Analysis and Modeling of Non-local Eddy Diffusivity in Turbulent Flows


Friday, 24 May, 2024 - 14:30 to 15:30

Speaker : Fujihiro Hamba, Institute of Industrial Science, The University of Tokyo

Time : 14:30 - 15.30 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

YouTube :

Organizers : Pavan Pranjivan Mehta* ( and Arran Fernandez** (

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Turbulence model, Non-local eddy diffusivity

Abstract: Local eddy viscosity and diffusivity models are widely used to understand and predict the mean velocity and mean scalar quantities in turbulent flows. In the eddy diffusivity model, the turbulent scalar flux at a point is assumed to be proportional to the mean scalar gradient at the same point. However, this local approximation is not always valid for real turbulent flow because the length scale of turbulence is often as large as that of the mean-field variation. In this talk, we present a non-local approach in which the scalar flux is expressed as spatial and time integrals of the mean scalar gradient. We first introduce our previous work on the analysis of non-local eddy diffusivity and viscosity using the Green’s function [1-3]. Profiles of the non-local eddy diffusivity were evaluated and the non-local expressions were validated with a direct numerical simulation (DNS) of turbulent channel flow. In some cases, the local eddy diffusivity model overpredicted the scalar flux, and the non-local expression accurately estimated it. We then present recent attempts to model the non-local eddy diffusivity from the viewpoint of statistical theory of turbulence [4,5]. The behavior of the non-local eddy diffusivity was carefully examined through a DNS of homogeneous isotropic turbulence with an inhomogeneous mean scalar. A model expression was proposed using the mean Green’s function and the two-point velocity correlation. The idea of energy density in scale space [6] was also used to allow the model to be applied to inhomogeneous wall-bounded flows.

Biography: Fujihiro Hamba is a full professor in fluid physics at the Institute of Industrial Science, the University of Tokyo in Japan. He studied physics and received his PhD degree from the Graduate School of Science, the University of Tokyo in 1990. His research interests are in physics and modeling of inhomogeneous turbulence, including non-local transport of turbulence, Reynolds-averaged Navier-Stokes model and large eddy simulation, and dynamo effects in magnetohydrodynamic turbulence.


[1] F. Hamba. "An analysis of nonlocal scalar transport in the convective boundary layer using the Green's function". In: Journal of the Atmospheric Sciences 52 (1995), pp. 1084-1095.;2

[2] F. Hamba. "Nonlocal expression for scalar flux in turbulent shear flow". In: Physics of Fluids 16 (2004), pp. 1493-1508

[3] F. Hamba. "Nonlocal analysis of the Reynolds stress in turbulent shear flow". In: Physics of Fluids 17 (2005), 115102

[4] F. Hamba. "Analysis and modelling of non-local eddy diffusivity for turbulent scalar flux". In: Journal of Fluid Mechanics 950 (2022), A38

[5] F. Hamba. "Non-local eddy diffusivity model based on turbulent energy density in scale space". In: Journal of Fluid Mechanics 977 (2023), A11

[6] F. Hamba. "Scale-space energy density for inhomogeneous turbulence based on filtered velocities". In: Journal of Fluid Mechanics 931 (2022), A34