Introduction

In this chapter, we discuss the breakdown of hydrodynamic instability, a theory that is initially characterized by a system of linear equations, as discussed in great detail in Chapters 2–8. Breakdown thus implies that the linear assumption is becoming invalid and the flow now has several modes interacting and amplifying. This interaction can then transfer energy to modes not yet dominant in the flow. The culmination of this breakdown process is a turbulent flow. One might suppose that the characteristics of the breakdown stage depends on the initial conditions – as receptivity – as well as freestream conditions such as vorticity and freestream turbulence. Today, we understand much about this initial stage and the linear amplification stage but have only limited knowledge for the nonlinear processes of many flows (cf. Chapter 9) because the complete Navier-Stokes equations must be solved and tracing measurements in this stage back to their origin to ascertain the cause and effect is challenging.

The major goal of this text has been to present the subject of hydrodynamic instability processes for many different engineering problems. The initial chapters demonstrated that this understanding can most often be achieved with linear systems. However, as was somewhat evident in Chapters 8 and 9, the transition from a laminar to turbulent flow is extremely complicated. This Chapter and the next will expose the reader to issues effecting hydrodynamic instabilities, the nonlinear breakdown of modes after linear growth, and we will summarize a condensed history of methods that have been used to predict loss of laminar flow and onset of transition to turbulence.