Reynolds decomposition and Reynolds Averaged Navier-Stokes (RANS) [Fluid Mechanics #11]

In this video, we take a deep dive into the Reynolds Averaged Navier-Stokes equations (a.k.a. RANS). In practice, RANS is a valuable tool to have in your toolbelt when approaching real-world flow scenarios. To get these equations, we need to apply Reynolds Decomposition, separating a time-varying signal into the mean and fluctuating components, to the Conservation Equations and then average them. We will explore the complexities of Reynolds Decomposition and Averaging, specifically with non-linear terms, and the rules we can apply to averages of mean and fluctuating quantities. Then, we fully derive the RANS equations in their entirety, and show how we can use it to study turbulent flows in a way we couldn't when considering the traditional Navier-Stokes equations. An important feature that makes turbulence different from laminar flows are the Reynolds Stresses, which are analogous to viscous forcing on a macroscopic scale. Free downloadable notes (PDF with white background) can be found at my website: https://sites.udel.edu/vanburen/education/