[Paper Review] A simulation of solar convection at supergranulation scale

M. Rieutord, H.‐G. Ludwig+3 more|arXiv (Cornell University)|Oct 9, 2001

Solar and Space Plasma Dynamics7 citations

TL;DR

This study presents a high-resolution 3D simulation of solar convection covering 30×30×3.2 Mm³ with 315×315×82 grid points to investigate supergranulation-scale dynamics. Despite capturing granular features and acoustic modes, no supergranulation-like structures emerge, suggesting that higher Reynolds numbers, magnetic fields, or greater depth may be necessary for their formation, while the simulation successfully reproduces granular vorticity rings and p-mode ridges in the k–ω diagram.

ABSTRACT

We present here numerical simulations of surface solar convection which cover a box of 30$ imes30 imes$3.2 Mm$^3$ with a resolution of 315$ imes315 imes$82, which is used to investigate the dynamics of scales larger than granulation. No structure resembling supergranulation is present; possibly higher Reynolds numbers (i.e. higher numerical resolution), or magnetic fields, or greater depth are necessary. The results also show interesting aspects of granular dynamics which are briefly presented, like extensive p-mode ridges in the k-$ω$ diagram and a ringlike distribution of horizontal vorticity around granules. At large scales, the horizontal velocity is much larger than the vertical velocity and the vertical motion is dominated by p-mode oscillations.

Motivation & Objective

• To investigate the formation mechanisms of supergranulation-scale convective structures in the solar photosphere.
• To assess whether supergranulation arises from deep thermal instability or surface-scale dynamics of granules.
• To evaluate the role of turbulent viscosity and nonlinear interactions in large-scale instability.
• To test the realism of granular dynamics, including vorticity structures and acoustic mode excitation.
• To determine whether current numerical resolution and domain depth are sufficient to produce supergranulation.

Proposed method

• Numerical simulation using a compressible radiation-hydrodynamics code with artificial hyperviscosity to stabilize the scheme.
• Solves hydrodynamic equations (mass, momentum, energy) and radiative transfer using a modified Feautrier method along ~500,000 rays for non-local radiation.
• Employs grey opacities and an equation of state including ionization of H, He, and H₂ formation.
• Uses periodic lateral boundaries and a free-flow lower boundary with mass flux relaxation and prescribed inflow entropy.
• Simulates a domain of 30×30×3.2 Mm³ with 315×315×82 grid points, focusing on the τ=1 level for analysis.
• Analyzes velocity spectra, k–ω diagrams, and vorticity distributions to study large-scale and granular dynamics.

Experimental results

Research questions

• RQ1 Does the absence of supergranulation in the simulation indicate insufficient numerical resolution or depth?
• RQ2 Can large-scale instabilities emerge from nonlinear interactions among granules due to turbulent viscosity?
• RQ3 What role do p-mode oscillations play in vertical velocity dominance at the solar surface?
• RQ4 How do vortex rings form around granules, and do they contribute to large-scale dynamics?
• RQ5 To what extent do the simulated granular features match observational persistence and morphology?

Key findings

• No supergranulation-like structures formed, suggesting that the simulation’s shallow depth, lack of magnetic fields, or insufficient Reynolds number may prevent their emergence.
• Horizontal velocities dominate over vertical velocities, with the largest horizontal motions occurring at scales roughly twice those dominating vertical motions.
• The velocity power spectrum shows a distinct break at 5 Mm, indicating a possible transition in dynamical regime that requires further investigation.
• The k–ω diagram reveals extensive p-mode ridges excited by convection, indicating strong acoustic mode excitation in the simulated domain.
• Granules are surrounded by ringlike distributions of horizontal vorticity, consistent with the vortex ring model of granular dynamics.
• Some granular features persist for up to 90 minutes in the simulation, matching observational timescales and validating the realism of granular evolution.