Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 58: Poster - Fluids

DY 58.4: Poster

Donnerstag, 19. März 2015, 16:00–18:00, Poster A

From low-dimensional chaos to complex behaviour in transitional pipe flow — •Paul Ritter — Lehrstuhl für Strömungsmechanik, Cauerstraße 4 91058 Erlangen

Turbulent pipe flow so far escapes an analytical explanation. The common approach of applying bifurcation theory to the linearized equations fails in this case because the transition occurs via finite amplitude perturbations and is characterized by localized turbulent spots surrounded by laminar flow (so-called ``puffs''). A recent proposition to explain the origin of puffs postulates that, in analogy to low dimensional chaotic systems, turbulence is organized around invariant solutions of the governing equations, glimpses of which can be observed experimentally as coherent structures.

The work presented here tries to link some of the theory of low-dimensional chaotic systems to the infinite-dimensional spatio-temporal complexity of the Navier-Stokes equations. I present a mechanism, which elucidates how mildly chaotic transients acquire more complexity with respect to size, speed and kinematic properties and hence approach the properties of actually observed turbulence. This mechanism consists of the interaction and merging of chaotic saddles with distinct dynamical characteristics. The link between the saddles suggests that invariant solutions with a varying degree of internal wavelengths, possibly created in a snaking-like mechanism, might be responsible for the creation of the saddles. Finally, results from a search for these elementary building blocks of turbulence will be presented in several symmetry subspaces.