Swaying oscillations in Rayleigh-Bénard convection cast new light on solar convection

TL;DR

The study tackles the problem of understanding the wave-like properties and dominant scale of solar convection, particularly supergranulation, by simulating 2D horizontally periodic Rayleigh-Bénard convection in the Boussinesq limit. Using the ANTARES code, it explores very low Prandtl numbers and high Rayleigh numbers to mimic solar near-surface conditions, parameterized by $Ra^* = Ra\,Pr$. It finds that for $Pr \lesssim 0.1$ and $Ra > 10^6$, large-scale convective structures spontaneously synchronize and exhibit long-lived swaying oscillations, with a main frequency near $\nu_0 \approx 2.4\,\mu\mathrm{Hz}$—close to the solar value of about $1.8\,\mu\mathrm{Hz}$—and with a cell-size preference around $kR \approx 50$. While this 2D, stratification-free model provides a plausible mechanism for solar-like oscillations, the authors stress the limitations of dimensionality and the need for 3D, stratified, and rotating extensions, alongside observational tests from helioseismology, to establish solar relevance.

Abstract

Horizontally-periodic Boussinesq Rayleigh-Bénard Convection (RBC) is a simple model system to study the formation of large-scale structures in turbulent convective flows. We performed a suite of 2D numerical simulations of RBC between no-slip boundaries at different Prandtl (Pr) and Rayleigh (Ra) numbers, such that their product is representative of the Sun's upper convection zone. When the fluid viscosity is sufficiently low (Pr $\lesssim 0.1$) and turbulence is strong (Ra $> 10^6$) we find that large structures begin to couple in time and space. For Pr = 0.01 we observe long-lived swaying oscillations of the upflows and downflows, which synchronize over multiple convection cells. This new regime of oscillatory convection may offer an interpretation for the wave-like properties of the dominant scale of convection on the Sun (supergranulation).

Figures (3)

• Figure 1: Evolution of the temperature field for the simulation with $\mathrm{Pr}=0.01$ (last row in Table 1). The snapshots shown here are separated by 18 simulation time steps (time increases downward). The full sequence covers a little more than two convective turnover times and shows a full period of the "swaying oscillations" of the hot and cold plumes. These oscillations are most easily seen in the movies on temperature (T-Pr001.mp4), horizontal velocity (u_x-Pr001.mp4), and vertical velocity (u_z-Pr001.mp4) included as supplemental material and which are available https://doi.org/10.17617/3.BHN9A4. In all three movies the corresponding quantity is shown in dimensionless units: temperature is scaled relative to the difference between bottom and top, velocities relative to the ratio between box size and diffusion time scale.
• Figure 2: Power spectra of the horizontal velocity at selected values of the horizontal wavenumber for $\mathrm{Pr}=1$ (top) and $\mathrm{Pr}=0.01$ (bottom) at fixed height $z_0=0.7H$. The insets show the symmetrized power averaged over $150 \le kR \le 250$ for $\mathrm{Pr}=1$, and averaged over $50 \le kR \le 150$ for $\mathrm{Pr}=0.01$. The arrows in the inset of the bottom panel point to the characteristic frequency $\nu_0=2.4\ \mu$Hz and to the first overtone at $2\nu_0$. Power is normalized with respect to maximum power (away from the central peak).
• Figure 3: Two-dimensional power spectrum $P(k,\nu)$ of the horizontal velocity at height $z_0=0.7 H$, for the simulation with $\mathrm{Pr}=0.01$ (gray shades). To reduce random noise, the data were binned down to the spectral resolutions $\Delta k = 50/R$ and $\Delta \nu = 0.2\ \mu$Hz. The gray scale is saturated to highlight the peaks near $\pm \nu_0$. For reference, the red curves correspond to the dispersion relation observed on the Sun Langfellner18a, together with the full widths at half maximum of the peaks of power (red shades).