An Introduction to Flight

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

Welcome back. In today’s post, I am excited to discuss the Reynolds number, which is one of the most important dimensionless quantities in all of fluid mechanics. By definition, the Reynolds number, denoted Re, is the ratio of inertial forces to viscous forces in a fluid, but its significance extends beyond this definition. It is a fundamental quantity that indicates how messy … [Read more...] about The Reynolds Number and its Dynamical Significance in Fluid Flows

Welcome back. I hope that all of my readers had a restful weekend, and are having a smooth return to classes. In today’s blog post, I look forward to sharing some of the fundamental concepts of thermodynamics. If we were to define thermodynamics, we could say that it is the study of energy and the ways in which energy can be transferred. Therefore, we will begin our discussion … [Read more...] about A Crash Course in Thermodynamics (With Some Fluid Mechanics)

Welcome back. I hope that all of my readers had a restful winter break and are having a fabulous start to their new semester. In this first blog post of 2024, I am excited to share some brief remarks on the rich and growing field of nonlinear dynamics and chaos. Fundamentally, this field is centered around studying nonlinear systems of ordinary differential equations (ODEs) … [Read more...] about Some Brief Words on Nonlinear Dynamical Systems and Chaos