Numerical convergence of hot-Jupiter atmospheric flow solutions

Abstract

ABSTRACT We perform an extensive study of numerical convergence for hot-Jupiter atmospheric flow solutions in simulations employing a setup commonly used in extrasolar planet studies – a resting state thermally forced to a prescribed temperature distribution on a short time-scale at high altitudes. Convergence is assessed rigorously with (i) a highly accurate pseudospectral model that has been explicitly verified to perform well under hot-Jupiter flow conditions and (ii) comparisons of the kinetic energy spectra, instantaneous (unaveraged) vorticity fields and temporal evolutions of the vorticity field from simulations that are numerically equatable. In the simulations, the (horizontal as well as vertical) resolution, dissipation operator order, and viscosity coefficient are varied with identical physical and initial setups. All of the simulations are compared against a fiducial reference simulation at high horizontal resolution and dissipation order (T682 and ∇ 16, respectively) – as well as against each other. Broadly, the reference solution features a dynamic, zonally (east–west) asymmetric jet with a copious amount of small-scale vortices and gravity waves. Here, we show that simulations converge to the reference simulation only at T341 resolution and with ∇ 16 dissipation order. Below this resolution and order, simulations either do not converge or converge to unphysical solutions. The general convergence behaviour is independent of the vertical range of the atmosphere modelled, from $\sim 2 \times 10^{-3}$MPa to   $\sim 2 \times 10^1$ MPa. Ramifications for current extrasolar planet atmosphere modelling and observations are discussed.