1.9 Turbulence

This chapter concludes with an introduction to the notion of turbulence. This is only a bare description. More concrete material is presented in Chapter 6.

So far, we have discussed fluid and vorticity dynamics without reference to whether the flow is laminar or turbulent. From the perspective of the governing equations, there is no need to distinguish: the laws of motion apply to either. From a practical perspective, the distinction is crucial. How computations are effected is very much dependent on whether the flow is laminar or turbulent. If laminar, we simply solve the governing equations with as much accuracy as possible. If turbulent, there are choices to be made: in most cases, simply solving the equations is not practical.

Turbulence is an intriguing and immensely important fluid dynamical phenomenon. Many eminent engineers, physicists, and mathematicians have tried their hands at theories and models of turbulence in fluids. The available methods of simulation, and the theoretical understanding of turbulence, are the fruits of their labor. However, most fluid dynamicists would acknowledge that available theories and models leave much room for improvement.

Turbulence is irregular fluid flow. It is a state of fluid motion characterized by its complexity. Vorticity becomes unoriented and entangled; chaotic velocities stir the fluid. Because of the inherent complexity, full-blown numerical solution to the Navier Stokes equations which is called direct numerical simulation (DNS) is extremely costly. Effecting DNS requires sufficient mesh points to resolve the smallest of eddies and to...