Modelling convective turbulence with a double-averaging procedure

Abstract

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, where a field quantity is decomposed into three parts: the spatiotemporal mean (spatial average of the time average), the dispersion fluctuation (deviation from the spatiotemporal mean), and the chaotic (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 or coherent correlation part and the chaotic or incoherent correlation part. Evolution equations of these two parts of correlations show what is responsible for the interaction between the coherent and incoherent fluctuations. By reckoning the plumes as the coherent fluctuations, a transport model for the convective turbulence is constructed.