arXiv subjects

C. Uhlig

Publications and source records attributed to C. Uhlig.

2 recordsLinked to original sources

arXiv1996

Singularities in cascade models of the Euler equation

The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial large-scale energy distribution, the energy rushes towards smaller scales, forming a universal front independent of initial conditions. The front results in a singularity of the vorticity in finite time, and has scaling form as function of the time difference from the singularity. Using a simplified model, we compute the values of the exponents and the shape of the front analytically. The results are in good agreement with numerical simulations.

chao-dyn↗

arXiv1996

Classical Kolmogorov scaling is inconsistent with local coupling

We consider cascade models of turbulence which are obtained by restricting the Navier-Stokes equation to local interactions. By combining the results of the method of extended self-similarity and a novel subgrid model, we investigate the inertial range fluctuations of the cascade. Significant corrections to the classical scaling exponents are found. The dynamics of our local Navier-Stokes models is described accurately by a simple set of Langevin equations proposed earlier as a model of turbulence [Phys. Rev. E {\bf 50}, 285 (1994)]. This allows for a prediction of the intermittency exponents without adjustable parameters. Excellent agreement with numerical simulations is found.

chao-dyn↗