Oscillations of stellar p modes, excited by turbulent convection, are investigated. We take into account the asymmetry of the up and downflows created by turbulent plumes through an adapted closure model. In a companion paper, we apply it to the formalism of excitation of solar p modes developed by Samadi & Goupil 2001. Using results from 3D numerical simulations of the upper most part of the solar convection zone, we show that the two-scale-mass-flux model (TFM) is valid only for quasi-laminar or highly skewed flows (Gryanik & Hartmann 2002). We build a generalized-Two-scale-Mass-Flux Model (GTFM) model which takes into account both the skew introduced by the presence of two flows and the effects of turbulence in each flow. In order to apply the GTFM to the solar case, we introduce the plume dynamics as modelled by Rieutord & Zahn (1995) and construct a Closure Model with Plumes (CMP). When comparing with 3D simulation results, the CMP improves the agreement for the fourth order moments, by approximatively a factor of two compared with the use of the quasi-normal approximation or a skewness computed with the classical TFM. The asymmetry of turbulent convection in the solar case has an important impact on the vertical-velocity fourth-order moment which has to be accounted for by models. The CMP is a significant improvement and is expected to improve the modelling of solar p-mode excitation.
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