Research of enstrophy decay lawin two-dimensional turbulence at finite Reynolds number

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We have studies on decaying law of enstrophy in two-dimensional turbulence, theoretically and numerically. The main results are summarized as follows:1. Two self-similar theories, Chasnov and Herring theory (1998) and Iwayama and Shepherd theory (2006), which derive the enstrophy decay law found from numerical simulations by Chasnov (1997) and Das, et. al. (2001), are compared. The latter has the advantage beyond the former in the sense that the latter can easily extend to systems with various form of viscosity and other two-dimensional fluid system. Indeed, a self-similar theory for a generalized two-dimensional turbulence is proposed using Iwayama and Shepherd theory.2. Numerical simulations are performed to examine the validity of self-similar hypothesis relying on Chasnov and Herring (1998) and Iwayama and Shepherd (3306). As the results, in general, it is shown no existence of the self-similarity, rather the self-similarity exists only at a certain initial Reynolds number and for a certain form of viscosity. Moreover the enstiophy decay law, which is found by both Chasnov (1997) and Das, et. al. (2001) and is considered as one in the high Reynolds number limit, should be considered as one at medium Reynolds number.We try to produce new paradigms for two-dimensional fluid system1. Non localness of interaction in wave number space for a generalized two-dimensional turbulence2. Stability of flows in a generalized two-dimensional fluid system3. Nonlinear Ekm an pumping induced by circular vortex