Remarks on compressible convection in Super-Earths
arXiv:2303.15153 · doi:10.1016/j.pepi.2023.107062
Abstract
The radial density of planets increases with depth due to compressibility, leading to impacts on their convective dynamics. To account for these effects, including the presence of a quasi-adiabatic temperature profile and entropy sources due to dissipation, the compressibility is expressed through a dissipation number, , proportional to the planet's radius and gravity. In Earth's mantle, compressibility effects are moderate, but in large rocky or liquid exoplanets (Super-Earths), the dissipation number can become very large. This paper explores the properties of compressible convection when the dissipation number is significant. We start by selecting a simple Murnaghan equation of state that embodies the fundamental properties of condensed matter at planetary conditions. Next, we analyze the characteristics of adiabatic profiles and demonstrate that the ratio between the bottom and top adiabatic temperatures is relatively small and probably less than 2. We examine the marginal stability of compressible mantles and reveal that they can undergo convection with either positive or negative superadiabatic Rayleigh numbers. Lastly, we delve into simulations of convection performed using the exact equations of mechanics, neglecting inertia (infinite Prandtl number case), and examine their consequences for Super-Earths dynamics.
arXiv comment31 pages, 15 figures
References in corpus (7)
- Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
- Thermal convection for large Prandtl numbers
- Iron under Earth's core conditions: Liquid-state thermodynamics and high-pressure melting curve
- Reflections on dissipation associated with thermal convection
- Rayleigh-Benard stability and the validity of quasi-Boussinesq or quasi-anelastic liquid approximations
- Convection in an ideal gas at high Rayleigh numbers
- A playground for compressible natural convection with a nearly uniform density