What is turbulence?

Revolution will not be televised
(but it will streamed live on Youtube).

Comment: “I am a turbulence expert. This is not turbulence.”

Response: You are correct - Re is low, in the transitional regime, and there is no inertial range in the Kolmogorov sense. Reynolds himself called this "sinuous motion" of a fluid.

However, a wall-bounded flow explores a wide range of Re, from the laminar at the wall itself, through the boundary layer, to large scale motions further away from the wall. A precise dynamical description of unstable coherent structures observed close to the wall in all kinds of wall-bounded flows is an important piece of the overall puzzle of turbulence.

The state space visualization described here is novel, and might be a useful tool for a fluid dynamics DNS expert. The idea: Pick a few typical coherent structures observed in your turbulent flow simulation, and use these to construct a low-dimensional state-space projection from your extremely high-dimensional data set.

The tutorial develops the theory behind this state space representation in a sequence of gentle steps.