论文标题
离散谐振歧管结构对离散波湍流的影响
The Effect of Discrete Resonant Manifold Structure on Discrete Wave Turbulence
论文作者
论文摘要
我们考虑有限周期域中非线性分散波的长期动力学。工作的目的是表明波场的统计特性批判性地依赖于离散谐振歧管（DRM）的结构。为了证明这一点，我们模拟了理性和非理性托里的二维MMT方程，从而在低非线性水平下产生了明显不同的幂律光谱和能量级联。差异是用DRM的不同结构来解释的，该结构利用了最近的数字理论结果。
We consider the long-term dynamics of nonlinear dispersive waves in a finite periodic domain. The purpose of the work is to show that the statistical properties of the wave field rely critically on the structure of the discrete resonant manifold (DRM). To demonstrate this, we simulate the two-dimensional MMT equation on rational and irrational tori, resulting in remarkably different power-law spectra and energy cascades at low nonlinearity levels. The difference is explained in terms of different structures of the DRM, which makes use of recent number theory results.
