Eigenvectors, Circulation, and Linear Instabilities for Planetary Science in 3 Dimensions (ECLIPS3D)

¹ Ecole Normale Supérieure de Lyon, CRAL, UMR CNRS 5574, 69364 Lyon Cedex 07, France
e-mail: florian_debras@hotmail.com
² School of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, UK
³ IRAP, Université de Toulouse, CNRS, UPS, Toulouse, France
⁴ College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK

Received: 29 March 2019
Accepted: 3 September 2019

Abstract

Context. The study of linear waves and instabilities is necessary to understand the physical evolution of an atmosphere, and can provide physical interpretation of the complex flows found in simulations performed using global circulation models (GCMs). In particular, the acceleration of superrotating flow at the equator of hot Jupiters has mostly been studied under several simplifying assumptions, the relaxing of which may impact final results.

Aims. We develop and benchmark a publicly available algorithm to identify the eigenmodes of an atmosphere around any initial steady state. We also solve for linear steady states indicated to be essential in existing theories of the acceleration of hot Jupiter superrotation.

Methods. We linearise the hydrodynamical equations of a planetary atmosphere in a steady state with arbitrary velocities and thermal profile. We then discretise the linearised equations on an appropriate staggered grid, and solve for eigenvectors and linear steady solutions with the use of a parallel library for linear algebra: ScaLAPACK. We also implement a posteriori calculation of an energy equation in order to obtain more information on the underlying physics of the mode.

Results. Our code is tested using classical wave and instability test cases in multiple geometries (2D, 3D, two-layer equivalent depth). The steady linear circulation calculations also reproduce expected results for the atmosphere of hot Jupiters. We finally show the robustness of our energy equation, and its power to obtain physical insight into the modes.

Conclusions. We developed and tested a code for the study of linear processes in planetary atmospheres with an arbitrary steady state. The calculation of an a posteriori energy equation provides both increased robustness and physical meaning to the obtained eigenmodes. This code can be applied to various problems, and notably used to further study the initial spin up of superrotation of GCM simulations of hot Jupiters.