  Non-equilibrium property of turbulence modifies characteristics of turbulent
transport. With the aid of response-function formalism, such non-equilibrium
effects in turbulent transport can be represented by the temporal variation of
the turbulent energy ($K$) and its dissipation rate ($\varepsilon$) along the
mean stream through the advective derivatives of $K$ and $\varepsilon$.
Applications of this effect to the turbulent convection with plumes are
considered for the first time in this work. The non-equilibrium transport
effects associated with plumes are addressed in two aspects. Firstly, the
effect associated with a single plume is evaluated using data measured in the
recent plume/jet experiments. The second argument is developed for the
collective turbulent transport associated with multiple plumes mimicking the
stellar convection zone. In this second case, for the purpose of capturing the
plume motions into the advective derivatives, use has to be made of the
time--space double averaging procedure, where the turbulent fluctuations are
divided into the coherent or dispersion component (which represents plume
motions) and incoherent or random component. With the aid of the transport
equations of the coherent velocity stress and the incoherent counterpart, the
interaction between the dispersion and random fluctuations are also discussed
in the context of convective turbulent flows with plumes. It is shown from
these analyses that the non-equilibrium effect associated with plume motions is
of a great deal of relevance in the convective turbulence modelling.
