Dual views of transitional turbulenceRevolution will not be televised Within the last few years the dynamical (as opposed to statistical) theory of moderate Re turbulence in wall-bounded flows has made great strides. The are as resolved as numerical simulations. The geometry of the infinite-dimensional Navier-Stokes state space (not low-dimensional models) can now be triangulated by sets of exact solutions (equilibria, traveling waves, periodic orbits, ...). They, together with their stable/unstable manifolds and heteroclinic connections, form a rigid backbone which enables us to describe, control and predict the sinuous motions of a turbulent fluid. This (if flash does not play try ) of the tutorial shows how the time evolution of typical unstable structures observed in turbulence is captured by unstable periodic orbits embedded in the turbulent regions of the state space. (Right frame and various symbols on it will be explained in what follows; so will be the left frame visualization of the 3D flow.)This state-space visualization is novel and might be of interest to a fluid dynamicist. The tutorial develops the theory behind this movie in a sequence of gentle steps. |