Analysis and modelling of non-local eddy diffusivity for turbulent scalar flux

Abstract

The local eddy diffusivity model for the turbulent scalar flux is widely used to understand and predict scalar transport in turbulence. However, local approximation in space and time is not always valid for actual turbulent flow. An exact non-local expression for the scalar flux was previously derived by the author using Green's function. Even though the profile of the non-local eddy diffusivity in a turbulent channel flow was evaluated, its model expression was only discussed phenomenologically. In this study, the non-local eddy diffusivity approach was validated with help of direct numerical simulation (DNS) data of homogeneous isotropic turbulence with an inhomogeneous mean scalar to propose a systematic model expression. Initially, it was verified that the non-local expression for the scalar flux agrees with the value directly obtained from the DNS. In addition, the non-local effect accounts for the overestimation of the scalar flux by the local model and the counter-gradient diffusion phenomenon. The temporal behaviour of the non-local eddy diffusivity was further evaluated using the DNS data. Its model expression being proportional to the two-point velocity correlation was proposed in a manner customary in the statistical theory of turbulence. The profile of the non-local eddy diffusivity obtained from the model expression agrees well with the DNS value, and the non-local model reproduced the scalar flux. These results substantiate the potential of the non-local eddy diffusivity model.