Connaughton C, Nazarenko S, Pushkarev A
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Apr;63(4 Pt 2):046306. doi: 10.1103/PhysRevE.63.046306. Epub 2001 Mar 27.
A numerical study is presented which deals with the kinematics of quasiresonant energy transfer in a system of capillary waves with a discrete wave number space in a periodic box. For a given set of initially excited modes and a given level of resonance broadening, the modes of the system are partitioned into two classes, one active, the other forbidden. For very weak nonlinearity the active modes are very sparse. It is possible that this sparsity explains discrepancies between the values of the Kolmogorov constant measured in numerical simulations of weakly turbulent cascades and the theoretical values obtained from the continuum theory. There is a critical level of nonlinearity below which the set of active modes has finite radius in wave number space. In this regime, an energy cascade to dissipative scales may not be possible and the usual Kolmogorov spectrum predicted by the continuum theory not realized.
本文给出了一项数值研究，该研究涉及在周期性盒子中具有离散波数空间的毛细波系统中的准共振能量转移运动学。对于给定的一组初始激发模式和给定的共振展宽水平，系统的模式被分为两类，一类是活跃的，另一类是被禁止的。对于非常弱的非线性，活跃模式非常稀疏。这种稀疏性有可能解释了在弱湍流级联的数值模拟中测量的科尔莫戈罗夫常数的值与从连续介质理论获得的理论值之间的差异。存在一个临界非线性水平，低于该水平时，活跃模式集在波数空间中具有有限半径。在这种情况下，可能无法实现向耗散尺度的能量级联，并且连续介质理论预测的通常的科尔莫戈罗夫谱也无法实现。
