Turbulent convection and pulsation stability of stars - I. Basic equations for calculations of stellar structure and oscillations

TL;DR

This paper develops a comprehensive set of hydrodynamic equations for stellar structure and oscillations, incorporating turbulence, non-locality, and anisotropy, and demonstrates their application to pulsation stability analysis.

Contribution

It introduces a self-consistent mathematical framework for stellar turbulence and oscillations, including calibration of convection parameters and analysis of pulsation stability.

Findings

The framework accounts for non-local and anisotropic turbulence effects.

Pulsation stability remains robust across a wide range of convection parameters.

Numerical solutions illustrate the structure of convective envelopes and oscillation characteristics.

Abstract

Starting from hydrodynamic equations, we have established a set of hydrodynamic equations for average flow and a set of dynamic equations of auto- and cross-correlations of turbulent velocity and temperature fluctuations, following the classic Reynold's treatment of turbulence. The combination of the two sets of equations leads to a complete and self-consistent mathematical expressions ready for the calculations of stellar structure and oscillations. In this paper, non-locality and anisotropy of turbulent convection are concisely presented, together with defining and calibrating of the three convection parameters ($c_1$, $c_2$ and $c_3$) included in the algorithm. With the non-local theory of convection, the structure of the convective envelope and the major characteristics of non-adiabatic linear oscillations are demonstrated by numerical solutions. Great effort has been exercised to the choice of convection parameters and pulsation instabilities of the models, the results of which show that within large ranges of all three parameters ($c_1$, $c_2$ and $c_3$) the main properties of pulsation stability keep unchanged.