arXiv subjects

Miroslav Mocák

Publications and source records attributed to Miroslav Mocák.

5 recordsLinked to original sources

arXiv2024

Shell mergers in the late stages of massive star evolution: new insight from 3D hydrodynamic simulations

One-dimensional (1D) stellar evolution models are widely used across various astrophysical fields, however they are still dominated by important uncertainties that deeply affect their predictive power. Among those, the merging of independent convective regions is a poorly understood phenomenon predicted by some 1D models but whose occurrence and impact in real stars remain very uncertain. Being an intrinsically multi-D phenomenon, it is challenging to predict the exact behaviour of shell mergers with 1D models. In this work, we conduct a detailed investigation of a multiple shell merging event in a 20 M$_\odot$ star using 3D hydrodynamic simulations. Making use of the active tracers for composition and the nuclear network included in the 3D model, we study the merging not only from a dynamical standpoint but also considering its nucleosynthesis and energy generation. Our simulations confirm the occurrence of the merging also in 3D, but reveal significant differences from the 1D case. Specifically, we identify entrainment and the erosion of stable regions as the main mechanisms that drive the merging, we predict much faster convective velocities compared to the mixing-length-theory velocities, and observe multiple burning phases within the same merged shell, with important effects for the chemical composition of the star, which presents a strongly asymmetric (dipolar) distribution. We expect that these differences will have important effects on the final structure of massive stars and thus their final collapse dynamics and possible supernova explosion, subsequently affecting the resulting nucleosynthesis and remnant.

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arXiv2021

3D Simulations and MLT: II. Onsager's Ideal Turbulence

We simulate stellar convection at high Reynolds number (Re$\lesssim$7000) with causal time stepping but no explicit viscosity. We use the 3D Euler equations with shock capturing (Colella & Woodward 1984). Anomalous dissipation of turbulent kinetic energy occurs as an emergent feature of advection ("Onsager damping"), caused by the moderate shocks which terminate the turbulent kinetic energy spectrum; see also (Perry 2021). In strongly stratified stellar convection the asymptotic limit for the global damping length of turbulent kinetic energy is $\ell_d \sim \langle u^3 \rangle /\langle ε\rangle$. This "dissipative anomaly" (Onsager 1949) fixes the value of the "mixing length parameter", $α= \ell_{\rm MLT}/H_P =\overline{\langleΓ_1\rangle}$, which is $\sim\, 5/3$ for complete ionization. The estimate is numerically robust, agrees to within 10% with estimates from stellar evolution with constant $α$. For weak stratification $\ell_d$ shrinks to the depth of a thin convective region. Our flows are filamentary, produce surfaces of separation at boundary layers, resolve the energy-containing eddies, and develop a turbulent cascade down to the grid scale which agrees with the $4096^3$ direct numerical simulation of Kaneda (2003). The cascade converges quickly, and satisfies a power-law velocity spectrum similar to Kolmogorov (1941). Our flows exhibit intermittency, anisotropy, and interactions between coherent structures, features missing from K41 theory. We derive a dissipation rate from Reynolds stresses which agrees with (i) our flows, (ii) experiment (Warhaft 2002), and (iii) high Re simulations of the Navier-Stokes equations (Iyer, et al. 2018).

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arXiv2018

Turbulent Mixing and Nuclear Burning in Stellar Interiors

The turbulent burning of nuclei is a common phenomenon in the evolution of stars. Here we examine a challenging case: the merging of the neon and oxygen burning shells in a 23 M$_{\odot}$ star. A previously unknown quasi-steady state is established by the interplay between mixing, turbulent transport, and nuclear burning. The resulting stellar structure has two burning shells within a single convection zone. We find that the new neon burning layer covers an extended region of the convection zone, with the burning peak occurring substantially below where the Damköhler number first becomes equal to unity. These characteristics differ from those predicted by 1D stellar evolution models of similar ingestion events. We develop the mean-field turbulence equations that govern compositional evolution, and use them to interpret our data set. An important byproduct is a means to quantify sub-grid-scale effects intrinsic to the numerical hydrodynamic scheme. For implicit large eddy simulations, the analysis method is particularly powerful because it can reveal where and how simulated flows are modified by resolution, and provide straightforward physical interpretations of the effects of dissipation or induced transport. Focusing on the mean-field composition variance equations for our analysis, we recover a Kolmogorov rate of turbulent dissipation without it being imposed, in agreement with previous results which used the turbulent kinetic energy equation.

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arXiv2015

Beyond Mixing-length Theory: a step toward 321D

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier-Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier-Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping. The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear {\it beyond} the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different Péclet numbers). The algorithms are based upon ILES solutions to the Navier-Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.

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arXiv2014

Compressible Hydrodynamic Mean-Field Equations in Spherical Geometry and their Application to Turbulent Stellar Convection Data

We present a statistical analysis of turbulent convection in stars within our Reynolds-Averaged Navier Stokes (RANS) framework in spherical geometry which we derived from first principles. The primary results reported in this document include: (1) an extensive set of mean-field equations for compressible, multi-species hydrodynamics, and (2) corresponding mean-field data computed from various simulation models. Some supplementary scale analysis data is also presented. The simulation data which is presented includes: (1) shell convection during oxygen burning in a 23 solar mass supernova progenitor, (2) envelope convection in a 5 solar mass red giant, (3) shell convection during the helium flash, and (4) a hydrogen injection flash in a 1.25 solar mass star. These simulations have been partially described previously in Meakin [2006], Meakin and Arnett [2007a,b, 2010], Arnett et al. [2009, 2010], Viallet et al. [2011, 2013a,b] and Mocak et al. [2009, 2011]. New data is also included in this document with several new domain and resolution configurations as well as some variations in the physical model such as convection zone depth and driving source term. The long term goal of this work is to aid in the development of more sophisticated models for treating hydrodynamic phenomena (e.g., turbulent convection) in the field of stellar evolution by providing a direct link between 3D simulation data and the mean fields which are modeled by 1D stellar evolution codes. As such, this data can be used to test previously proposed turbulence models found in the literature and sometimes used in stellar modeling. This data can also serve to test basic physical principles for model building and inspire new prescriptions for use in 1D evolution codes.

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