| Research Abstract |
Due to the progress of a computer technology, several properties of nonlinear-nonequilibrium systems are clarified. Since then the studies of nonlinear dynamics on the bases of dissipative dynamical system were started and encouraged for Japanese scientists, particularly, physicists, mathematicians, biologists, chemists, engineers, geologists and even for socialists.
The goal of our study is to construct a statistical physical theory of anomalous diffusion phenomena in an inviscid fluid. By making use of sufficient computer resources, we have performed successfully theoretical formulation and direct computer simulation of the two-dimensional decaying turbulence. In the turbulence, it is known there are three stages in the temporal developement of the vortices. In the first stage, fluid self-organizes into a set of coherent vortices. Once the coherent vortices emerge, the second stage begins. In the second stage, the coherent vortices governs dynamics of the system. When they become close, within a critical distance, same sign vortices merge and become a larger vortex. A pair of opposite-sign vortices ultimately construct a dipole structure. In the final stage, the dipole structure decays diffusively. In the present study, we clarified the scaling law hold in the second stage. We also succeeded to formulate a theory to the scaling exponent xi and decided the numerical value of xi that is consistent with the result of numerical simulations.
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