Two basic pieces of background needed for this discussion are those of the Navier-Stokes equations and turbulence.
It is well-known that the equations which model the behavior of an incompressible and viscous Newtonian fluid are the celebrated Navier-Stokes equations (NSE) [1,4,6]:
$$\frac{\partial \mathbf{u}}{\partial t} + \mathbf{u}\cdot\nabla\mathbf{u} -\nu\Delta\mathbf{u}+\nabla p = \mathbf{f} $$ $$ \nabla \cdot \mathbf{u} =0 \,(incompressibilit\!y)$$
where $\mathbf{u}=(u,v,w)$ is the velocity, $\nu$ is the kinematic viscosity, $\mathbf{f}$ is the external forcing of the fluid (including rotational effects), and $\Delta=\nabla\cdot\nabla=\nabla^2$ for those more familiar with gradient notation. To be formulated as a well-posed problem, the NSE must also be specified with boundary and initial conditions. It should be mentioned that the incompressible NSE in 3-Dimensions are not in general solvable analytically; the problem is difficult and is one of the six open Millenium Prize Problems of the Clay Mathematics Institute.
An important feature of the NSE is that the solutions to the system can exhibit irregular behavior with unpredictable small-scale features [8]. The extent to which the system expresses these features may be described by a parameter called the Reynolds number of the flow [1]:
$$Re=\frac{UL}{\nu}$$ where $U$ and $L$ are the characteristic length scales of the velocity and domain, respectively, and $\nu$ is the kinematic viscosity.
The Reynolds number, $Re$, may be interpreted as the ratio of the inertial forces on a fluid to its internal viscous forces [3]. It is a non-dimensional measure of the persistence of motion in the fluid compared to the frictional fluid forces that reduce that motion. For flows with large values of $Re$, the effects of molecular viscosity do not damp the motion sufficiently, giving rise to a complex of motions called turbulence.
Turbulence can be considered to consist of eddies of different sizes, and the behavior and interaction of the eddies is chaotic [7,8]. These scales of motion can be thought of as a superposition of interacting (coupled) hierarchy of eddies [6]. Along with the boundaries of the domain of the NSE, turbulent structures below a critical scale are aspects of a flow where friction, in the form of viscosity, become extremely important and MUST be considered [3].