Turbulence Physical Picture

Since a precise definition of turbulence is difficult, pictures and other visualizations of turbulent flows may give some idea of the complex characteristics of turbulence. Several such visualizations are available, including the famous painting The Deluge by Leonardo da Vinci. Banerjee (1992) included several such pictures in his excellent paper on turbulence structures. Van Dyke (1982) published an album of fluid motion which is a must see for any turbulence researcher. Several websites hold treasures of visual information on turbulence (see, for example, links listed at sites such as www.cfd-online.com and www.efluids.com). Pictures included in these resources show various aspects of turbulent flows and may give some intuitive understanding of turbulence. 

Turbulence is intrinsically unsteady, even when constant boundary conditions are imposed. Velocity and all other flow properties fluctuate in a random and chaotic way. Turbulent fluctuations always have a three-dimensional spatial character. There have been many attempts to analyze and to construct a physical picture of turbulence, following several different approaches. These different approaches, broadly classified into three categories, are discussed in this section. 

In this approach, the unsteady processes occurring in turbulent flows are visualized as a combination of some mean process and small-scale fluctuations around it. The typical time variation of fluid velocity at a point in a turbulent flow is shown in Fig. 3.1. In the statistical approach, an instantaneous velocity, U, is visualized as a mean velocity, U (shown by a horizontal line in Fig. 3.1) and fluctuations around it, u. Based on such an approach, the statistical theory of turbulence flows has been developed (see Hinze, 1975 and references cited therein). It has been the basis for most of the engineering modeling of turbulent flow processes. Some of the key concepts of the statistical approach are discussed below. 

FIGURE 3.1 Typical point velocity behavior in turbulent flows. 

FIGURE 3.2 Energy spectrum for isotropic turbulence (from Hinze, 1975). 

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As we have just seen, the closure problem is the fundamental impediment to obtaining solutions for the mean velocities in turbulent flows. In order to progress at all, from a purely mathematical point of view, we must obtain a closed set of equations. The simplest approach to closing the equations is based on an appeal to a physical picture of the actual nature of turbulent momentum transport. 

The quantity S can be interpreted as the mean thickness of a diffusion layer at the electrode surface as schematically depicted in Fig. 37. In this simple picture, the electrode is separated from the turbulent bulk by a laminar sub-layer inside of which the concentration of the electroactive species depletes from the bulk value to that at the electrode surface across the (physically smaller) diffusion layer. Within this model the effects of the ultrasonic intensity and the horn-to-electrode separation emerge through their effects on the size of 8. 

However, there exists a class of chains with independent links which do not obey this condition and which nevertheless have a well-defined asymptotic limit.14 These chains do not correspond to our current picture of a polymer, but it is better to be aware of their existence. They are interesting in themselves and exhibit the intermittence phenomenon, a concept which can be met in other branches of physics for instance, hydrodynamics (theory of turbulence) and astrophysics. ... 

Even though we cannot provide a detailed mathematical description of turbulent flow, we can provide several physical descriptions, which help the student form an intuitive picture of turbulent flow. 

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