Jacobitz Frank G, Schneider Kai, Bos Wouter J T, Farge Marie
Mechanical Engineering Program, University of San Diego, San Diego, CA 92110, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056319. doi: 10.1103/PhysRevE.84.056319. Epub 2011 Nov 21.
Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A wavelet-based scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity.
在均匀湍流剪切流中研究螺旋度统计。利用将流动分解为复值螺旋波的方法，将初始平均螺旋度施加到各向同性湍流场。在存在强平均螺旋度的情况下，湍动能的初始衰减会减弱，这与速度相关性谱张量的解析分析一致。虽然获得了平均湍动能的指数增长，但平均螺旋度却衰减了。螺旋度的概率分布函数（PDFs）是不对称的，并且表明在整个模拟过程中，所施加的平均螺旋度占主导地位。基于小波的尺度相关分析表明，大尺度运动有二维化趋势，小尺度运动则更倾向于螺旋运动。对于较小尺度，PDFs的不对称程度减小。联合PDFs表明，在所有情况下，螺旋度和超螺旋度的符号都有很强的相关性。这种相关性支持了超螺旋度耗散螺旋度的猜想。
