Viscosity and Prandtl Number of Warm Dense Water as in Ice Giant Planets

Abstract

The thermophysical properties in water-rich planets are important for understanding their radius, luminosity, and magnetic field. Here we calculate the shear viscosity, isobaric heat capacity, and Prandtl number of warm dense fluid water using ab initio simulations. More specifically, the density (0.2–6 g cm −3 )–temperature (1000–50,000 K) conditions considered here include states present in mini-Neptune to Neptune-sized planets. As a general result, we find that Pr ≳ 1 in their deep interiors if they are adiabatic, whereas Pr ≲ 1 if they are super-adiabatic. Our results lend some support to the suggestion of turbulent convection at Pr ≈ 1 to explain the peculiar magnetic fields of Uranus and Neptune. Finally, we argue that double-diffusive convection in these Ice Giants would require fine-tuning of the compositional-to-superadiabaticity ratio within a small factor of 2; instead we conclude that compositional gradients in Uranus and Neptune would be diffusive in nature and thus primordial heat could still be trapped inside.