Physical background

11.1 Physical background

One of the most outstanding results in turbulence theory was obtained by Kolmogorov (s. Fig. 11.1) in 1941. The Kolmogorov theory known as K41 is based on the hypothesis of local isotropy of the turbulent motion at small scales. The physical model behind the Kolmogorov theory is the vortex cascado illustrated in Fig. 11.2. Big vortices with scales L (corresponds to

in turn split into even smaller and so on up to the smalles vortices with the reconnection described above. The energy is transferred from big vortices to

small ones almost without the loss. The massive dissipation " takes place at small vortices referred to as the dissipative or the Kolmogorov vortices. The real turbulent vortices are similar to these calculated by Isazawa et al. (Fig. 11.3). Vortices are displayed at three different time instants. The upper pictures are obtained from the lower ones by filtering out the hight frequencies. As seen big vortices are revealed in low frequency simulation. If the resolution is increased, more and more small scale vortex filaments appears on the place of big smooth vortices. Thus, the most important physical processes during the vortex break up are:

Transfer energy from large scales to small ones and Dissipation of the energy in small vortices.

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Figure 11.1: Andrey Kolmogorov was a mathematician, preeminent in the 20th century, who advanced various scientific fields (among them probabil- ity theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity).

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Figure 11.2: Illustration of the vortex cascado.

Figure 11 .3: Turbulent vortices revealed in DNS calculations performed by Isazawa et al. (2007).