Cascades of energy and helicity in the GOY shell model of turbulence

The effect of extreme hyperviscous damping, $\nu k_n^p, p=\infty$ is studied numerically in the GOY shell model of turbulence. It has resently been demonstrated [Leveque and She, Phys. Rev. Lett, 75,2690 (1995)] that the inertial range scaling in the GOY model is non-universal and depending on the viscous damping. The present study shows that the deviation from Kolmogorov scaling is due to the cascade of the second inviscid invariant. This invariant is non-positive definite and in this sense analogous to the helicity of 3D turbulent flow.Comment: 4 pages, 2 figure

A note on dissipation in helical turbulence

In helical turbulence a linear cascade of helicity accompanying the energy cascade has been suggested. Since energy and helicity have different dimensionality we suggest the existence of a characteristic inner scale, $\xi=k_H^{-1}$, for helicity dissipation in a regime of hydrodynamic fully developed turbulence and estimate it on dimensional grounds. This scale is always larger than the Kolmogorov scale, $\eta=k_E^{-1}$, and their ratio $\eta / \xi$ vanishes in the high Reynolds number limit, so the flow will always be helicity free in the small scales.Comment: 2 pages, submitted to Phys. Fluid

A stochastic model of cascades in 2D turbulence

The dual cascade of energy and enstrophy in 2D turbulence cannot easily be understood in terms of an analog to the Richardson-Kolmogorov scenario describing the energy cascade in 3D turbulence. The coherent up- and downscale fluxes points to non-locality of interactions in spectral space, and thus the specific spatial structure of the flow could be important. Shell models, which lack spacial structure and have only local interactions in spectral space, indeed fail in reproducing the correct scaling for the inverse cascade of energy. In order to exclude the possibility that non-locality of interactions in spectral space is crucial for the dual cascade, we introduce a stochastic spectral model of the cascades which is local in spectral space and which shows the correct scaling for both the direct enstrophy - and the inverse energy cascade.Comment: 4 pages, 3 figure

Two modes of glacial climate during the late stage 5 identified in Greenland ice core records

International audienceFrom a detailed analysis of marine and terrestrial aerosol tracers in the NGRIP ice core we identified two distinct glacial atmospheric flow patterns. The climate transition from Marine Isotope Stage 5 (MIS 5) to MIS 4, at approximately 75 kyr BP, marks a shift between two different atmospheric flow regimes. Before this transition, during MIS 5d-a, the state of atmospheric flow was alternating between the two modes of different flow patterns, while a more persistent flow pattern was prevailing through the glacial period afterwards. These changes are accompanied by strong changes in an independent Greenland ice core proxy, namely the deuterium excess from the GRIP ice core, reflecting changes in the hydrological cycle and moisture source temperatures as well. The changes in atmospheric flow pattern are correlated with changed extent of ice-rafted detritus (IRD) deposition in the North Atlantic, indicating that the state of the atmospheric flow was highly sensitive to the waxing and waning of the Laurentide ice sheet

Levy flights and Levy -Schroedinger semigroups

We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.Comment: To appear in Cent. Eur. J. Phys. (2010

Anomalous jumping in a double-well potential

Noise induced jumping between meta-stable states in a potential depends on the structure of the noise. For an $\alpha$-stable noise, jumping triggered by single extreme events contributes to the transition probability. This is also called Levy flights and might be of importance in triggering sudden changes in geophysical flow and perhaps even climatic changes. The steady state statistics is also influenced by the noise structure leading to a non-Gibbs distribution for an $\alpha$-stable noise.Comment: 11 pages, 7 figure