Simulations of Global Solar Convection with a Fully Compressible CHORUS++ Code

Abstract

Fluid-dynamics simulations of global solar convection are a critically important tool for assessing the dynamics of the solar interior. However, simulation studies with a fully compressible hydrodynamics code are not yet common. The CHORUS++ code solves robustly and efficiently the fully compressible hydrodynamics equations using a compact local spectral method and semi-unstructured grid system. Using the CHORUS++ code, we simulate the solar interior plasma flows from 0.7 to 0.99 of the solar radius using the values of the solar total luminosity and the sidereal rotation rate. In this paper, we analyze the simulated global flow structures before the statistically stable state to assess the compressibility of the plasma flows obtained with the fully compressible hydrodynamic code. The divergence of mass flux with the compressible model is overall small in the examined state before reaching the equilibrium state of the convection, which implies that the differences between the fully compressible flows and those obtained with the anelastic, incompressible, or linear-equation models are small in the simulated inner part of the convection zone. Although a fully-relaxed stationary convection has not been achieved yet in the examined state, the model qualitatively reproduces the solar-type differential rotation. Simulations for longer periods are needed to achieve the system relaxation state. This work, assessing the early phase of the hydrodynamic evolution of solar convection, is our first step toward a better understanding of the nature of solar convection and the dynamo processes.

Figures (11)

• Figure 2: Radial profile of the simulated plasma quantities in the solar convective shell at $t=1\cdot 10^{7} s$: (a) mass density $\varrho$ and (c) temperature ($T$). In panels (b) and (d), the deviations of the simulated variable from the initial values, $\varrho_0$ and $T_0$, are given as $(\varrho/\varrho_0-1)$ and $(T/T_0-1)$, respectively. The deviations from the initial radial profile are less than $3\cdot 10^{-5}$ at $r < 0.9R_\odot$ and about $2\cdot10^{-3}$ near the top boundary. The contrast of the plasma density is tiny as $|\varrho/\left<\varrho\right>-1| < 3\cdot 10^{-4}$, where $\left<\varrho\right>$ is the averaged density over the spherical layer. Panels (e) and (f) show the relative deviation of the mass density and temperature from the averages, $(\varrho-\left<\varrho\right>)/\left<\varrho\right>$ and $(T_p -\left<T_p \right>)/\left<T_p \right>$, respectively, with four lines representing the maximum, +1 standard deviation, -1 standard deviation, and the minimum values at each radius. In the bottom row, the radial profile of the square of buoyancy frequency ($N^2$) of the initial value and the buoyancy frequency averaged horizontally (latitudinally and longitudinally) are given in panels (e) and (f), respectively. In these two plots, cross (+) marks are placed where $N^2 > 0$.
• Figure 3: The simulated radial component of the plasma flow ($V_r$) at $t=10^{7} s$. An octant section has been removed to display the meridional and equatorial cross-sections. The red (blue) colors represent the positive (negative) values.
• Figure 4: Temporal profile of the average kinetic energy density. The vertical dashed line indicates the moment ($t \simeq \cdot 10^7$ s for which most figures in this article are made using the simulation data.
• Figure 5: The plasma quantities of the simulated solar convection zone at $t=10^{7}$ s in the Mollweide projection mapping. (a) The plasma temperature subtracted by the average ($7.4132\cdot 10^4$ K). (b), (c), and (e) The radial, latitudinal, and longitudinal components of the plasma flow ($V_r$, $V_\theta$, and $V_\phi$), at $r=0.982\,R_\odot$. Panels (b), (d) and (f) in the right column compare the radial component at three depths, near the top boundary, at the middle depth of the simulated convection zone (at $r=0.846\,R_\odot$), and near the bottom boundary surface (at $r=0.709\,R_\odot$). The colors are truncated at the largest absolute value so that the red (for positive values) and blue (for negative values) are assigned evenly across the zero values.
• Figure 6: (a) The radial component of the curl of plasma velocity (or the curl of the horizontal flows). (b) --- (d) The $x$, $y$, and $z$ components of the simulated plasma flows around the north pole.