An Introduction to Flight

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

Welcome back. In this post, we will continue our discussion of hydrodynamic stability by exploring the linearized Navier-Stokes equations in three dimensions. These equations are important because they describe how tiny disturbances grow in a fluid flow and ultimately lead to turbulence. They are also the basis for more specialized stability equations applied in aerospace … [Read more...] about Hydrodynamic Stability: General Form of the Linearized Disturbance Equations

Background  Welcome back. Today’s post will be the first part of a multi-part series about hydrodynamic stability, which is the study of how fluid flows transition from laminar states to turbulent states. Although “hydro” is in its name, this topic covers all types of fluids, such as water, air, honey, and liquid nitrogen. Predicting when a fluid will become unstable is … [Read more...] about Hydrodynamic Stability: Background and Basic Definitions