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Alfv\'enic fluctuations in the solar wind display many properties reflectingan ongoing nonlinear cascade, e.g. a well-defined spectrum in frequency,together with some characteristics more commonly associated with the linearpropagation of waves from the Sun, such as the variation of fluctuationamplitude with distance, dominated by solar wind expansion effects. Thereforeboth nonlinearities and expansion must be included simultaneously in anysuccessful model of solar wind turbulence evolution. Because of the disparatespatial scales involved, direct numerical simulations of turbulence in thesolar wind represent an arduous task, especially if one wants to go beyond theincompressible approximation. Indeed, most simulations neglect solar windexpansion effects entirely. Here we develop a numerical model to simulateturbulent fluctuations from the outer corona to 1 AU and beyond, including thesub-Alfv\'enic corona. The accelerating expanding box (AEB) extends thevalidity of previous expanding box models by taking into account both theacceleration of the solar wind and the inhomogeneity of background density andmagnetic field. Our method incorporates a background accelerating wind within amagnetic field that naturally follows the Parker spiral evolution using atwo-scale analysis in which the macroscopic spatial effect couplingfluctuations with background gradients becomes a time-dependent coupling termin a homogeneous box. In this paper we describe the AEB model in detail anddiscuss its main properties, illustrating its validity by studying Alfv\'enwave propagation across the Alfv\'en critical point.

Evolving waves and turbulence in the outer corona and inner heliosphere: the accelerating expanding box