Fluid mechanics is one of the fields that is contributing significantly to the current resurgence of interest in variational methods. Historically, calculus of variations has not been taught or utilized as a core mathematical tool in the arsenal of the fluid mechanics practitioner; it is a rare fluid mechanics textbook that even mentions variational calculus. However, recent research developments are revolutionizing the field by reframing certain fluid mechanics phenomena within a variational framework. This is particularly the case in the areas of flow control and hydrodynamic stability.

Traditionally, flow control has been implemented in an ad hoc manner involving a significant amount of trial and error within an empirical (experimental or numerical) framework. Beginning in the 1990s, flow control is increasingly being framed within the context of optimal control theory. As will be seen in Chapter 10, the solution to optimal control formulations, particularly for large problems involving many degrees of freedom, is very computationally intensive. It is only recently that the computational resources have become available that are capable of solving realistic fluid mechanics scenarios within such an optimal control framework.

Similarly, significant advances are being made in our understanding of stability of fluid flows through the application of transient growth analysis that seeks the “optimal,” or most unstable, initial perturbation (disturbance) that results in the greatest growth of the instability.