Mizuta Atsushi, Matsumoto Takeshi, Toh Sadayoshi
Software Cradle Co., Ltd., 3-4-5, Umeda, Kita-ku Osaka, Japan and Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):053009. doi: 10.1103/PhysRevE.88.053009. Epub 2013 Nov 11.
We numerically investigate the inverse energy cascade range of two-dimensional Navier-Stokes turbulence. Our focus is on the universality of the Kolmogorov's phenomenology. In our direct numerical simulations, two types of forcing processes, the random forcing and the deterministic forcing, are employed besides the systematically varied numerical parameters. We first calculate the two-dimensional Navier-Stokes equations and confirm that results in the quasi steady state are consistent with the classical phenomenology for both types of forcing processes. It is also found that the difference in forcing process appears after the inverse energy cascade range reaches the system size; the dipole coherent vortices emerge and grow only when the random forcing is adopted. Then we add a large-scale drag term to the Navier-Stokes equations to obtain the statistically stationary state. When the random forcing is used, the scaling exponent of the energy spectrum in the stationary state starts to differ from the predicted -5/3 in the inverse energy cascade range as the infrared Reynolds number Re(d) increases, where Re(d) is defined as k(f)/k(d) with the forcing wave number k(f) and the large-scale drag wave number k(d). That can be interpreted as a transition phenomenon in which the local maximum vorticity grows like an order parameter caused by excitation of strong coherent vortices. Strong coherent vortices emerge and grow after the quasi steady state and destroy the scaling law when Re(d) is over a critical value. These coherent vortices are not due to the finite-size effect, unlike the dipole coherent vortices. On the other hand, when the deterministic forcing is adopted, strong coherent vortices are hardly seen and the -5/3 scaling law holds independently of Re(d). We examine the cases of the combination of both types of forcing processes and find that formation of such coherent vortices is sensitive to the mechanism of the external forcing process as well as the numerical parameters. Several types of large-scale drag terms are also tested and their insignificant influence on these qualitative properties is revealed.
我们对二维纳维 - 斯托克斯湍流的逆能量串级范围进行了数值研究。我们关注的是柯尔莫哥洛夫现象学的普遍性。在我们的直接数值模拟中，除了系统变化的数值参数外，还采用了两种强迫过程，即随机强迫和确定性强迫。我们首先求解二维纳维 - 斯托克斯方程，并确认两种强迫过程在准稳态下的结果都与经典现象学一致。还发现，在逆能量串级范围达到系统尺寸后，强迫过程的差异才会显现出来；只有采用随机强迫时，偶极相干涡旋才会出现并增长。然后我们在纳维 - 斯托克斯方程中添加一个大尺度阻力项以获得统计稳态。当使用随机强迫时，随着红外雷诺数Re(d)的增加，稳态下能量谱的标度指数在逆能量串级范围内开始与预测的 -5/3不同，其中Re(d)定义为强迫波数k(f)与大尺度阻力波数k(d)的比值k(f)/k(d)。这可以解释为一种转变现象，即局部最大涡度像由强相干涡旋激发引起的序参量一样增长。当Re(d)超过临界值时，强相干涡旋在准稳态之后出现并增长，并破坏标度律。与偶极相干涡旋不同，这些相干涡旋不是由有限尺寸效应引起的。另一方面，当采用确定性强迫时，几乎看不到强相干涡旋，并且 -5/3标度律与Re(d)无关而成立。我们研究了两种强迫过程组合的情况，并发现这种相干涡旋的形成对外加强迫过程的机制以及数值参数都很敏感。还测试了几种类型的大尺度阻力项，并揭示了它们对这些定性性质的影响不大。
