Analysis of multifractal natures in turbulence based on the dynamics of fine-scale coherent structures

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It has shown that two dimensional Boussinesq turbulence has characteristics similar to those of three- dimensional Navier-Stokes turbulence. In particular, the existence of both cascade process and fine-scale coherent structures suggests that turbulence should be maintained by some universal mechanism. We believe that these results will contribute to the fundamental understanding of turbulence considerably. The main results are the following:1. The fine scale coherent structures formed by T vorticity have been found and defined.We found that strings-like temperature shocks maintained by the balance of stretching and dissipation are regarded as fine scale coherent structures in 2D Boussinesq turbulence, which have a life time longer than the characteristic times of small scales and quite long correlation length. These characters of fine-scale coherent structures are quite similar to those in 3D Navier-Stokes turbulence. Moreover it is shown that these structures are approximated by anal … More ytic solutions corresponding to the Burgers' vortex layer.2. The role of fine scale coherent structures in turbulence diffusion has been understood partially.We have shown that although fine scale coherent structures have quite long correlation length, they essentially contribute to the relative turbulent diffusion in a sense pf Kolmogorov scaling. This means that fine scale coherent structures play an important role even in lower order characteristics of turbulence.3. The result suggesting the existence of finite time singularity has been obtained.We developed a high resolution scheme in which new meshes are piled up at local regions where finer spatial resolution is required : adaptive mesh refinement method. With this scheme we have obtained the result suggesting the existence of finite-time singularity in ideal two dimensional Boussinesq system.The singularity seems to be triggered by a self-similar instability of a fine scale coherent structure. This suggests that even in the invisid limit structures become unstable and then characteristics of turbulence might be different from those accepted presently. Less