Numerical Study and Lagrangian Modelling of Turbulent Heat Transport

A stochastic Lagrangian model for both fluid velocities and temperature fluctuations is evaluated from Direct Numerical Simulation of heat transport in homogeneous isotropic turbulence submitted to a linear mean temperature gradient. The first stage lies on the study of the Lagrangian fluid turbulence statistics (Lagrangian correlations functions) computed from predictions of DNS. They are crucial for the analysis and the modelling of the fluid turbulent properties along discrete particle trajectories. In the second stage, a velocity-scalar Lagrangian stochastic model is proposed and evaluated from the DNS data. The coefficients of the drift and diffusion terms of the model are determined by only Lagrangian timescales, temperature variance and turbulent flux. The shapes of correlation functions present a good agreement between DNS results and stochastic modelling approach.