Structure of Convection Zone and Stellar Evolution

“…During the past 20 years, rapid progress has been made in numerical simulations, and these have become an important means to study stellar convection. We have tried to use 2D or 3D simulations to test some basic assumptions of our non-local and time-dependent theory of convection and to calibrate the convection parameters (Kupka, 2002;Deng et al, 2006;Kupka and Muthsam, 2007;Kupka, 2007a;Kupka, 2007b;Kupka, 2007c;Cai, 2008;Tian et al, 2009;Chan et al, 2008;Chan et al, 2011;Cai and Chan, 2012;Cai, 2014;Kupka, 2017;Cai, 2018;Cai, 2020a;Cai, 2020b;Cai, 2020c). Some meaningful results were obtained.…”