
Note on the problem of compressible nonNewtonian fluids
Caggio, M. ; Nečasová, Šárka
The aim of the paper is to consider the compressible nonNewtonian fluids of power law type when the viscosity coeffcients depend not only on invariants of velocity field but also on the density. We introduce approximation scheme using model of multipolar fluids. After then passing with higher viscosity to zero we get the measure valued solution of the problem.


On the mechanisms of dimensional transition in stably stratified turbulent fluid layers
Caggio, M. ; Bodnár, Tomáš ; Schiavon, M.
The purpose of this short review communication is to present some recent results on the effects of stable density stratification on the threedimensional turbulent dynamics of 'thin' fluid layers forced at intermediate scales. In particular, how the strati cation and the confinement affect the mechanism of kinetic and potential energy transfer between different scales. Results on twodimensional vertically stratifed flows and possible applications for stably stratifed atmospheric boundary layer will be shortly discussed.


Analysis of the turbulence parameterisations for the atmospheric surface layer
Caggio, Matteo ; Bodnár, Tomáš
The purpose of this short communication is to present a method that aims to express the turbulent variables in the atmospheric surfacelayer in function of the stability of the atmosphere. The case of very stable conditions (strong strati cation), where theoretical approaches provide conflicting results (see Luhar et al. [11]), is analysed in detail to provide some insight into the limits of applicability for some of the most popular models of turbulence. The problem of the existence of the critical flux Richardson number is also taken into account.


Note on the use of CamassaHolm equations for simulation of incompressible fluid turbulence
Caggio, Matteo ; Bodnár, Tomáš
The aim of this short communication is to briefly introduce the CamassaHolm equations as a working model for simulation of incompressible fluid turbulence. In particular we discuss its application for turbulent boundary layer flows. This model (and related models) is studied for several years in mathematical community, starting from Leray [23]. It can be understood as a generalization of some classical fluid models (NavierStokes equations, Prandtl boundary layer equations), showing some interesting mathematical properties in the analysis of the behavior of it's solution (e.g. Layton and Lewandowski [22]). It has been found however, that the model predictions can lead to surprising extensions of the use of the model in technical applications, namely in simulating the turbulent fluid flows. This brief paper should be understood as an introductory note to this novel class of models for applied scientists.

 