ENME E6370: Turbulence Theory and Modeling

Course Overview

This course offers an in-depth exploration of turbulence, one of the most complex and practically significant phenomena in fluid dynamics. Through a rigorous blend of theoretical and applied content, you will gain a solid foundation in turbulence phenomenology and the statistical tools necessary to describe and analyze turbulent flows. 

The course begins with the governing equations of fluid motion and transitions into the statistical framework of turbulence, covering Reynolds decomposition, filtering techniques, and the energy dynamics of mean and fluctuating fields. A major focus is placed on the Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) frameworks, both essential for practical modeling of turbulence in engineering and environmental systems.

Throughout the course, you’ll develop analytical skills to interpret turbulence dynamics across a variety of canonical flows, including free shear flows and wall-bounded flows, while building an understanding of the spatial and temporal scales that define turbulent motion. They will examine spectral energy transfers, turbulence structure, and the closure problem—an enduring challenge in turbulence modeling. You’ll also learn how to assess turbulence models critically and understand the trade-offs between computational cost and physical fidelity in different modeling approaches, including Direct Numerical Simulation (DNS), LES, and RANS.

While the course is primarily theoretical, it is also designed to be highly relevant to real-world engineering problems. Turbulence modeling is essential for a wide array of applications, from designing more fuel-efficient aircraft and wind turbines to predicting pollutant dispersion in urban environments and the atmosphere. Completing this course will equip you to work with computational fluid dynamics (CFD) tools and interpret turbulence data for engineering decision-making. Depending on the instructor, you may also be introduced to industry-standard CFD software, gaining practical insights into simulation setup, model selection, and result interpretation.

By bridging fundamental turbulence theory with applied modeling frameworks, the course prepares you for both academic research and industry roles in aerospace, mechanical, civil, and environmental engineering. Understanding turbulence is critical not only for optimizing designs and reducing operational costs, but also for addressing broader societal needs such as climate prediction, urban sustainability, and renewable energy.

To undertake this course, you must have a solid understanding of fluid mechanics, ordinary differential equations and partial differential equations.

Course Instructor

Marco Giometto

Assistant Professor

Marco Giometto is an Assistant Professor in the Civil Engineering and Engineering Mechanics department at Columbia University and an Amazon Visiting Academic. He studies both fundamental and applied problems related to fluid dynamics and turbulence, with an emphasis on atmospheric boundary layer processes. He received his PhD in Mechanical Engineering from École Polytechnique Fédérale de Lausanne and held postdoctoral positions at the University of British Columbia and at the Center for Turbulence Research at Stanford University.