In the first paragraph one reads: “…turbulent flow, which is characterized by small scale velocity components that appear to be stochastic in nature” and “Usually, laminar flows are unstable and will, unless controlled, evolve into turbulent flows”.
The goal of this book is to stabilize or destabilize (with the intention of mixing) simple fluid flows (2D and 3D channel flows, 3D pipe flows). In the first case a Lyapunov function approach, which is related to the energy, is used. The control terms which appear in the computation of the time derivative of the Lyapunov function are chosen so that it becomes negative definite. However there is not even a statement of the Lyapunov direct method in infinite-dimensional spaces. In the second case the approach is based on methods of dynamical systems with “chaotic” behaviour (2D channel flow) and on an optimal cost related to a mixing property (3D pipe flows); a limit (in a defining quantity) when time goes to infinity is taken, but the authors do not say if this is allowed.