This study presents a numerical procedure, which we call the macroscopic forcing method (MFM), which reveals the differential operators acting upon the mean fields of quantities transported by underlying fluctuating flows. Specifically, MFM can reveal differential operators associated with turbulent transport of scalars and momentum. We present this methodology by considering canonical problems with increasing complexity. For spatially homogeneous and statistically stationary systems, we observe that eddy diffusivity can be approximated by an operator of the form , where is the mixing length, which in turbulent flows is on the order of the large-eddy size and is the Boussinesq limit eddy diffusivity. We show a cost-effective generalization of MFM for analysis of non-homogeneous and wall-bounded flows, where eddy diffusivity is found to be a non-local and non-isotropic operator acting on the macroscopic gradient of transported quantities. Towards the end of this talk, application of MFM on a canonical separated flow will be presented where the tensorial eddy viscosity is quantified, and its anisotropy is shown to be the key missing piece in RANS predictions.
About the Speaker
Ali Mani is an associate professor of Mechanical Engineering at Stanford University. He is a faculty affiliate of the Center for Turbulence Research and a member of Institute for Computational and Mathematical Engineering at Stanford. He received his PhD in Mechanical Engineering from Stanford in 2009. Prior to joining the faculty in 2011, he was a senior postdoctoral associate at Massachusetts Institute of Technology in the Department of Chemical Engineering. His research group builds and utilizes large-scale high-fidelity numerical simulations, as well as methods of applied mathematics, to develop quantitative understanding of transport processes that involve strong coupling with fluid flow and commonly involve turbulence or chaos. His teaching includes the undergraduate engineering math classes and graduate courses on fluid mechanics and numerical analysis. He is the recipient of an Office of Naval Research Young Investigator Award (2015), NSF Career Award (2016), and Tau Beta Pi Teaching Honor Roll (2019).
Host: Leonardo Chamorro