Oberseminar Numerische Mathematik / Scientific Computing
Rainer Grauer
Ruhr-Universitaet Bochum
Open Problems in Lagrangian Turbulence
Abstract:
We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magnetohydrodynamic (MHD) flows. Numerical simulations were performed with up to $1024^3$ collocation points and 10 million particles in the Navier-Stokes case and $512^3$ collocation points and 1 million particles in the MHD case. In the hydrodynamics case our findings compare with recent experiments from Mordant et al (2004) and Xu et al (2005). They differ from the simulations of Biferale et al (2004) due to differences of the ranges choosen for evaluating the structure functions. In Navier-Stokes turbulence intermittency is stronger than predicted by a multifractal approach of Biferale et al (2004) whereas in MHD turbulence the predictions from the multifractal approach are more intermittent than observed in our simulations. In addition, our simulations reveal that Lagrangian Navier-Stokes turbulence is more intermittent than MHD turbulence, whereas the situation is reversed in the Eulerian case. Those findings can not consistently be described by the multifractal modeling. The crucial point is that the geometry of the dissipative structures have different implications for Lagrangian and Eulerian intermittency. This motivates a new definition of a Lagrangian structure function which allows to establish a connection to Eulerian transversal structure functions.
| Datum: | 04.02.08 | Zeit: | 16:15 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | 032 im Erdgeschoss |