Recent advances in experimental measurements and numerical analysis of unstable coherent structures observed in transitional (i.e., close to the onset of) turbulence in wall-bounded shear flows give us a detailed dynamical systems insights in the nature of this type of turbulence.

This opens new perspectives:

  1. Computation of dynamical averages such as turbulent drag, velocity correlations, etc.: in contrast to probabilistic and scaling approaches to large Re turbulence, the predictions here are exact (obtained by periodic orbit theory) and transport properties are sensitive to the precise value of Re (lack of structural stability).

  2. New approaches to nonlinear control: now that we have a detailed picture of the invariant solutions of the flow, their linear stability eigenvectors and their unstable manifolds, body forcing or boundary forcing algorithms can be constructed to chaperon the fluid toward a desired state.