Τυρβώδης ροή

Abstract

In this study we will analyze various theorems concerning the phenomenon of turbulent flow in incompressible fluids in order to deepen our understanding of this particular section of classical physics which still remains unexplained. At first a general reference is made to the issue of turbulent flow in fluids such as certain terminologies that are used in the following chapters. The next step is to note the experimental procedures that were implemented previously to detect and determine the effect of turbulence as the experiments of Taylor, Benard and Reynolds. Through these experiments the first general conclusions concerning the effect of turbulent flow are identified. Then we will analyze the energy cascade in turbulent flow based on publications by Kolmogorov and Richardson, which was a very important piece of knowledge of some general characteristics of the phenomenon. References are also made for DNS (Direct Numerical Simulations) which are vital in the study of turbulent flow since they allow the representation of this phenomenon by the use of computational methods. In greater depth after that, the study concentrates on the linearly forced isotropic turbulence inspired by the publication of Lundgren, where a simplified and easily applicable model of forcing which is linear and stems from the equation of Karman-Howarth was introduced. At the end, various more recent studies which try to use the linearly forced turbulence proposed by Lundgren to export some data, reach some conclusions, and compare them with data from DNS are mentioned. The ultimate goal is to continue the investigation of finding a simplified relationship that describes the phenomenon of isotropic turbulence at a later stage, without the mediation of computational models. The first chapter is a general reference to the turbulent flow and isotropy. In the second chapter there 's a historical separation between recent studies analyzing turbulent flow. In the third chapter various experimental setups are analyzed that contributed significantly to the analysis of turbulent flow. After that, the fourth chapter explains the equation of Navier-Stokes for fluid movement. The fifth chapter contains studies of Kolmogorov and Richardson concerning the escalation of energy in turbulent flow. In the sixth chapter we make a reference to DNS (Direct Numerical Simulations). Then in the seventh chapter we study the linear forcing of isotropic turbulence as discussed by Lundgren and various comparisons of this method in other studies. In the last chapter conclusions about turbulent flow are derived using the above information.