Context. Atmospheric superrotating flows at the equator are an almost ubiquitous result of simulations of hot Jupiters, and a theory explaining how this zonally coherent flow reaches an equilibrium has been developed in the literature. However, this understanding relies on the existence of either an initial superrotating or a sheared flow, coupled with a slow evolution such that a linear steady state can be reached. Aims. A consistent physical understanding of superrotation is needed for arbitrary drag and radiative timescales, and the relevance of considering linear steady states needs to be assessed. Methods. We obtain an analytical expression for the structure, frequency and decay rate of propagating waves in hot Jupiter atmospheres around a state at rest in the 2D shallow water beta plane limit. We solve this expression numerically and confirm the robustness of our results with a 3D linear wave algorithm. We then compare with 3D simulations of hot Jupiter atmospheres and study the non linear momentum fluxes. Results. We show that under strong day night heating the dynamics does not transit through a linear steady state when starting from an initial atmosphere in solid body rotation. We further show that non linear effects favour the initial spin up of superrotation and that the acceleration due to the vertical component of the eddy momentum flux is critical to the initial development of superrotation. Conclusions. Overall, we describe the initial phases of the acceleration of superrotation, including consideration of differing radiative and drag timescales, and conclude that eddy-momentum driven superrotating equatorial jets are robust, physical phenomena in simulations of hot Jupiter atmospheres.
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