The dynamics of coherent structures in developed turbulence

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I obtained mainly the following three results on the dynamics and the structures in developed turbulence.1. In two-dimensional free convection (FC) turbulence, entropy cascade governs turbulent transfers in scales. Entropy cascade is intermittent like energy cascade in three dimensional Navier-Stokes turbulence. I have determined the exponents of structure of functions of temperature differences and velocity differences in terms of ESS (Extended Self-Similarity) hypothesis. As a result, it is shown that ESS method works well even for the free convection system and gives plausible results. However, the intermittency observed is not explained by the existing models. This is because the existing models are based on the intermittency of the dissipation rate and deal with directly the statistics of the velocity differences. and temperature differences. I am trying to construct a new model.2. I have examined the intermittency of entropy cascade from the dynamical perspective focusing on its character-istic times. It is shown that the large fluctuations which seem to cause the intermittency and are observed as structures, highly correlate both in time and scale and fluctuations of their correlation times are weak. These large fluctuations On the other hand, homogeneous fluctuations which are the background of the structures, contain the greater part of the entropy of the system. The scaling of their average over space determines the characteristic times of the intermittency or the structures.3. In channel flow turbulence, Iproposed the definition of streak by which whole structure of streak from the viscous sub-layr to the log-layr is well visualized. The importance of the roll of structures in the viscous sub-layr is examined. It is also shown that the dynamics of the boundary layr is explained by the dynamics of streak. The three dimensional structure of streaks observed in their evolutions is explained by the simple argument based on the symmetry of the configuration.