Regensburg 2019 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 50: Poster: Nonlinear Systems, Patterns, Flows ..
DY 50.2: Poster
Donnerstag, 4. April 2019, 15:00–18:00, Poster B2
Reduced order model for the velocity gradient dynamics in fully developed turbulence — •Leonhard A. Leppin1,2 and Michael Wilczek2 — 1Georg-August-Universität Göttingen, Germany — 2Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
Fully developed homogeneous isotropic turbulence exhibits statistically and geometrically complex small-scale structures. A promising approach to advance the understanding of these structures has been to formulate low-dimensional dynamical systems for the velocity gradient. However, the evolution equation of the velocity gradient tensor along Lagrangian fluid particle trajectories contains non-local terms, e.g. the pressure Hessian, which prohibit a statistically closed description of the dynamics. Here, we formulate a general closure by employing results from the theory of tensor function representation. We find that the conditional pressure Hessian can be expressed in terms of only seven known tensors with unknown coefficients that depend on the tensor invariants. To investigate the influence of the different terms of the closure we numerically integrate an ensemble of stochastic differential equations whose coefficients are dynamically adapted such that the ensemble fulfills a number of physical constraints of homogeneous turbulence. By exploring the general tensorial structure of the unclosed terms and the resulting nonlinear dynamics, our work contributes to an improved understanding of the small-scale motions in turbulence by means of low-dimensional dynamical systems.