Tsang Yue-Kin, Ott Edward, Antonsen Thomas M, Guzdar Parvez N
Department of Physics, University of Maryland, College Park, Maryland 20742 USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):066313. doi: 10.1103/PhysRevE.71.066313. Epub 2005 Jun 30.
We consider the enstrophy cascade in forced two-dimensional turbulence with a linear drag force. In the presence of linear drag, the energy wave-number spectrum drops with a power law faster than in the case without drag, and the vorticity field becomes intermittent, as shown by the anomalous scaling of the vorticity structure functions. Using previous theory, we compare numerical simulation results with predictions for the power law exponent of the energy wave-number spectrum and the scaling exponents of the vorticity structure functions zeta(2q). We also study, both by numerical experiment and theoretical analysis, the multifractal structure of the viscous enstrophy dissipation in terms of its Rényi dimension spectrum D(q). We derive a relation between D(q) and zeta(2q), and discuss its relevance to a version of the refined similarity hypothesis. In addition, we obtain and compare theoretically and numerically derived results for the dependence on separation r of the probability distribution of delta(r)omega, the difference between the vorticity at two points separated by a distance r. Our numerical simulations are done on a 4096 x 4096 grid.
我们考虑具有线性阻力的强迫二维湍流中的涡量级串。在线性阻力存在的情况下，能量波数谱以比无阻力情况更快的幂律下降，并且涡度场变得间歇性，如涡度结构函数的反常标度所示。利用先前的理论，我们将数值模拟结果与能量波数谱的幂律指数以及涡度结构函数ζ(2q)的标度指数的预测进行比较。我们还通过数值实验和理论分析，从其Rényi维数谱D(q)的角度研究了粘性涡量耗散的多重分形结构。我们推导了D(q)与ζ(2q)之间的关系，并讨论了其与精细化相似假设版本的相关性。此外，我们在理论上和数值上获得并比较了关于两点涡度差值δ(r)ω的概率分布对间距r的依赖性的结果。我们的数值模拟是在4096×4096的网格上进行的。
