http://arxiv.org/abs/2111.08921
Plumes in a convective flow, whose flow structure is localised in space and time, 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 (deviation from the spatiotemporal mean), and the random or incoherent fluctuation. With this double-averaging framework, turbulent correlations such as the Reynolds stress, turbulent mass flux, turbulent internal-energy flux, etc., in the mean-field equations are divided into the dispersion/coherent correlation part and the random/incoherent correlation part. The evolution equations of these two parts of the correlation show what are responsible for the conversion of the fluctuation energy between the coherent and incoherent components. 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 along plume motions, and 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 with the non-equilibrium effect. Our results show that the incorporation of plume motion into turbulent transport model through the non-equilibrium effect is an important and very relevant extension of mean-field theory beyond the heuristic gradient transport model with MLT.
N. Yokoi, Y. Masada and T. Takiwaki
Thu, 18 Nov 21
17/92
Comments: 18 pages, 8 figures