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

本文从理论和数值两方面研究了二维湍流中涡度拟能的衰减规律。主要研究结果如下：1. Chasnov和Herring（1998）和Iwayama和Shepherd（2006）两个自相似理论推导了Chasnov（1997）和Das等人在数值模拟中发现的涡度拟能衰减规律。（2001）比较。后者的优点是可以很容易地推广到具有各种粘性形式的系统和其他二维流体系统。实际上，利用Iwayama和Shepherd理论提出了一个广义二维湍流的自相似理论.通过数值模拟验证了Chasnov和Herring（1998）以及Iwayama和Shepherd（3306）提出的自相似假设的有效性。结果表明，在一般情况下，自相似性不存在，而自相似性只存在于一定的初始雷诺数和一定形式的粘性。此外，Chasnov（1997）和Das，et.（2001），并被认为是一个在高雷诺数限制，应被认为是一个在中等雷诺数。波数空间中广义二维相干相互作用的非定域性2。广义二维流体系统中流动的稳定性3。圆涡诱导的非线性Ekm_a泵送

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