Our goal is to improve the theoretical modelling of stochastic excitation of p modes by turbulent convection. With the help of the closure model with plume (CMP) developed in a companion paper, we refine the theoretical description of the excitation by the turbulent Reynolds stress term. The CMP is generalized for two-point correlation products so as to apply it to the formalism developed by Samadi & Goupil (2001). The excitation source terms are then computed with this improvement, and a comparison with solar data from the GOLF instrument is performed. The present model provides a significant improvement when comparing absolute values of theoretical ampplitudes with observational data. It gives rise to a frequency dependence of the power supplied to solar p modes, which agrees with GOLF observations. It is shown that the asymmetry of the turbulent convection zone (up- and downflows) plays a major role in the excitation processes. Despite an increase in the Reynolds stress term contribution due to our improved description, an additional source of excitation, identified as the entropy source term, is still necessary for reproducing the observational data. Theoretical excitation rates in the frequency range [2.5 mHz, 4 mHz] now are in agreement with the observational data from the GOLF instrument. However, at lower frequencies, it exhibits small discrepancies at the maximum level of a few per cent. Improvements are likely to come from a better physical description of the excitation by entropy fluctuations in the superadiabatic zone.
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