  Plumes in a convective flow are considered to be relevant to the turbulent
transport in convection. The effective mass, momentum, and heat transports in
the convective turbulence are investigated in the framework of time--space
double averaging procedure, where a field quantity is decomposed into three
parts: the spatiotemporal mean (spatial average of the time-averaged) field,
the dispersion or coherent fluctuation, and the random or incoherent
fluctuation. With this framework, turbulent correlations in the mean-field
equations are divided into the dispersion/coherent and random/incoherent
correlation part. By reckoning the plume as the coherent fluctuation, a
transport model for the convective turbulence is constructed with the aid of
the non-equilibrium effect, in which the change of turbulence characteristics
along the mean stream is taken into account for the modelling of the turbulent
transport coefficients. In this work, for the first time, change of turbulence
properties along plume motions is incorporated into the expression of the
turbulent transport coefficients. This non-equilibrium model is applied to a
stellar convective flow. One of the prominent characteristics of a surface
cooling-driven convection, the enhanced and localised turbulent mass flux below
the surface layer, which cannot be reproduced at all by the usual
eddy-diffusivity model with mixing length theory (MLT), is well reproduced by
the present model. Our results show that the incorporation of plume motion into
turbulent transport model is an important and very relevant extension of
mean-field theory beyond the heuristic gradient transport model with MLT.
