Nakayama Y, Watanabe T, Fujisaka H
Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Nov;64(5 Pt 2):056304. doi: 10.1103/PhysRevE.64.056304. Epub 2001 Oct 24.
Both static and dynamic multiscalings of fluctuations of energy flux and energy dissipation rate in the Gledzer-Ohkitani-Yamada (GOY) shell model of turbulence are numerically investigated. We compute the large deviation rate function of energy flux not only in the inertial range (IR) but also around the crossover between the inertial range and the dissipation range (DR). The rate function in IR exists to be concave, which assures the applicability of the Legendre transformation with the anomalous scaling exponents that have been investigated so far, and turns out to be independent of the Reynolds number. On the contrary, near the crossover scale, an intermediate dissipation range (IMDR) scaling is observed with the rate function in IMDR, which is accounted with the argument on dissipation scale fluctuation dominated by the energy flux fluctuation in the inertial range. Furthermore, to study the difference between IR intermittency and DR intermittency, we compute finite time-averaged quantities of energy flux and energy dissipation rate and investigate their multiscaling behavior. The difference observed in terms of their dynamic multiscaling is discussed.
在湍流的Gledzer-Ohkitani-Yamada（GOY）壳模型中，对能量通量和能量耗散率波动的静态和动态多尺度进行了数值研究。我们不仅计算了惯性范围（IR）内能量通量的大偏差率函数，还计算了惯性范围与耗散范围（DR）之间交叉区域附近的能量通量大偏差率函数。IR中的率函数呈现为凹函数，这确保了与迄今为止所研究的反常标度指数相关的勒让德变换的适用性，并且结果表明它与雷诺数无关。相反，在交叉尺度附近，观察到一个中间耗散范围（IMDR）标度以及IMDR中的率函数，这可以通过惯性范围内由能量通量波动主导的耗散尺度波动的论点来解释。此外，为了研究IR间歇性和DR间歇性之间的差异，我们计算了能量通量和能量耗散率的有限时间平均量，并研究了它们的多尺度行为。讨论了在它们的动态多尺度方面观察到的差异。
