An Introduction to Flight

Welcome back. In this blog, I was hoping to take a short break from hydrodynamic stability, and share an old essay I have written about computing finite-time Lyapunov exponent (FTLE) fields to analyze Lagrangian coherent structures (LCSs):  My project was to develop numerical integration code that could compute particle trajectories in unsteady flows. While previous … [Read more...] about Computing Finite-Time Lyapunov Exponent Fields around Airfoils

Welcome back. In today’s blog post, we will continue our discussion of hydrodynamic stability by discussing resolvent analysis, which is complementary to classical linear stability analysis. While linear stability analysis looks at the growth of small perturbations to an unforced base flow, resolvent analysis finds maximum gain input-output structures in a flow field that … [Read more...] about Hydrodynamic Stability: Resolvent Analysis

Welcome back. Last week, we derived the Orr-Sommerfeld equation, which governs the evolution of small disturbances in 2D parallel shear flows. This equation was cast as an eigenvalue problem, L𝜑 = c𝜑, that determined stream function amplitudes, 𝜑, and their associated complex wave speeds, c, that characterized the behavior of small perturbations. The governing Orr-Sommerfeld … [Read more...] about Hydrodynamic Stability: Non-Normality and Transient Energy Growth

Welcome back. In this post, we will discuss the celebrated Orr-Sommerfeld equation, which is an eigenvalue problem governing the 2D stability of viscous parallel shear flows. Although this equation might initially seem narrow in scope since it only accounts for two spatial dimensions, it can actually be applied to a substantial range of 3D flows. This works because of Squire’s … [Read more...] about Hydrodynamic Stability: The Orr-Sommerfeld Equation

Welcome back. In today’s post, I hope to take a small break from our discussion last week, and present an introduction I wrote to a project on the Orr-Sommerfeld equation. This work examined the effects of non-normality in plane Poiseuille flow, a canonical shear flow between two flat plates, and the overall motivation was to show the limitations of traditional eigenvalue … [Read more...] about An Introduction to a Project on the Orr-Sommerfeld Equation