Turbulence in a three-dimensional deflagration model for Type Ia supernovae: I. Scaling properties

TL;DR

This study investigates the turbulent velocity field in a 3D deflagration model of Type Ia supernovae, confirming isotropy at small scales and the need for subgrid-scale models for accurate flame speed calculations.

Contribution

It provides detailed analysis of turbulence scaling properties in supernova models, validating the use of isotropic assumptions and subgrid models at unresolved scales.

Findings

Turbulence is isotropic at small scales

Scaling follows Kolmogorov theory until fuel is burned

Anisotropy appears at larger scales due to Rayleigh-Taylor instability

Abstract

We analyze the statistical properties of the turbulent velocity field in the deflagration model for Type Ia supernovae. In particular, we consider the question of whether turbulence is isotropic and consistent with the Kolmogorov theory at small length scales. Using numerical data from a high-resolution simulation of a thermonuclear supernova explosion, spectra of the turbulence energy and velocity structure functions are computed. We show that the turbulent velocity field is isotropic at small length scales and follows a scaling law that is consistent with the Kolmogorov theory until most of the nuclear fuel is burned. At length scales greater than a certain characteristic scale, turbulence becomes anisotropic. Here, the radial velocity fluctuations follow the scaling law of the Rayleigh-Taylor instability, whereas the angular component still obeys Kolmogorov scaling. In the late phase of the explosion, this characteristic scale drops below the numerical resolution of the simulation. The analysis confirms that a subgrid-scale model for the unresolved turbulence energy is required for the consistent calculation of the flame speed in deflagration models of Type Ia supernovae, and that the assumption of isotropy on these scales is appropriate.