Νέες προσεγγίσεις στη θεωρία της ισοτροπικής τύρβης

Abstract

The aim of the project is to bring new understanding in the field of isotropic turbulence. The renormalized perturbation theories (RPTs) are mathematical schemes which are the nearest thing we have to a fundamental theory of isotropic turbulence. The modern direct numerical simulations (DNS) of isotropic turbulence have reached high enough Reynolds numbers so that the characteristics of interesting phenomena can now be identified with clarity. Also, a detailed assessment of RPTs against real data is lacking. We propose a novel method to assess the RPTs against the modern DNS. The method employs the modal decay rate η(k), which is the semi-empirical ingredient of a simplification of the RPTs called markovian approximation (EDQNM). It also possesses a specific meaning within the original theory. For a given set of DNS data we will run the EDQNM in reverse in order to obtain the η(k) corresponding to the DNS. That is, we will be able to encode the phenomenology on an object which carries, in part, the dynamics of the EDQNM and carries important information about the dynamics of the theory. Preliminary unpublished work has shown that the η(k)‟s obtained this way have differences with respect to the EDQNM which show identifiable patterns that can be studied and described through simple analytical functions. Similarly the predictions of the RPTs, after coding and implementation for the set of DNS cases of interest, will be examined quantitatively in detail. The theory operates at a deeper level than the markovian approximation, that is, that of their two-time correlations functions. The shape of the correlation functions with respect to time determines the η(k). Hence, the comparative analysis will be now extended to the RPTs allowing us to identify specific dynamical weaknesses of the theory. Finally, with the information acquired, new highly effective markovian approximations will be developed and specific modifications/reformulations of the theory will be suggested.