An Introduction to the Mechanics of Incompressible Fluids

This open access book brings the reader a pedestrian pace to grasp the main bulk of fluid flow problems. Starting with the basic concepts of conservation laws elaborated through continuum mechanics, the incompressibility of a fluid is explained and modeled leading to the famous Navier–Stokes equations that govern the dynamics of fluids. Even though the Navier–Stokes equations are difficult to handle by analytical methods, a few exact solutions are proposed for transient and steady-state cases in Cartesian and axisymmetric coordinates. Vorticity and vortex dynamics allow for the concept of irrotational flows that are the main topic of the chapter devoted to complex potential, conformal mapping and Joukowski transformation. A particular set of examples is connected to creeping flows or Stokes flows where the viscosity is the dominating physical phenomenon. Boundary layer theory examines the Prandtl's equations, discusses the solution for the flat plate case, the various thicknesses and the von Karman integral equation. Then instability of fluid flows is investigated for parallel flows through the Orr-Sommerfeld equation. The stability of the circular Couette flow is also considered. The book ends with the modeling of turbulence via the Reynolds averaged Navier-Stokes equations and large eddy simulations. Solutions of the exercices listed at the end of each chapter are also provided.