Abstract

The most important results in turbulence theory concern the idealization of the flow as composed by different ingredients. Turbulence theories are then genuine results of their first fundamental step: the conceptual decomposition of turbulence. Famous examples are the Reynolds decomposition of the flow in a mean and fluctuating part and the spectral decomposition in a hierarchy of scales of motion. The general aim is to provide a description of turbulence simpler than that given by the full Navier-Stokes equations. However, the nonlinearity of the problem challenges for a reduced description of turbulence giving rise to the well-known closure problem in statistical theories of turbulence. It consists in a coupling of the different levels and scales composing turbulence which interact themselves exchanging momentum and kinetic energy. In the present seminar, a review of the turbulence decompositions and of the related results is presented. Particular attention is devoted to the generalized central moments introduced by the filtering decomposition and to their analogy with the two-point velocity increment. Different flow cases will be considered to present the issue.

Short Bio

Andrea Cimarelli is currently a researcher and lecturer of the University of Modena and Reggio Emilia. He obtained the master degree in aerospace engineering in 2007 at the University of Bologna where he also obtained the PhD degree in 2011. He was post-doc researcher at the University of Bologna from 2011 to 2014, at the University of Modena and Reggio Emilia from 2014 to 2017, at the Universita Politecnica delle Marche from 2017 to 2018 and at the Cardiff University from 2018 to 2019. He was lecturer of different courses in fluid mechanincs both at the University of Bologna and at the Universita Politecnica delle Marche.