Tsallis Extended Thermodynamics Applied to Turbulence: Lévy Statistics and -Fractional Generalized Kraichnanian Energy and Enstrophy Spectra.

The extended thermodynamics of Tsallis is reviewed in detail and applied to turbulence. It is based on a generalization of the exponential and logarithmic functions with a parameter . By applying this nonequilibrium thermodynamics, the Boltzmann-Gibbs thermodynamic approach of Kraichnan to turbulence is generalized.

Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulation.

This paper presents a new model and discussions about the motion of avalanches from initiation to run-out over moderately curved and twisted channels of complicated topography and its numerical simulations. The model is a generalization of a well established and widely used depth-averaged avalanche model of Savage & Hutter and is published with all its details in Pudasaini & Hutter (Pudasaini & Hutter 2003 J. Fluid Mech.

The Savage-Hutter avalanche model: how far can it be pushed?

The Savage-Hutter (SH) avalanche model is a depth-averaged dynamical model of a fluid-like continuum implementing the following simplifying assumptions: (i) density preserving, (ii) shallowness of the avalanche piles and small topographic curvatures, (iii) Coulomb-type sliding with bed friction angle delta and (iv) Mohr-Coulomb behaviour in the interior with internal angle of friction phi> or =delta and an ad hoc assumption reducing the number of Mohr's circles in three-dimensional stress states to one. We scrutinize the available literature on information regarding these assumptions and thus delineate the ranges of validity of the proposed model equations. The discussion is limited to relatively large snow avalanches with negligible powder snow component and laboratory sand avalanches starting on steep slopes.

Geophysical granular and particle-laden flows: review of the field.

An introduction is given to the title theme, in general, and the specific topics treated in detail in the articles of this theme issue of the Philosophical Transactions. They fit into the following broader subjects: (i) dense, dry and wet granular flows as avalanche and debris flow events, (ii) air-borne particle-laden turbulent flows in air over a granular base as exemplified in gravity currents, aeolian transport of sand, dust and snow and (iii) transport of a granular mass on a two-dimensional surface in ripple formations of estuaries and rivers and the motion of sea ice.