Aha, this is low dimensional chaosIf you want gratitude, get a dog Professor Zweitemann: Yes of course, this is low dimensional chaos / spatiotemporal chaos / center manifold / inertial manifold / ..., I have already done all this - have a look at my 1980's papers with Erstermann. A: Yes, your fundamental paper of 1969 has been a great inspiration to us, and the insights of low-dimensional dynamical systems have been essential guide to the recent progress described here. The state space visualization is a novel and useful tool. Such low-dimensional projections are a visualization, not a reduction of Navier-Stokes to a low-dimensional model. We do not seek a smaller set of `modes' to represent the fluid dynamics; all calculations have to be done in high-dimensional state-spaces, with fully resolved DNS. If you prefer terms `low dimensional chaos / spatiotemporal chaos / center manifold / inertial manifold /' ... to term `turbulence' when referring to the exact solutions of Navier-Stokes equations in this transitional Re regime, feel free to do so. Just remember to spell our names right. |