2018/10/10 by W. David Arnett, Arnett, W. David, Raphaël Hirschi +17
Earth and Planetary Sciences · Engineering · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Solar and Stellar Astrophysics (astro-ph.SR)
paper · pdf · doi:10.48550/arxiv.1810.04659
openalex publication_date 2018/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We simulate stellar convection at high Reynolds number (Re\lesssim7000) 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 ℓd ∼ ⟨ u3 ⟩ /⟨ ε⟩. This "dissipative anomaly" (Onsager 1949) fixes the value of the "mixing length parameter", α= ℓ\rm MLT/HP =⟨Γ1⟩, which is ∼ 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 ℓd 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 40963 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).