论文标题
四个空间维度的均质各向同性湍流
Homogeneous isotropic turbulence in four spatial dimensions
论文作者
论文摘要
直接数值模拟是在四个空间维度中对强制的Navier-Stokes方程进行的。良好的平衡，以足够的分辨率进行长时间运行，以可靠地测量光谱量，速度导数偏度和无量纲耗散速率。与相应的两个和三维结果进行比较。测量能量波动，并显示出从三个维度移动到四个维度的明显降低。该动力学似乎在四个维度上显示出简化，并显示出增加的前向能传递的图片，从而导致惯性范围增加，而Kolmogorov量表较小。这种增强的正向转移与我们发现增加的耗散性异常和速度衍生物偏度有关。
Direct Numerical Simulation is performed of the forced Navier-Stokes equation in four spatial dimensions. Well equilibrated, long time runs at sufficient resolution were obtained to reliably measure spectral quantities, the velocity derivative skewness and the dimensionless dissipation rate. Comparisons to corresponding two and three dimensional results are made. Energy fluctuations are measured and show a clear reduction moving from three to four dimensions. The dynamics appear to show simplifications in four dimensions with a picture of increased forward energy transfer resulting in an extended inertial range with smaller Kolmogorov scale. This enhanced forwards transfer is linked to our finding of increased dissipative anomaly and velocity derivative skewness.
