各向同性三波动力学方程的数值解
Numerical Solutions of the Isotropic 3-Wave Kinetic Equation
摘要：
我们表明，各向同性的3波动力学方程是等价的平均场速率方程的聚集-碎裂问题与一个不寻常的碎裂机制。这个类比几乎完全用一个标度参数来描述3波湍流理论。通过推广求解凝聚方程的Lee方法，发展了一种求解大频率范围内动力学方程的数值方法。新的算法进行了验证，对一些家庭的模型相互作用系数的Kolmogorov-Zakharov常数的解析计算。然后，该算法被应用到研究一些波湍流问题，其中的耗散尺度的有限性是一个基本特征。首先，它表明，对于有限容量的叶栅，能量的耗散变得独立的截止频率，因为这个截止取到无穷大。这是耗散异常存在的明确指示。其次，对波浪湍流中的瓶颈效应进行了初步的数值研究。研究发现，瓶颈的结构依赖于非平凡的相互作用系数。最后提出了一些结果的互补现象的热化在封闭的波系统，这表明第一次明确存在所谓的混合解决方案的动力学方程表现出方面的柯尔莫哥洛夫-扎哈罗夫和平衡均分谱。
英文摘要：
We show that the isotropic 3-wave kinetic equation is equivalent to the mean field rate equations for an aggregation-fragmentation problem with an unusual fragmentation mechanism. This analogy is used to write the theory of 3-wave turbulence almost entirely in terms of a single scaling parameter. A new numerical method for solving the kinetic equation over a large range of frequencies is developed by extending Lee's method for solving aggregation equations. The new algorithm is validated against some analytic calculations of the Kolmogorov-Zakharov constant for some families of model interaction coefficients. The algorithm is then applied to study some wave turbulence problems in which the finiteness of the dissipation scale is an essential feature. Firstly, it is shown that for finite capacity cascades, the dissipation of energy becomes independent of the cut-off frequency as this cut-off is taken to infinity. This is an explicit indication of the presence of a dissipative anomaly. Secondly, a preliminary numerical study is presented of the so-called bottleneck effect in a wave turbulence context. It is found that the structure of the bottleneck depends non-trivially on the interaction coefficient. Finally some results are presented on the complementary phenomenon of thermalisation in closed wave systems which demonstrates explicitly for the first time the existence of so-called mixed solutions of the kinetic equation which exhibit aspects of both Kolmogorov-Zakharov and equilibrium equipartition spectra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
