 

Hidden symmetry in turbulence and analytic study of shell models
Caggio, Matteo
This short communication concerns symmetries in developed turbulence and analytic study of shell models. However scaleinvariance is broken due to the intermittency phenomenon, is possible to established a hidden selfsimilarity in turbulent flows. Using a shell model, the author in [18] (see also [19]) addressed the problem deriving a scaling symmetry for the inviscid equations. Here, first we discuss the analysis presented in [18], then, from the mathematical perspective, we propose an analytic study for the shell model with the presence of the viscous terms. This brief paper should be understood as an introductory note to this new scaling symmetry with implications for mathematical analysis [5].


Numerical assessment of stratification influence in simple algebraic turbulence model
Uhlíř, V. ; Bodnár, Tomáš ; Caggio, Matteo
This paper presents rst few results obtained using a newly developed test code aimed at validation and crosscomparison of turbulence models to be applied in environmental flows. A simple code based on nite di erence discretization is constructed to solve steady flows of incompresible nonhomogeneous (variable denstity) fluids. For the rst tests a simple algebraic turbulence model was implemented, containing stability function depending on the stratification via the gradient Richardson number. Numerical tests were performed in order to explore the capabilities of the new code and to get some insight into its behavior under di erent stratification. The twodimensional simulations were performed using immersed boundary method for the flow over low smooth hill. The resulting flow fields are compared for selected Richarson numbers ranging from stable up to unstable strati cation conditions.


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.

 